(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 260468, 14561]*) (*NotebookOutlinePosition[ 261596, 14596]*) (* CellTagsIndexPosition[ 261552, 14592]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData["Numerical Methods"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "Calculating Numerical Solutions Using the Euler Method"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "Find approximate values of the solution of the initial value problem\n", StyleBox[" y'[t] == t^2 - y[t]^2, y[0] == 1", FontFamily->"Courier", FontWeight->"Bold"] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "at ", StyleBox["t == 1\n ", FontFamily->"Courier", FontWeight->"Bold"], "1) using the Euler method with ", StyleBox["h = 0.1\n ", FontFamily->"Courier", FontWeight->"Bold"], "2) using the Euler method with ", StyleBox["h = 0.05\n", FontFamily->"Courier", FontWeight->"Bold"], "Compare the results with ", StyleBox["NDSolve[]", FontFamily->"Courier", FontWeight->"Bold"], " by superimposing the plots of the data." }], "Text", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Solution"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["EMStep[{t_,y_}] := N[{t+h,y+h*f[t,y]}];"], "Input", AspectRatioFixed->True], Cell[TextData["f[t_,y_] = t^2 - y^2;\nh = 0.1;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["EMStep[{0,1}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {0.1, 0.9}\ \>", "\<\ {0.1, 0.9}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["EMStep[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {0.2, 0.82}\ \>", "\<\ {0.2, 0.82}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["EMStep[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {0.3, 0.75676}\ \>", "\<\ {0.3, 0.75676}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["soln1=NestList[EMStep, {0,1}, 10]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {{0, 1}, {0.1, 0.9}, {0.2, 0.82}, {0.3, 0.75676}, {0.4, 0.70849143024}, {0.5, 0.6742954195676479214}, {0.6, 0.6538279882826568867}, {0.7, 0.6470788844564822756}, {0.8000000000000000001, 0.6542077761855377216}, {0.9000000000000000001, 0.67540899474337506}, {1., 0.7107912637253494161}}\ \>", "\<\ {{0, 1}, {0.1, 0.9}, {0.2, 0.82}, {0.3, 0.75676}, {0.4, 0.708491}, {0.5, 0.674295}, {0.6, 0.653828}, {0.7, 0.647079}, {0.8, 0.654208}, {0.9, 0.675409}, {1., 0.710791}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p1 = ListPlot[soln1,PlotRange->{0,1},\n PlotJoined->True, \ PlotStyle->{RGBColor[0,1,0]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0 0.618034 [ [(0)] .02381 0 0 2 Msboxa [(0.2)] .21429 0 0 2 Msboxa [(0.4)] .40476 0 0 2 Msboxa [(0.6)] .59524 0 0 2 Msboxa [(0.8)] .78571 0 0 2 Msboxa [(1)] .97619 0 0 2 Msboxa [(0.2)] .01131 .12361 1 0 Msboxa [(0.4)] .01131 .24721 1 0 Msboxa [(0.6)] .01131 .37082 1 0 Msboxa [(0.8)] .01131 .49443 1 0 Msboxa [(1)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(0.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(0.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(0.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(0.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(1)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(0.2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(0.4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(0.6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(0.8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(1)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 1 0 r .004 w .02381 .61803 m .11905 .55623 L .21429 .50679 L .30952 .4677 L .40476 .43787 L .5 .41674 L .59524 .40409 L .69048 .39992 L .78571 .40432 L .88095 .41743 L .97619 .43929 L s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData["h = 0.05;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["soln2 = NestList[EMStep,{0,1},20]"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ {{0, 1}, {0.05, 0.95}, {0.1, 0.905}, {0.15, 0.86454875}, {0.2, 0.828301522943671875}, {0.25, 0.7959973522981315657}, {0.3, 0.7674417630548497768}, {0.35, 0.7424934200708129674}, {0.4, 0.7210535961283903312}, {0.45, 0.7030576817039061394}, {0.5, 0.6884681765137625895}, {0.5500000000000000001, 0.6772687550101533214}, {0.6000000000000000001, 0.6694591066845031674}, {0.6500000000000000001, 0.6650503319083625178}, {0.7000000000000000001, 0.6640607347097913604}, {0.7500000000000000001, 0.6665119017406259654}, {0.8000000000000000001, 0.6724249959825306733}, {0.8500000000000000002, 0.6818172272214253538}, {0.9000000000000000002, 0.6946984906546297153}, {0.9500000000000000002, 0.7110681910087386828}, {1., 0.7309122923955166788}}\ \>", "\<\ {{0, 1}, {0.05, 0.95}, {0.1, 0.905}, {0.15, 0.864549}, {0.2, 0.828302}, {0.25, 0.795997}, {0.3, 0.767442}, {0.35, 0.742493}, {0.4, 0.721054}, {0.45, 0.703058}, {0.5, 0.688468}, {0.55, 0.677269}, {0.6, 0.669459}, {0.65, 0.66505}, {0.7, 0.664061}, {0.75, 0.666512}, {0.8, 0.672425}, {0.85, 0.681817}, {0.9, 0.694698}, {0.95, 0.711068}, {1., 0.730912}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p2 = ListPlot[soln2,PlotRange->{0,1},\n PlotJoined->True, \ PlotStyle->{RGBColor[1,0,0]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0 0.618034 [ [(0)] .02381 0 0 2 Msboxa [(0.2)] .21429 0 0 2 Msboxa [(0.4)] .40476 0 0 2 Msboxa [(0.6)] .59524 0 0 2 Msboxa [(0.8)] .78571 0 0 2 Msboxa [(1)] .97619 0 0 2 Msboxa [(0.2)] .01131 .12361 1 0 Msboxa [(0.4)] .01131 .24721 1 0 Msboxa [(0.6)] .01131 .37082 1 0 Msboxa [(0.8)] .01131 .49443 1 0 Msboxa [(1)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(0.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(0.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(0.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(0.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(1)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(0.2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(0.4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(0.6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(0.8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(1)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 1 0 0 r .004 w .02381 .61803 m .07143 .58713 L .11905 .55932 L .16667 .53432 L .21429 .51192 L .2619 .49195 L .30952 .47431 L .35714 .45889 L .40476 .44564 L .45238 .43451 L .5 .4255 L .54762 .41858 L .59524 .41375 L .64286 .41102 L .69048 .41041 L .7381 .41193 L .78571 .41558 L .83333 .42139 L .88095 .42935 L .92857 .43946 L .97619 .45173 L s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "soln = NDSolve[{y'[t] == t^2 - y[t]^2, y[0] == 1},\n y[t],{t,0,1}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {{y[t] -> InterpolatingFunction[{0., 1.}, {{0., 0., {1., 0}, {0}}, {0.0008944271909999158787, 0., {0.9991071699493907832, -0.9982143427583931571}, {0}}, {0.001788854381999831757, 0.0008944271909999158787, {0.9982159342025207508, -0.9964318569895940383}, {0}}, {0.0148048848179710272, 0.001788854381999831757, {0.9854130317566282949, -0.9708196040257801222, 0.9838734278398623457}, {0, 0}}, {0.02782091525394222265, 0.0148048848179710272, {0.9729394015820729989, -0.9458369735561348377, 0.9596870025980850177}, {0, 0}}, {0.0408369456899134181, 0.02782091525394222265, {0.9607871078282673553, -0.9214441170322026255, 0.9370313262528926724}, {0, 0}}, {0.06957501970124971844, 0.0408369456899134181, {0.9350610110306434923, -0.869498168113233785, 0.8746530460219727363, -0.6757508217928225328}, {0, 0, 0}}, {0.0983130937125860188, 0.06957501970124971844, {0.910791885490706227, -0.8198768922488099534, 0.843113900361515915, -0.4691322763536624148}, {0, 0, 0}}, {0.1270511677239223191, 0.0983130937125860188, {0.8879192272694443421, -0.7722587035045125212, 0.8110607058400186617, -0.4042344012902591979}, {0, 0, 0}}, {0.1557892417352586195, 0.1270511677239223191, {0.8663896276924270464, -0.7263608234495926817, 0.7835898413454051175, -0.3471681017254505568}, {0, 0, 0}}, {0.2029701625696649742, 0.1557892417352586195, {0.8338373656432043966, -0.6540882614629724263, 0.7496581411738819975, -0.1873743353578872324, 0.6715710825718453189}, {0, 0, 0, 0}}, {0.250151083404071329, 0.2029701625696649742, {0.804620109884019046, -0.5848375234643266434, 0.7220187517919379613, -0.1383806501895795948, 0.4655882356320749106}, {0, 0, 0, 0}}, {0.2973320042384776838, 0.250151083404071329, {0.7786148846906612585, -0.5178345060808953837, 0.7008891556561202805, -0.1103317784009518502, 0.3071061259661976523}, {0, 0, 0, 0}}, {0.3445129250728840386, 0.2973320042384776838, {0.7557307354937052473, -0.4524396901366895417, 0.686759469052142667, -0.07252659220402404063, 0.253713216516385324}, {0, 0, 0, 0}}, {0.3916938459072903933, 0.3445129250728840386, {0.7359045243083693012, -0.3881313179857798901, 0.677594548164733805, -0.04227883949946356593, 0.2069942787657342235}, {0, 0, 0, 0}}, {0.466327833560608289, 0.3916938459072903933, {0.7106931951532635638, -0.2876228260860665592, 0.6708501658763055722, -0.01260414261990418885, 0.07254085754482922896, -0.2629453052657524399}, {0, 0, 0, 0, 0}}, {0.5409618212139261847, 0.466327833560608289, {0.6929615390523554721, -0.187556084989575824, 0.6702118798887168373, -0.0002641149968293920455, -0.01027734133912214833, -0.2465398203859654064}\\ , {0, 0, 0, 0, 0}}, {0.6155958088672440803, 0.5409618212139261847, {0.682707245427463967, -0.08713156288725774115, 0.6749687163585719556, 0.02160426329874035787, 0.008747159930196046632, -0.1275315730027701423}\\ , {0, 0, 0, 0, 0}}, {0.6902297965205619759, 0.6155958088672440803, {0.6799749299223687362, 0.01405116838501780361, 0.6806251360483072779, 0.02372110384140863255, -0.01986745746704013678, -0.1071908864883145568}\\ , {0, 0, 0, 0, 0}}, {0.7648637841738798716, 0.6902297965205619759, {0.6848248514568502234, 0.1160314810650867579, 0.6853577485158189555, 0.01513957596156289273, -0.05033448200198440201, -0.09697206553727588786} , {0, 0, 0, 0, 0}}, {0.8394977718271977673, 0.7648637841738798716, {0.6973076545927616492, 0.2185185016561274419, 0.6870921580459653264, -0.002599857027384833525, -0.07880161411062317632, -0.08869709286680843322} , {0, 0, 0, 0, 0}}, {0.9545885094927918478, 0.8394977718271977673, {0.731541413385729432, 0.3760861504664097085, 0.6793341884564626691, -0.04670429168630214094, -0.1179038180876603409, -0.06579539690157148186, 0.02337423784222639391}, {0, 0, 0, 0, 0, 0}}, {1., 0.9545885094927918478, {0.7500164504521358383, 0.4374753114054785399, 0.6720680122959777601, -0.06201371597314458397, -0.08582253483027299696, 0.08450453262415759897, 0.1994569062481811866}, {0, 0, 0, 0, 0, 0}}}][t]} }\ \>", "\<\ {{y[t] -> InterpolatingFunction[{0., 1.}, <>][t]}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p = Plot[y[t]/.First[soln],{t,0,1},\nPlotRange->{0,1}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0 0.618034 [ [(0)] .02381 0 0 2 Msboxa [(0.2)] .21429 0 0 2 Msboxa [(0.4)] .40476 0 0 2 Msboxa [(0.6)] .59524 0 0 2 Msboxa [(0.8)] .78571 0 0 2 Msboxa [(1)] .97619 0 0 2 Msboxa [(0.2)] .01131 .12361 1 0 Msboxa [(0.4)] .01131 .24721 1 0 Msboxa [(0.6)] .01131 .37082 1 0 Msboxa [(0.8)] .01131 .49443 1 0 Msboxa [(1)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(0.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(0.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(0.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(0.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(1)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(0.2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(0.4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(0.6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(0.8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(1)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p .004 w .02381 .61803 m .06349 .59333 L .10317 .57061 L .14286 .54975 L .18254 .53063 L .22222 .51319 L .2619 .49734 L .30159 .48304 L .34127 .47025 L .38095 .45894 L .42063 .44908 L .46032 .44068 L .5 .43372 L .53968 .42819 L .55952 .42597 L .57937 .42411 L .59921 .42261 L .60913 .42199 L .61905 .42147 L .62897 .42103 L .63889 .42069 L .64881 .42044 L .65377 .42035 L .65625 .42031 L .65873 .42028 L .66121 .42025 L .66369 .42023 L .66493 .42022 L .66617 .42022 L .66741 .42021 L .66865 .42021 L .66989 .4202 L .67113 .4202 L .67237 .4202 L .67361 .42021 L .67485 .42021 L .67609 .42021 L .67857 .42023 L .68105 .42025 L .68353 .42027 L .68849 .42034 L .69345 .42043 L .69841 .42054 L .70833 .42084 L .71825 .42122 L .7381 .42227 L .75794 .42369 L .77778 .42547 L .81746 .43014 L .85714 .43629 L Mistroke .89683 .44391 L .93651 .45299 L .97619 .46354 L Mfstroke P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Show[p,p1,p2]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0 0.618034 [ [(0)] .02381 0 0 2 Msboxa [(0.2)] .21429 0 0 2 Msboxa [(0.4)] .40476 0 0 2 Msboxa [(0.6)] .59524 0 0 2 Msboxa [(0.8)] .78571 0 0 2 Msboxa [(1)] .97619 0 0 2 Msboxa [(0.2)] .01131 .12361 1 0 Msboxa [(0.4)] .01131 .24721 1 0 Msboxa [(0.6)] .01131 .37082 1 0 Msboxa [(0.8)] .01131 .49443 1 0 Msboxa [(1)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(0.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(0.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(0.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(0.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(1)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(0.2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(0.4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(0.6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(0.8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(1)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p p .004 w .02381 .61803 m .06349 .59333 L .10317 .57061 L .14286 .54975 L .18254 .53063 L .22222 .51319 L .2619 .49734 L .30159 .48304 L .34127 .47025 L .38095 .45894 L .42063 .44908 L .46032 .44068 L .5 .43372 L .53968 .42819 L .55952 .42597 L .57937 .42411 L .59921 .42261 L .60913 .42199 L .61905 .42147 L .62897 .42103 L .63889 .42069 L .64881 .42044 L .65377 .42035 L .65625 .42031 L .65873 .42028 L .66121 .42025 L .66369 .42023 L .66493 .42022 L .66617 .42022 L .66741 .42021 L .66865 .42021 L .66989 .4202 L .67113 .4202 L .67237 .4202 L .67361 .42021 L .67485 .42021 L .67609 .42021 L .67857 .42023 L .68105 .42025 L .68353 .42027 L .68849 .42034 L .69345 .42043 L .69841 .42054 L .70833 .42084 L .71825 .42122 L .7381 .42227 L .75794 .42369 L .77778 .42547 L .81746 .43014 L .85714 .43629 L Mistroke .89683 .44391 L .93651 .45299 L .97619 .46354 L Mfstroke P P p 0 1 0 r .004 w .02381 .61803 m .11905 .55623 L .21429 .50679 L .30952 .4677 L .40476 .43787 L .5 .41674 L .59524 .40409 L .69048 .39992 L .78571 .40432 L .88095 .41743 L .97619 .43929 L s P p 1 0 0 r .004 w .02381 .61803 m .07143 .58713 L .11905 .55932 L .16667 .53432 L .21429 .51192 L .2619 .49195 L .30952 .47431 L .35714 .45889 L .40476 .44564 L .45238 .43451 L .5 .4255 L .54762 .41858 L .59524 .41375 L .64286 .41102 L .69048 .41041 L .7381 .41193 L .78571 .41558 L .83333 .42139 L .88095 .42935 L .92857 .43946 L .97619 .45173 L s P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData["y[t_] = y[t] /. soln;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["y[1]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {0.7500164504521358383}\ \>", "\<\ {0.750016}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Last[soln1]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1., 0.7107912637253494161}\ \>", "\<\ {1., 0.710791}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Last[soln2]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1., 0.7309122923955166788}\ \>", "\<\ {1., 0.730912}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "Calculating Numerical Solutions Using the Euler Method"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "Find an approximate value of ", StyleBox["y[2]", FontFamily->"Courier", FontWeight->"Bold"], " given that\n", StyleBox[" y'[t] == t^(1/2) + y[t]^(3/2), y[1] == 3\n", FontFamily->"Courier", FontWeight->"Bold"], "1) using the Euler method with ", StyleBox["h = 0.1\n", FontFamily->"Courier", FontWeight->"Bold"], "2) using the Euler method with ", StyleBox["h = 0.05\n", FontFamily->"Courier", FontWeight->"Bold"], "Compare the results with ", StyleBox["NDSolve[]", FontFamily->"Courier", FontWeight->"Bold"], " by superimposing the plots of the data." }], "Text", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Solution"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["EMStep[{t_,y_}] := N[{t+h,y+h*f[t,y]}];"], "Input", AspectRatioFixed->True], Cell[TextData["f[t_,y_] = t^(1/2) + y^(3/2);"], "Input", AspectRatioFixed->True], Cell[TextData["h = 0.1;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["EMStep[{1,3}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1.1, 3.619615242270663188}\ \>", "\<\ {1.1, 3.61962}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["EMStep[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1.2, 4.413138295053569746}\ \>", "\<\ {1.2, 4.41314}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["EMStep[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1.3, 5.449771545348763583}\ \>", "\<\ {1.3, 5.44977}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["soln1 = NestList[EMStep,{1,3},10]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {{1, 3}, {1.1, 3.619615242270663188}, {1.2, 4.413138295053569746}, {1.3, 5.449771545348763583}, {1.4, 6.83602439954627751}, {1.5, 8.741678716629180392}, {1.6, 11.44874678361447742}, {1.7, 15.44903548352415696}, {1.8, 21.65170326234757878}, {1.9, 31.86070599260320654}, {2., 49.98241391106012194}}\ \>", "\<\ {{1, 3}, {1.1, 3.61962}, {1.2, 4.41314}, {1.3, 5.44977}, {1.4, 6.83602}, {1.5, 8.74168}, {1.6, 11.4487}, {1.7, 15.449}, {1.8, 21.6517}, {1.9, 31.8607}, {2., 49.9824}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p1 = ListPlot[soln1,PlotRange->{0,100},\n PlotJoined->True, \ PlotStyle->{RGBColor[0,1,0]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00618034 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(20)] .01131 .12361 1 0 Msboxa [(40)] .01131 .24721 1 0 Msboxa [(60)] .01131 .37082 1 0 Msboxa [(80)] .01131 .49443 1 0 Msboxa [(100)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(20)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(40)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(60)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(80)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(100)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 1 0 r .004 w .02381 .01854 m .11905 .02237 L .21429 .02727 L .30952 .03368 L .40476 .04225 L .5 .05403 L .59524 .07076 L .69048 .09548 L .78571 .13381 L .88095 .19691 L .97619 .30891 L s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData["h = 0.05;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["soln2 = NestList[EMStep,{1,3},20]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {{1, 3}, {1.05, 3.309807621135331594}, {1.1, 3.66211698449431631}, {1.15, 4.064960837453392344}, {1.2, 4.52836344477052675}, {1.25, 5.064952477510142273}, {1.3, 5.690799332645476886}, {1.35, 6.426589470999003323}, {1.4, 7.299277535973328585}, {1.45, 8.344467632439103469}, {1.5, 9.609900117661060374}, {1.55, 11.16066413864717809}, {1.6, 13.08716754732535206}, {1.65, 15.51763242807303493}, {1.699999999999999999, 18.63824454294574642}, {1.749999999999999999, 22.72669113195055423}, {1.799999999999999999, 28.21002804279841807}, {1.849999999999999999, 35.76872216010576393}, {1.899999999999999999, 46.5328218186046483}, {1.949999999999999999, 62.47291736908108827}, {1.999999999999999999, 87.23197650430275756}}\ \>", "\<\ {{1, 3}, {1.05, 3.30981}, {1.1, 3.66212}, {1.15, 4.06496}, {1.2, 4.52836}, {1.25, 5.06495}, {1.3, 5.6908}, {1.35, 6.42659}, {1.4, 7.29928}, {1.45, 8.34447}, {1.5, 9.6099}, {1.55, 11.1607}, {1.6, 13.0872}, {1.65, 15.5176}, {1.7, 18.6382}, {1.75, 22.7267}, {1.8, 28.21}, {1.85, 35.7687}, {1.9, 46.5328}, {1.95, 62.4729}, {2., 87.232}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p2 = ListPlot[soln2,PlotRange->{0,100},\n PlotJoined->True, \ PlotStyle->{RGBColor[1,0,0]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00618034 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(20)] .01131 .12361 1 0 Msboxa [(40)] .01131 .24721 1 0 Msboxa [(60)] .01131 .37082 1 0 Msboxa [(80)] .01131 .49443 1 0 Msboxa [(100)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(20)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(40)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(60)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(80)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(100)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 1 0 0 r .004 w .02381 .01854 m .07143 .02046 L .11905 .02263 L .16667 .02512 L .21429 .02799 L .2619 .0313 L .30952 .03517 L .35714 .03972 L .40476 .04511 L .45238 .05157 L .5 .05939 L .54762 .06898 L .59524 .08088 L .64286 .0959 L .69048 .11519 L .7381 .14046 L .78571 .17435 L .83333 .22106 L .88095 .28759 L .92857 .3861 L .97619 .53912 L s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "soln = NDSolve[{y'[t] == t^(1/2)+y[t]^(3/2),y[1]==3},\n \ y[t],{t,1,2}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {{y[t] -> InterpolatingFunction[{1., 2.}, {{1., 1., {3., 0}, {0}}, {1.000614350868478, 1., {3.003812888090469, 6.206368845730114}, {0}}, {1.001228701736956, 1.000614350868478, {3.007632066525278, 6.216607855165395}, {0}}, {1.007867339483049, 1.001228701736956, {3.049273675696699, 6.328619272473178, 8.43632546253318}, {0, 0}}, {1.014505977229141, 1.007867339483049, {3.091667912548081, 6.44334945750784, 8.64109395803328}, {0, 0}}, {1.021144614975233, 1.014505977229141, {3.134833106699992, 6.560882977774311, 8.85223179526972}, {0, 0}}, {1.038389354494731, 1.021144614975233, {3.250691233903926, 6.879902469052498, 9.58564252798182, 12.98482885041416}, {0, 0, 0}}, {1.055634094014229, 1.038389354494731, {3.372236218161132, 7.220097704176451, 10.1707279095235, 11.86790734191237}, {0, 0, 0}}, {1.072878833533726, 1.055634094014229, {3.499843225512719, 7.583258416485382, 10.86254305197931, 12.87096015513403}, {0, 0, 0}}, {1.090123573053224, 1.072878833533726, {3.633925262716485, 7.971388852482284, 11.61557985227712, 13.99423648304324}, {0, 0, 0}}, {1.116624484266774, 1.090123573053224, {3.853639460425489, 8.62166100295555, 12.93266751085363, 17.58505503130275, 25.0794074799102}, {0, 0, 0, 0}}, {1.143125395480325, 1.116624484266774, {4.091536756344128, 9.34534641595667, 14.41266206662639, 19.91774648653548, 23.54258698251294}, {0, 0, 0, 0}}, {1.169626306693876, 1.143125395480325, {4.349703724388021, 10.15320983628193, 16.10398724358442, 22.5314401720511, 24.09961337643824}, {0, 0, 0, 0}}, {1.196127217907426, 1.169626306693876, {4.630533472190307, 11.05796826599548, 18.06437762423368, 26.01269104824019, 28.47023676388869}, {0, 0, 0, 0}}, {1.222628129120977, 1.196127217907426, {4.936788081072449, 12.07471482850668, 20.33461531495178, 30.15842344222057, 33.7897874675329}, {0, 0, 0, 0}}, {1.255360351727063, 1.222628129120977, {5.354954809301997, 13.51220261659736, 23.66701037991104, 37.00354810258466, 53.39409892418628, 72.00210657377099}\\ , {0, 0, 0, 0, 0}}, {1.28809257433315, 1.255360351727063, {5.823974790573881, 15.18988677205054, 27.7167520523269, 45.44484266298781, 69.62343409304126, 82.8669728432047}, {0, 0, 0, 0, 0}}, {1.320824796939236, 1.28809257433315, {6.352542796713295, 17.16038037256838, 32.64703370775075, 55.32182386176009, 82.3569073793184, 80.841744718182}, {0, 0, 0, 0, 0}}, {1.353557019545323, 1.320824796939236, {6.951293299589426, 19.49071538868184, 38.74170825209781, 68.4604820974071, 105.3395635025957, 104.6763772043101}, {0, 0, 0, 0, 0}}, {1.386289242151409, 1.353557019545323, {7.633357150008475, 22.26724171183835, 46.33407866247768, 85.5967450796169, 137.0226648225796, 140.2416954385254}, {0, 0, 0, 0, 0}}, {1.419021464757495, 1.386289242151409, {8.41509722957569, 25.60238730417424, 55.88454496359664, 108.1067091951099, 180.0545404435941, 189.3181395136348}\\ , {0, 0, 0, 0, 0}}, {1.451753687363582, 1.419021464757495, {9.3171105697131, 29.64435685378881, 68.03276584731903, 138.1098416513018, 239.8466038785994, 259.7271584233284}\\ , {0, 0, 0, 0, 0}}, {1.484485909969668, 1.451753687363582, {10.36561491494558, 34.59115140078011, 83.6737631033973, 178.6563393807186, 323.9965231964769, 361.5049912023119}\\ , {0, 0, 0, 0, 0}}, {1.511269217853774, 1.484485909969668, {11.35582967011137, 39.49665169960634, 100.0012729639291, 224.8208271419218, 443.298014441927, 573.2487956558457}, {0, 0, 0, 0, 0}}, {1.538052525737881, 1.511269217853774, {12.49005426281528, 45.38160086942898, 120.4280740342568, 282.4246560727759, 568.0674634704239, 716.6275128628103}\\ , {0, 0, 0, 0, 0}}, {1.564835833621987, 1.538052525737881, {13.79780460460422, 52.50338069507192, 146.3867665919677, 360.3282573264825, 759.2763152769929, 1001.104921381742}\\ , {0, 0, 0, 0, 0}}, {1.591619141506093, 1.564835833621987, {15.31657946639687, 61.20510660791449, 179.7295580553409, 465.0596000508832, 1023.002354789697, 1388.395493272133}\\ , {0, 0, 0, 0, 0}}, {1.613658707136682, 1.591619141506093, {16.75821550532528, 69.87302170537909, 214.6698681370678, 584.4563658975115, 1394.438481179606, 2181.289371764218}\\ , {0, 0, 0, 0, 0}}, {1.635698272767271, 1.613658707136682, {18.40917893655415, 80.2651817716873, 258.3542067858146, 733.7217199834785, 1787.834992413138, 2736.738285619864}\\ , {0, 0, 0, 0, 0}}, {1.657737838397861, 1.635698272767271, {20.31220741470123, 92.8326758820002, 313.8109789695897, 935.128875397133, 2385.974163231955, 3813.189829143558}, {0, 0, 0, 0, 0}}, {1.67977740402845, 1.657737838397861, {22.52154392732775, 108.1761397811876, 384.9678269624535, 1205.608019207862, 3210.778300285555, 5281.817319643746}\\ , {0, 0, 0, 0, 0}}, {1.697940608259341, 1.67977740402845, {24.62120251201767, 123.4727752862001, 459.5757639933438, 1513.931165736134, 4370.314332915993, 8276.27750652833}, {0, 0, 0, 0, 0}}, {1.716103812490232, 1.697940608259341, {27.02521662702376, 141.8026429473479, 552.7947869537415, 1899.317737327429, 5600.537754075894, 10384.29687123008}\\ , {0, 0, 0, 0, 0}}, {1.734267016721123, 1.716103812490232, {29.79552231869438, 163.956457544915, 671.0419301715329, 2418.732630119056, 7466.917666314717, 14451.06560286928}\\ , {0, 0, 0, 0, 0}}, {1.752430220952014, 1.734267016721123, {33.01066803283176, 190.9860889145597, 822.6371134245, 3115.611589403345, 10038.27202870062, 19996.19328799495}\\ , {0, 0, 0, 0, 0}}, {1.76742036727267, 1.752430220952014, {36.06980080912359, 217.9578108722251, 981.697423165656, 3910.085344219583, 13647.54128753737, 31259.80551685045}\\ , {0, 0, 0, 0, 0}}, {1.782410513593326, 1.76742036727267, {39.57174785062683, 250.2653074973617, 1180.345570595476, 4903.149809659074, 17484.43535411749, 39232.76984346177}\\ , {0, 0, 0, 0, 0}}, {1.797400659913982, 1.782410513593326, {43.60640326765222, 289.2959500438134, 1432.183999553124, 6240.394275765316, 23294.12630105925, 54545.04809866502}\\ , {0, 0, 0, 0, 0}}, {1.812390806234638, 1.797400659913982, {48.28770829963641, 336.8940781091938, 1754.849207314332, 8033.30107270318, 31293.63237829543, 75419.10620717298}, {0, 0, 0, 0, 0}}, {1.824775273451708, 1.812390806234638, {52.74564446450095, 384.4221452195672, 2093.583914567351, 10077.50758076637, 42509.61896401873, 117703.4240008929}\\ , {0, 0, 0, 0, 0}}, {1.837159740668778, 1.824775273451708, {57.84815384297139, 441.3365596669744, 2516.488009014581, 12632.73641982125, 54450.20625944041, 147754.7212234648}\\ , {0, 0, 0, 0, 0}}, {1.849544207885848, 1.837159740668778, {63.72585891730395, 510.0733991586431, 3052.410208355827, 16071.38440249242, 72504.95259280845, 205281.1608932925}\\ , {0, 0, 0, 0, 0}}, {1.861928675102918, 1.849544207885848, {70.54425780054352, 593.8695633573181, 3738.755853286349, 20679.49758983846, 97354.7280589155, 283690.9057230188}, {0, 0, 0, 0, 0}}, {1.87216822157653, 1.861928675102918, {77.04126515872522, 677.5833118708566, 4459.565732062894, 25933.94377184157, 132168.6297562884, 442210.1970467022}\\ , {0, 0, 0, 0, 0}}, {1.882407768050143, 1.87216822157653, {84.4768663537272, 777.8095053844086, 5359.277605982899, 32502.02896664481, 169270.5336716509, 555197.5808829307}\\ , {0, 0, 0, 0, 0}}, {1.892647314523755, 1.882407768050143, {93.0410277184867, 898.828084878065, 6499.100569099629, 41336.91174268699, 225314.2235673262, 770979.2685536428}\\ , {0, 0, 0, 0, 0}}, {1.902886860997368, 1.892647314523755, {102.974367207871, 1046.324004183627, 7958.400670139284, 53172.40601801072, 302427.936486961, 1.065065126859205*10^6}, {0, 0, 0, 0, 0}}, {1.911357607755081, 1.902886860997368, {112.4435616048078, 1193.726622139048, 9491.41324462903, 66668.82789527236, 410401.7890635383, 1.658773044464931*10^6}, {0, 0, 0, 0, 0}}, {1.919828354512795, 1.911357607755081, {123.2798408416996, 1370.178989486231, 11404.6045353927, 83539.6447716073, 525558.185172459, 2.082831658915778*10^6}, {0, 0, 0, 0, 0}}, {1.928299101270509, 1.919828354512795, {135.7596486430236, 1583.203708807345, 13827.88461526744, 106225.7398892935, 699382.1626643511, 2.891339171487233*10^6}, {0, 0, 0, 0, 0}}, {1.936769848028222, 1.928299101270509, {150.2330679504189, 1842.790477080622, 16929.70369347568, 136609.3817139709, 938507.726284509, 3.993169339669659*10^6}, {0, 0, 0, 0, 0}}, {1.943780063811309, 1.936769848028222, {164.0343758315458, 2102.277961890244, 20188.86495232633, 171258.5989161006, 1.273197080983671*10^6, 6.215348708487302*10^6}, {0, 0, 0, 0, 0}}, {1.950790279594396, 1.943780063811309, {179.8272469980232, 2412.873308805874, 24255.8205379394, 214571.3081365136, 1.630340752260807*10^6, 7.804903124715611*10^6}, {0, 0, 0, 0, 0}}, {1.957800495377484, 1.950790279594396, {198.014150391871, 2787.802631652613, 29406.35625897376, 272800.6307852315, 2.169164349128673*10^6, 1.083195198853035*10^7}, {0, 0, 0, 0, 0}}, {1.964810711160571, 1.957800495377484, {219.1046930813551, 3244.626670883155, 35998.08121797769, 350774.2737616509, 2.910305647843299*10^6, 1.495701410862677*10^7}, {0, 0, 0, 0, 0}}, {1.970613812191503, 1.964810711160571, {239.2200980390264, 3701.356864822122, 42925.17686752168, 439697.8941618323, 3.947349383464873*10^6, 2.327061626636813*10^7}, {0, 0, 0, 0, 0}}, {1.976416913222435, 1.970613812191503, {262.2371900213685, 4248.004656035816, 51568.49461227613, 550856.3410794701, 5.054385170256008*10^6, 2.922366927386068*10^7}, {0, 0, 0, 0, 0}}, {1.982220014253368, 1.976416913222435, {288.7421039178894, 4907.829132977589, 62513.60028388185, 700273.6109420662, 6.723984447299285*10^6, 4.05508510163085*10^7}, {0, 0, 0, 0, 0}}, {1.9880231152843, 1.982220014253368, {319.4769320276927, 5711.708483972696, 76519.8027483609, 900331.278416156, 9.02025743452372*10^6, 5.598631635894725*10^7}, {0, 0, 0, 0, 0}}, {1.992827883807837, 1.9880231152843, {348.7950381069408, 6515.522881134712, 91240.1067335875, 1.128489382180647*10^6, 1.223270415936744*10^7, 8.70794316712732*10^7}, {0, 0, 0, 0, 0}}, {1.997632652331375, 1.992827883807837, {382.3412717577407, 7477.538824285043, 109606.4291754151, 1.413698749866174*10^6, 1.566287231728986*10^7, 1.093603900926183*10^8}, {0, 0, 0, 0, 0}}, {2., 1.997632652331375, {400.6772541774949, 8021.74005834785, 120465.5326563221, 1.622900331776467*10^6, 2.191359476406161*10^7, 2.76847479203514*10^8}, {0, 0, 0, 0, 0}}}][t]}}\ \>", "\<\ {{y[t] -> InterpolatingFunction[{1., 2.}, <>][t]}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["y[t] /. soln /. t->2"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {400.6772541774949}\ \>", "\<\ {400.677}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p = Plot[y[t]/.First[soln],{t,1,2},\n PlotRange->{0,100}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00618034 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(20)] .01131 .12361 1 0 Msboxa [(40)] .01131 .24721 1 0 Msboxa [(60)] .01131 .37082 1 0 Msboxa [(80)] .01131 .49443 1 0 Msboxa [(100)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(20)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(40)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(60)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(80)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(100)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p .004 w .02381 .01854 m .06349 .02023 L .10317 .02213 L .14286 .02427 L .18254 .0267 L .22222 .02947 L .2619 .03265 L .30159 .03633 L .34127 .04062 L .38095 .04566 L .42063 .05164 L .46032 .05881 L .5 .06751 L .53968 .07822 L .57937 .0916 L .61905 .10865 L .65873 .13082 L .69841 .16042 L .71825 .17908 L .7381 .20118 L .75794 .22759 L .77778 .25953 L .79762 .29866 L .81746 .34731 L .8373 .40883 L .85714 .48822 L .87698 .59314 L s .88045 .61803 m .87698 .59314 L s s s s s s s s s s P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Show[p,p1,p2]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00618034 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(20)] .01131 .12361 1 0 Msboxa [(40)] .01131 .24721 1 0 Msboxa [(60)] .01131 .37082 1 0 Msboxa [(80)] .01131 .49443 1 0 Msboxa [(100)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .12361 m .03006 .12361 L s P [(20)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(40)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(60)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(80)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(100)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p p .004 w .02381 .01854 m .06349 .02023 L .10317 .02213 L .14286 .02427 L .18254 .0267 L .22222 .02947 L .2619 .03265 L .30159 .03633 L .34127 .04062 L .38095 .04566 L .42063 .05164 L .46032 .05881 L .5 .06751 L .53968 .07822 L .57937 .0916 L .61905 .10865 L .65873 .13082 L .69841 .16042 L .71825 .17908 L .7381 .20118 L .75794 .22759 L .77778 .25953 L .79762 .29866 L .81746 .34731 L .8373 .40883 L .85714 .48822 L .87698 .59314 L s .88045 .61803 m .87698 .59314 L s s s s s s s s s P P p 0 1 0 r .004 w .02381 .01854 m .11905 .02237 L .21429 .02727 L .30952 .03368 L .40476 .04225 L .5 .05403 L .59524 .07076 L .69048 .09548 L .78571 .13381 L .88095 .19691 L .97619 .30891 L s P p 1 0 0 r .004 w .02381 .01854 m .07143 .02046 L .11905 .02263 L .16667 .02512 L .21429 .02799 L .2619 .0313 L .30952 .03517 L .35714 .03972 L .40476 .04511 L .45238 .05157 L .5 .05939 L .54762 .06898 L .59524 .08088 L .64286 .0959 L .69048 .11519 L .7381 .14046 L .78571 .17435 L .83333 .22106 L .88095 .28759 L .92857 .3861 L .97619 .53912 L s P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["h = 0.025;\n1/h"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ 40.\ \>", "\<\ 40.\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["soln3 = NestList[EMStep,{1,3},40]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {{1, 3}, {1.025, 3.154903810567665797}, {1.05, 3.320308270861689931}, {1.075, 3.497179909288403391}, {1.1, 3.686600165011700588}, {1.125, 3.88978199829242997}, {1.15, 4.108089360495491569}, {1.175, 4.343060097101904942}, {1.2, 4.596432989126342827}, {1.225, 4.870179804928842589}, {1.25, 5.166543445675562666}, {1.275, 5.488083537133441501}, {1.3, 5.837731166110218954}, {1.325, 6.218854905956117919}, {1.35, 6.635340855062654987}, {1.375, 7.091690170247388131}, {1.4, 7.593138575336802498}, {1.425, 8.145803650365974134}, {1.45, 8.756867479493317989}, {1.475, 9.434804627106097769}, {1.5, 10.18966866633044269}, {1.525, 11.03345495577665282}, {1.55, 11.98056356540304209}, {1.575, 13.04839495468106357}, {1.6, 14.25812334957975168}, {1.625, 15.63571048528881076}, {1.65, 17.21324815218289495}, {1.674999999999999999, 19.03075598319634896}, {1.699999999999999999, 21.13861779642462812}, {1.724999999999999999, 23.60092631028156408}, {1.749999999999999999, 26.50013991691995452}, {1.774999999999999999, 29.94366630253695158}, {1.799999999999999999, 34.07332748503741949}, {1.824999999999999999, 39.07922009613983277}, {1.849999999999999999, 45.2204280532003835}, {1.874999999999999999, 52.85667936522782949}, {1.899999999999999999, 62.49795696793628223}, {1.924999999999999999, 74.88445852030017582}, {1.949999999999999999, 91.11961219267453918}, {1.974999999999999999, 112.8994422172989114}, {1.999999999999999999, 142.9246613348439893}}\ \>", "\<\ {{1, 3}, {1.025, 3.1549}, {1.05, 3.32031}, {1.075, 3.49718}, {1.1, 3.6866}, {1.125, 3.88978}, {1.15, 4.10809}, {1.175, 4.34306}, {1.2, 4.59643}, {1.225, 4.87018}, {1.25, 5.16654}, {1.275, 5.48808}, {1.3, 5.83773}, {1.325, 6.21885}, {1.35, 6.63534}, {1.375, 7.09169}, {1.4, 7.59314}, {1.425, 8.1458}, {1.45, 8.75687}, {1.475, 9.4348}, {1.5, 10.1897}, {1.525, 11.0335}, {1.55, 11.9806}, {1.575, 13.0484}, {1.6, 14.2581}, {1.625, 15.6357}, {1.65, 17.2132}, {1.675, 19.0308}, {1.7, 21.1386}, {1.725, 23.6009}, {1.75, 26.5001}, {1.775, 29.9437}, {1.8, 34.0733}, {1.825, 39.0792}, {1.85, 45.2204}, {1.875, 52.8567}, {1.9, 62.498}, {1.925, 74.8845}, {1.95, 91.1196}, {1.975, 112.899}, {2., 142.925}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p3 = ListPlot[soln3,PlotRange->{0,200},\n PlotJoined->True, \ PlotStyle->{RGBColor[0,0,1]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00309017 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(25)] .01131 .07725 1 0 Msboxa [(50)] .01131 .15451 1 0 Msboxa [(75)] .01131 .23176 1 0 Msboxa [(100)] .01131 .30902 1 0 Msboxa [(125)] .01131 .38627 1 0 Msboxa [(150)] .01131 .46353 1 0 Msboxa [(175)] .01131 .54078 1 0 Msboxa [(200)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .07725 m .03006 .07725 L s P [(25)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(50)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(75)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(100)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(125)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(150)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(175)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(200)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 0 1 r .004 w .02381 .00927 m .04762 .00975 L .07143 .01026 L .09524 .01081 L .11905 .01139 L .14286 .01202 L .16667 .01269 L .19048 .01342 L .21429 .0142 L .2381 .01505 L .2619 .01597 L .28571 .01696 L .30952 .01804 L .33333 .01922 L .35714 .0205 L .38095 .02191 L .40476 .02346 L .42857 .02517 L .45238 .02706 L .47619 .02916 L .5 .03149 L .52381 .0341 L .54762 .03702 L .57143 .04032 L .59524 .04406 L .61905 .04832 L .64286 .05319 L .66667 .05881 L .69048 .06532 L .71429 .07293 L .7381 .08189 L .7619 .09253 L .78571 .10529 L .80952 .12076 L .83333 .13974 L .85714 .16334 L .88095 .19313 L .90476 .23141 L .92857 .28158 L .95238 .34888 L .97619 .44166 L s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Show[p,p2,p3,PlotRange->{0,400}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00154508 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(50)] .01131 .07725 1 0 Msboxa [(100)] .01131 .15451 1 0 Msboxa [(150)] .01131 .23176 1 0 Msboxa [(200)] .01131 .30902 1 0 Msboxa [(250)] .01131 .38627 1 0 Msboxa [(300)] .01131 .46353 1 0 Msboxa [(350)] .01131 .54078 1 0 Msboxa [(400)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .07725 m .03006 .07725 L s P [(50)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(100)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(150)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(200)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(250)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(300)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(350)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(400)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p p .004 w .02381 .00464 m .06349 .00506 L .10317 .00553 L .14286 .00607 L .18254 .00667 L .22222 .00737 L .2619 .00816 L .30159 .00908 L .34127 .01015 L .38095 .01141 L .42063 .01291 L .46032 .0147 L .5 .01688 L .53968 .01955 L .57937 .0229 L .61905 .02716 L .65873 .0327 L .69841 .0401 L .71825 .04477 L .7381 .05029 L .75794 .0569 L .77778 .06488 L .79762 .07467 L .81746 .08683 L .8373 .10221 L .85714 .12206 L .87698 .14829 L .89683 .18396 L .91667 .23422 L .92659 .26744 L .93651 .30826 L .94643 .35918 L .95635 .42385 L .96627 .50768 L s .9761 .61803 m .96627 .50768 L s s P P p 1 0 0 r .004 w .02381 .00464 m .07143 .00511 L .11905 .00566 L .16667 .00628 L .21429 .007 L .2619 .00783 L .30952 .00879 L .35714 .00993 L .40476 .01128 L .45238 .01289 L .5 .01485 L .54762 .01724 L .59524 .02022 L .64286 .02398 L .69048 .0288 L .7381 .03511 L .78571 .04359 L .83333 .05527 L .88095 .0719 L .92857 .09653 L .97619 .13478 L s P p 0 0 1 r .004 w .02381 .00464 m .04762 .00487 L .07143 .00513 L .09524 .0054 L .11905 .0057 L .14286 .00601 L .16667 .00635 L .19048 .00671 L .21429 .0071 L .2381 .00752 L .2619 .00798 L .28571 .00848 L .30952 .00902 L .33333 .00961 L .35714 .01025 L .38095 .01096 L .40476 .01173 L .42857 .01259 L .45238 .01353 L .47619 .01458 L .5 .01574 L .52381 .01705 L .54762 .01851 L .57143 .02016 L .59524 .02203 L .61905 .02416 L .64286 .0266 L .66667 .0294 L .69048 .03266 L .71429 .03647 L .7381 .04094 L .7619 .04627 L .78571 .05265 L .80952 .06038 L .83333 .06987 L .85714 .08167 L .88095 .09656 L .90476 .1157 L .92857 .14079 L .95238 .17444 L .97619 .22083 L s P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "Calculating Numerical Solutions Using the Runge-Kutta Method"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "Find an approximate value of ", StyleBox["y[2]", FontFamily->"Courier", FontWeight->"Bold"], " given that\n", StyleBox[" y'[t] == t^(1/2) + y[t]^(3/2), y[1] == 3\n", FontFamily->"Courier", FontWeight->"Bold"], "1) using the Runge-Kutta method with ", StyleBox["h = 0.1\n", FontFamily->"Courier", FontWeight->"Bold"], "2) using the Runge-Kutta method with ", StyleBox["h = 0.05\n", FontFamily->"Courier", FontWeight->"Bold"], "Compre the results with ", StyleBox["NDSolve[]", FontFamily->"Courier", FontWeight->"Bold"], " by superimposing the plots of the data." }], "Text", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Solution"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "The Runge-Kutta method is based on ideas similar to Simpson's rule for \ approximating integrals.\nThe procedure is basically the same as the Euler \ method except the formula for predicting the next\npoint is based on a \ special average of tangent slopes:\n", StyleBox[" t1 = t0 + h;", FontFamily->"Courier", FontWeight->"Bold"], "\n", StyleBox[" y1 = y0 + (h/6)*(k1 + 2*k2 + 2*k3 + k4);\n", FontFamily->"Courier", FontWeight->"Bold"], "where\n", StyleBox[ " k1 = f[t0,y0];\n k2 = f[t0+h/2,y0+h*k1/2];\n k3 = \ f[t0+h/2,y0+h*k2/2];\n k2 = f[t0+h,y0+h*k3];\n ", FontFamily->"Courier", FontWeight->"Bold"] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "RKStep[{t_,y_}] :=\n( k1 = N[f[t,y]];\n k2 = N[f[t+0.5*h,y+0.5*h*k1]];\n \ k3 = N[f[t+0.5*h,y+0.5*h*k2]];\n k4 = N[f[t+h,y+h*k3]];\n \ N[{t+h,y+(h/6)*(k1+2*k2+2*k3+k4)}] )\n"], "Input", AspectRatioFixed->True], Cell[TextData["f[t_,y_] = t^(1/2) + y^(3/2);"], "Input", AspectRatioFixed->True], Cell[TextData["h = 0.1;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["RKStep[{1,3}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1.1, 3.713774406673987}\ \>", "\<\ {1.1, 3.71377}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["RKStep[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1.2, 4.673554243369107}\ \>", "\<\ {1.2, 4.67355}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["RKStep[%]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {1.3, 6.008664155477799}\ \>", "\<\ {1.3, 6.00866}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["soln1 = NestList[RKStep, {1,3}, 10]"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ {{1, 3}, {1.1, 3.713774406673987}, {1.2, 4.673554243369107}, {1.3, 6.008664155477799}, {1.4, 7.947112470127041}, {1.5, 10.92177135973145}, {1.6, 15.83828983890608}, {1.700000000000001, 24.86186263001076}, {1.800000000000001, 44.2878122356718}, {1.900000000000001, 99.2900318703454}, {2.000000000000001, 378.4459300570622}}\ \>", "\<\ {{1, 3}, {1.1, 3.71377}, {1.2, 4.67355}, {1.3, 6.00866}, {1.4, 7.94711}, {1.5, 10.9218}, {1.6, 15.8383}, {1.7, 24.8619}, {1.8, 44.2878}, {1.9, 99.29}, {2., 378.446}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p1 = ListPlot[soln1,PlotRange->{0,400},\n PlotJoined->True, \ PlotStyle->{RGBColor[0,1,0]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00154508 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(50)] .01131 .07725 1 0 Msboxa [(100)] .01131 .15451 1 0 Msboxa [(150)] .01131 .23176 1 0 Msboxa [(200)] .01131 .30902 1 0 Msboxa [(250)] .01131 .38627 1 0 Msboxa [(300)] .01131 .46353 1 0 Msboxa [(350)] .01131 .54078 1 0 Msboxa [(400)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .07725 m .03006 .07725 L s P [(50)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(100)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(150)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(200)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(250)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(300)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(350)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(400)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 1 0 r .004 w .02381 .00464 m .11905 .00574 L .21429 .00722 L .30952 .00928 L .40476 .01228 L .5 .01688 L .59524 .02447 L .69048 .03841 L .78571 .06843 L .88095 .15341 L .97619 .58473 L s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData["h = 0.05;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["soln2 = NestList[RKStep, {1,3}, 20]"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ {{1, 3}, {1.05, 3.33186907291004}, {1.1, 3.713789300660541}, {1.15, 4.156452420464085}, {1.2, 4.673606329401915}, {1.25, 5.28316373810863}, {1.3, 6.008810504011375}, {1.35, 6.882388545144333}, {1.4, 7.947510871333187}, {1.45, 9.26519438359331}, {1.5, 10.92290809293408}, {1.55, 13.04962582772934}, {1.6, 15.84190919448197}, {1.650000000000001, 19.61132534348475}, {1.700000000000001, 24.87574607642441}, {1.750000000000001, 32.54789321823551}, {1.800000000000001, 44.36033070246526}, {1.850000000000001, 63.93786225381128}, {1.900000000000001, 99.9471358915117}, {1.950000000000001, 177.590171449259}, {2.000000000000001, 397.6730081700572}}\ \>", "\<\ {{1, 3}, {1.05, 3.33187}, {1.1, 3.71379}, {1.15, 4.15645}, {1.2, 4.67361}, {1.25, 5.28316}, {1.3, 6.00881}, {1.35, 6.88239}, {1.4, 7.94751}, {1.45, 9.26519}, {1.5, 10.9229}, {1.55, 13.0496}, {1.6, 15.8419}, {1.65, 19.6113}, {1.7, 24.8757}, {1.75, 32.5479}, {1.8, 44.3603}, {1.85, 63.9379}, {1.9, 99.9471}, {1.95, 177.59}, {2., 397.673}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p2 = ListPlot[soln2,PlotRange->{0,400},\n PlotJoined->True, \ PlotStyle->{RGBColor[1,0,0]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00154508 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(50)] .01131 .07725 1 0 Msboxa [(100)] .01131 .15451 1 0 Msboxa [(150)] .01131 .23176 1 0 Msboxa [(200)] .01131 .30902 1 0 Msboxa [(250)] .01131 .38627 1 0 Msboxa [(300)] .01131 .46353 1 0 Msboxa [(350)] .01131 .54078 1 0 Msboxa [(400)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .07725 m .03006 .07725 L s P [(50)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(100)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(150)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(200)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(250)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(300)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(350)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(400)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 1 0 0 r .004 w .02381 .00464 m .07143 .00515 L .11905 .00574 L .16667 .00642 L .21429 .00722 L .2619 .00816 L .30952 .00928 L .35714 .01063 L .40476 .01228 L .45238 .01432 L .5 .01688 L .54762 .02016 L .59524 .02448 L .64286 .0303 L .69048 .03844 L .7381 .05029 L .78571 .06854 L .83333 .09879 L .88095 .15443 L .92857 .27439 L .97619 .61444 L s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Show[p1,p2,p]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00154508 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(50)] .01131 .07725 1 0 Msboxa [(100)] .01131 .15451 1 0 Msboxa [(150)] .01131 .23176 1 0 Msboxa [(200)] .01131 .30902 1 0 Msboxa [(250)] .01131 .38627 1 0 Msboxa [(300)] .01131 .46353 1 0 Msboxa [(350)] .01131 .54078 1 0 Msboxa [(400)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .07725 m .03006 .07725 L s P [(50)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(100)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(150)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(200)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(250)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(300)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(350)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(400)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 1 0 r .004 w .02381 .00464 m .11905 .00574 L .21429 .00722 L .30952 .00928 L .40476 .01228 L .5 .01688 L .59524 .02447 L .69048 .03841 L .78571 .06843 L .88095 .15341 L .97619 .58473 L s P p 1 0 0 r .004 w .02381 .00464 m .07143 .00515 L .11905 .00574 L .16667 .00642 L .21429 .00722 L .2619 .00816 L .30952 .00928 L .35714 .01063 L .40476 .01228 L .45238 .01432 L .5 .01688 L .54762 .02016 L .59524 .02448 L .64286 .0303 L .69048 .03844 L .7381 .05029 L .78571 .06854 L .83333 .09879 L .88095 .15443 L .92857 .27439 L .97619 .61444 L s P p p .004 w .02381 .00464 m .06349 .00506 L .10317 .00553 L .14286 .00607 L .18254 .00667 L .22222 .00737 L .2619 .00816 L .30159 .00908 L .34127 .01015 L .38095 .01141 L .42063 .01291 L .46032 .0147 L .5 .01688 L .53968 .01955 L .57937 .0229 L .61905 .02716 L .65873 .0327 L .69841 .0401 L .71825 .04477 L .7381 .05029 L .75794 .0569 L .77778 .06488 L .79762 .07467 L .81746 .08683 L .8373 .10221 L .85714 .12206 L .87698 .14829 L .89683 .18396 L .90675 .20682 L .91667 .23422 L .92659 .26744 L .93651 .30826 L .94643 .35918 L .95635 .42385 L .96627 .50768 L s .9761 .61803 m .96627 .50768 L s s P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[TextData["h = 0.025;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["soln3 = NestList[RKStep, {1,3}, 40]"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ {{1, 3}, {1.025, 3.160250179583817}, {1.05, 3.331869456648199}, {1.075, 3.515966418253209}, {1.1, 3.713790297428252}, {1.125, 3.926752862146523}, {1.149999999999999, 4.156454390617769}, {1.174999999999999, 4.404714627993218}, {1.199999999999999, 4.673609846407066}, {1.224999999999999, 4.965517422816339}, {1.249999999999999, 5.283169728906662}, {1.274999999999999, 5.629719623921192}, {1.299999999999999, 6.008820495394658}, {1.324999999999999, 6.424724661203479}, {1.349999999999999, 6.882405108916949}, {1.374999999999999, 7.387707118576735}, {1.399999999999999, 7.94753845560629}, {1.424999999999998, 8.57010976808535}, {1.449999999999998, 9.26524092481209}, {1.474999999999998, 10.04475480517944}, {1.499999999999998, 10.92298828067626}, {1.524999999999998, 11.91746200882653}, {1.549999999999998, 13.04976805914575}, {1.574999999999998, 14.3467602627104}, {1.599999999999998, 15.84217129263906}, {1.624999999999998, 17.57884069977324}, {1.649999999999998, 19.61183267794386}, {1.674999999999998, 22.01287404376962}, {1.699999999999997, 24.87679223016651}, {1.724999999999997, 28.33105380217965}, {1.749999999999997, 32.55023522001795}, {1.774999999999997, 37.7785713183026}, {1.799999999999997, 44.36617753590896}, {1.824999999999997, 52.82931295094805}, {1.849999999999997, 63.95480973881799}, {1.874999999999997, 78.9899374790564}, {1.899999999999997, 100.0080087449089}, {1.924999999999997, 130.6635004598998}, {1.949999999999997, 177.8944123326042}, {1.974999999999996, 256.2187890952162}, {1.999999999999996, 400.3571464467082}}\ \>", "\<\ {{1, 3}, {1.025, 3.16025}, {1.05, 3.33187}, {1.075, 3.51597}, {1.1, 3.71379}, {1.125, 3.92675}, {1.15, 4.15645}, {1.175, 4.40471}, {1.2, 4.67361}, {1.225, 4.96552}, {1.25, 5.28317}, {1.275, 5.62972}, {1.3, 6.00882}, {1.325, 6.42472}, {1.35, 6.88241}, {1.375, 7.38771}, {1.4, 7.94754}, {1.425, 8.57011}, {1.45, 9.26524}, {1.475, 10.0448}, {1.5, 10.923}, {1.525, 11.9175}, {1.55, 13.0498}, {1.575, 14.3468}, {1.6, 15.8422}, {1.625, 17.5788}, {1.65, 19.6118}, {1.675, 22.0129}, {1.7, 24.8768}, {1.725, 28.3311}, {1.75, 32.5502}, {1.775, 37.7786}, {1.8, 44.3662}, {1.825, 52.8293}, {1.85, 63.9548}, {1.875, 78.9899}, {1.9, 100.008}, {1.925, 130.664}, {1.95, 177.894}, {1.975, 256.219}, {2., 400.357}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "p3 = ListPlot[soln3,PlotRange->{0,400},\n PlotJoined->True, \ PlotStyle->{RGBColor[0,0,1]}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00154508 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(50)] .01131 .07725 1 0 Msboxa [(100)] .01131 .15451 1 0 Msboxa [(150)] .01131 .23176 1 0 Msboxa [(200)] .01131 .30902 1 0 Msboxa [(250)] .01131 .38627 1 0 Msboxa [(300)] .01131 .46353 1 0 Msboxa [(350)] .01131 .54078 1 0 Msboxa [(400)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .07725 m .03006 .07725 L s P [(50)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(100)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(150)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(200)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(250)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(300)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(350)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(400)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 0 1 r .004 w .02381 .00464 m .04762 .00488 L .07143 .00515 L .09524 .00543 L .11905 .00574 L .14286 .00607 L .16667 .00642 L .19048 .00681 L .21429 .00722 L .2381 .00767 L .2619 .00816 L .28571 .0087 L .30952 .00928 L .33333 .00993 L .35714 .01063 L .38095 .01141 L .40476 .01228 L .42857 .01324 L .45238 .01432 L .47619 .01552 L .5 .01688 L .52381 .01841 L .54762 .02016 L .57143 .02217 L .59524 .02448 L .61905 .02716 L .64286 .0303 L .66667 .03401 L .69048 .03844 L .71429 .04377 L .7381 .05029 L .7619 .05837 L .78571 .06855 L .80952 .08163 L .83333 .09882 L .85714 .12205 L .88095 .15452 L .90476 .20189 L .92857 .27486 L .95238 .39588 L s .97613 .61803 m .95238 .39588 L s s P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Show[p3,p]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0 0.00154508 [ [(1)] .02381 0 0 2 Msboxa [(1.2)] .21429 0 0 2 Msboxa [(1.4)] .40476 0 0 2 Msboxa [(1.6)] .59524 0 0 2 Msboxa [(1.8)] .78571 0 0 2 Msboxa [(2)] .97619 0 0 2 Msboxa [(50)] .01131 .07725 1 0 Msboxa [(100)] .01131 .15451 1 0 Msboxa [(150)] .01131 .23176 1 0 Msboxa [(200)] .01131 .30902 1 0 Msboxa [(250)] .01131 .38627 1 0 Msboxa [(300)] .01131 .46353 1 0 Msboxa [(350)] .01131 .54078 1 0 Msboxa [(400)] .01131 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(1)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(1.2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(1.4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(1.6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(1.8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(2)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .02381 .07725 m .03006 .07725 L s P [(50)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(100)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(150)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(200)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(250)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(300)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(350)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(400)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r .004 w .02381 .00464 m .04762 .00488 L .07143 .00515 L .09524 .00543 L .11905 .00574 L .14286 .00607 L .16667 .00642 L .19048 .00681 L .21429 .00722 L .2381 .00767 L .2619 .00816 L .28571 .0087 L .30952 .00928 L .33333 .00993 L .35714 .01063 L .38095 .01141 L .40476 .01228 L .42857 .01324 L .45238 .01432 L .47619 .01552 L .5 .01688 L .52381 .01841 L .54762 .02016 L .57143 .02217 L .59524 .02448 L .61905 .02716 L .64286 .0303 L .66667 .03401 L .69048 .03844 L .71429 .04377 L .7381 .05029 L .7619 .05837 L .78571 .06855 L .80952 .08163 L .83333 .09882 L .85714 .12205 L .88095 .15452 L .90476 .20189 L .92857 .27486 L .95238 .39588 L s .97613 .61803 m .95238 .39588 L s s P p p .004 w .02381 .00464 m .06349 .00506 L .10317 .00553 L .14286 .00607 L .18254 .00667 L .22222 .00737 L .2619 .00816 L .30159 .00908 L .34127 .01015 L .38095 .01141 L .42063 .01291 L .46032 .0147 L .5 .01688 L .53968 .01955 L .57937 .0229 L .61905 .02716 L .65873 .0327 L .69841 .0401 L .71825 .04477 L .7381 .05029 L .75794 .0569 L .77778 .06488 L .79762 .07467 L .81746 .08683 L .8373 .10221 L .85714 .12206 L .87698 .14829 L .89683 .18396 L .90675 .20682 L .91667 .23422 L .92659 .26744 L .93651 .30826 L .94643 .35918 L .95635 .42385 L .96627 .50768 L s .9761 .61803 m .96627 .50768 L s s P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "soln = NDSolve[{y'[t] == t^(1/2)+y[t]^(3/2),y[1]==3},\n \ y[t],{t,1,3}]"], "Input", AspectRatioFixed->True], Cell[TextData[ "NDSolve::mxst: \n Maximum number of 500 steps reached at the point \ 2.09991."], "Message", Evaluatable->False, AspectRatioFixed->True], Cell[OutputFormData[ "\<\ {{y[t] -> InterpolatingFunction[{1., 2.099910321086326446}, {{1., 1., {3., 0}, {0}}, {1.00063111518375961, 1., {3.003917109902656312, 6.206648173668926992}, {0}}, {1.00126223036751922, 1.00063111518375961, {3.007840858878685705, 6.217167764298219279}, {0}}, {1.007900578658844056, 1.00126223036751922, {3.04948439784444092, 6.329187786276329483, 8.437341418534851726}, {0, 0}}, {1.014538926950168892, 1.007900578658844056, {3.091880589381552057, 6.443926752626538002, 8.642132147551849827}, {0, 0}}, {1.021177275241493728, 1.014538926950168892, {3.135047763505049767, 6.561469237189085421, 8.853292973205017965}, {0, 0}}, {1.038421351962722497, 1.021177275241493728, {3.250911767832675314, 6.880514602370158842, 9.586786204915957775, 12.98679412758929709}, {0, 0, 0}}, {1.055665428683951266, 1.038421351962722497, {3.372462870622505074, 7.220737288452727606, 10.17193765153691892, 11.86970360199085233}, {0, 0, 0}}, {1.072909505405180035, 1.055665428683951266, {3.500076251316727158, 7.583927145524166172, 10.86383019001017279, 12.87289896026830879}, {0, 0, 0}}, {1.090153582126408804, 1.072909505405180035, {3.634164931102823679, 7.972088549198584487, 11.61695066233036021, 13.99633400463520498}, {0, 0, 0}}, {1.116653647501174128, 1.090153582126408804, {3.853891386430699882, 8.622416636036958127, 12.93419203679453667, 17.587666481869171, 25.08383574522480883}, {0, 0, 0, 0}}, {1.143153712875939452, 1.116653647501174128, {4.091801922680538417, 9.346164221336088557, 14.41435944175608984, 19.92070392503265558, 23.54678432373972184}, {0, 0, 0, 0}}, {1.169653778250704775, 1.143153712875939452, {4.34998322405549528, 10.15409693538105979, 16.10588143414744912, 22.5347788182931335, 24.10390369218163921}, {0, 0, 0, 0}}, {1.196153843625470099, 1.169653778250704775, {4.630828523825865842, 11.05893282153442207, 18.06649920393930551, 26.01653604080782847, 28.47529445522923356}, {0, 0, 0, 0}}, {1.222653909000235423, 1.196153843625470099, {4.937100047313719127, 12.07576623338631684, 20.3369993744292801, 30.16286987699272277, 33.79577745081983475}, {0, 0, 0, 0}}, {1.255385121220127195, 1.222653909000235423, {5.355290260960626259, 13.51337807953117516, 23.66978199403420635, 37.00898937528791046, 53.40351294115848471, 72.0169450346885816}, {0, 0, 0, 0, 0}}, {1.288116333440018968, 1.255385121220127195, {5.824336542857060386, 15.19120677967721283, 27.71999350597458034, 45.45151162794339533, 69.63570214299297285, 82.88407605365901036}, {0, 0, 0, 0, 0}}, {1.320847545659910741, 1.288116333440018968, {6.352934136594613103, 17.16186980668531325, 32.6508455703702734, 55.32992468254971723, 82.37139033883923608, 80.85838091375247715}, {0, 0, 0, 0, 0}}, {1.353578757879802514, 1.320847545659910741, {6.951718087593018415, 19.49240470600807485, 38.74622310155012025, 68.47048246905369266, 105.3580461199196236, 104.697868649995555}, {0, 0, 0, 0, 0}}, {1.386309970099694287, 1.353578757879802514, {7.633819950247170567, 22.26916851601383672, 46.33946640370321966, 85.60921576633539065, 137.0466486348781439, 140.2704264359163915}, {0, 0, 0, 0, 0}}, {1.41904118231958606, 1.386309970099694287, {8.415603476749352062, 25.6045984546605641, 55.89102682689106972, 108.1224142019384872, 180.0859722755287239, 189.3568288006950535}, {0, 0, 0, 0, 0}}, {1.451772394539477833, 1.41904118231958606, {9.317666785923637714, 29.64691133960887152, 68.040634028285906, 138.1298421586828175, 239.8883509725843169, 259.7800951549762455}, {0, 0, 0, 0, 0}}, {1.484503606759369606, 1.451772394539477833, {10.36622899465104241, 34.59412431055810596, 83.6834085289892501, 178.6821217655121229, 324.0527347882743466, 361.57845547423659}, {0, 0, 0, 0, 0}}, {1.511286121039095685, 1.484503606759369606, {11.35649948765251796, 39.50004439032346191, 100.0127876818318328, 224.8532121864677485, 443.3746185053113145, 573.3643460492925379}, {0, 0, 0, 0, 0}}, {1.538068635318821764, 1.511286121039095685, {12.49078786455772746, 45.38549638227881575, 120.4419243403321823, 282.4652961437755629, 568.1656535888760672, 716.7723641445999701}, {0, 0, 0, 0, 0}}, {1.564851149598547843, 1.538068635318821764, {13.79861166178295629, 52.50788364776663519, 146.4035792647750429, 360.3800271580899567, 759.4073193066023385, 1001.306771430641144}, {0, 0, 0, 0, 0}}, {1.591633663878273922, 1.564851149598547843, {15.31747170667347636, 61.21035029531504252, 179.7501682314600769, 465.1263080743579266, 1023.178594332511354, 1388.675064490235255}, {0, 0, 0, 0, 0}}, {1.613672585675761786, 1.591633663878273922, {16.7591891157975037, 69.87900572547316409, 214.6944656860239924, 584.5401115361897448, 1394.678279090437622, 2181.72721476637409}, {0, 0, 0, 0, 0}}, {1.63571150747324965, 1.613672585675761786, {18.41024567057922972, 80.27205242269933391, 258.3837846614301182, 733.8267687304244839, 1788.142335042897333, 2737.287890593880764}, {0, 0, 0, 0, 0}}, {1.657750429270737513, 1.63571150747324965, {20.31338140034305288, 92.84061744527849309, 313.8468713131650506, 935.2626227704354138, 2386.383888004398581, 3813.954660037257619}, {0, 0, 0, 0, 0}}, {1.679789351068225377, 1.657750429270737513, {22.52284229897838826, 108.1853870116121091, 385.0118105514929541, 1205.780261495948921, 3211.329092142102078, 5282.87574573284718}, {0, 0, 0, 0, 0}}, {1.697952029537405844, 1.679789351068225377, {24.62261955852237347, 123.4833268389821333, 459.6282413383299449, 1514.147297213941007, 4371.063116067294043, 8277.932481520497329}, {0, 0, 0, 0, 0}}, {1.71611470800658631, 1.697952029537405844, {27.02676947898622054, 141.8147562083355553, 552.8578693531678708, 1899.588730342089044, 5601.497051961002393, 10386.37394933049367}, {0, 0, 0, 0, 0}}, {1.734277386475766777, 1.71611470800658631, {29.79723156635730833, 163.9704566344991308, 671.1184529012566984, 2419.077481759371342, 7468.195678352370039, 14453.95363124390636}, {0, 0, 0, 0, 0}}, {1.752440064944947244, 1.734277386475766777, {33.01255864615699425, 191.0023866020457802, 822.7308505069354848, 3116.055450087621772, 10039.98887991802251, 20000.18687713293698}, {0, 0, 0, 0, 0}}, {1.767429780164576478, 1.752440064944947244, {36.07186445413198787, 217.9764054680881827, 981.8092373709489108, 3910.642094320480977, 13649.87339864756496, 31266.03928146600618}, {0, 0, 0, 0, 0}}, {1.782419495384205712, 1.767429780164576478, {39.5740094901631844, 250.2866517879701053, 1180.479949662397247, 4903.847670847666194, 17487.42251640045478, 39240.5950164362191}, {0, 0, 0, 0, 0}}, {1.797409210603834946, 1.782419495384205712, {43.60889290428708643, 289.3206140922953377, 1432.346967193751345, 6241.282004136443295, 23298.10387235220792, 54555.92071638278704}, {0, 0, 0, 0, 0}}, {1.812398925823464181, 1.797409210603834946, {48.29046231568897065, 336.9227877253955699, 1755.048778827468216, 8034.443210100757732, 31298.97308418592187, 75434.1326322152004}, {0, 0, 0, 0, 0}}, {1.824783038549093977, 1.812398925823464181, {52.7486507272929797, 384.454898554153547, 2093.821936284763957, 10078.93981555337981, 42516.86932129312587, 117726.8499080873514}, {0, 0, 0, 0, 0}}, {1.837167151274723774, 1.824783038549093977, {57.85144872973104883, 441.3741532810243304, 2516.774017881760643, 12634.53127890575725, 54459.49185318109124, 147784.1320695016086}, {0, 0, 0, 0, 0}}, {1.849551264000353571, 1.837167151274723774, {63.72948614796063417, 510.1168357816331384, 3052.757000967003799, 16073.66698031442322, 72517.31235323637924, 205322.004628309258}, {0, 0, 0, 0, 0}}, {1.861935376725983367, 1.849551264000353571, {70.54827038981287887, 593.9201194643335759, 3739.180452873463221, 20682.43347415262253, 97371.31768452269471, 283747.3313249222654}, {0, 0, 0, 0, 0}}, {1.872174631096195175, 1.861935376725983367, {77.04564543997825247, 677.6409856606245083, 4460.072081710825005, 25937.6246544113194, 132191.1418438973139, 442298.0844491976609}, {0, 0, 0, 0, 0}}, {1.882413885466406983, 1.872174631096195175, {84.48166734034494975, 777.8756982616190067, 5359.88596984430297, 32506.64111521960488, 169299.3623835219978, 555307.934940189514}, {0, 0, 0, 0, 0}}, {1.892653139836618791, 1.882413885466406983, {93.04631312332557194, 898.9045607808027919, 6499.838130766355789, 41342.77605734885222, 225352.5866704675886, 771132.4650470709225}, {0, 0, 0, 0, 0}}, {1.902892394206830599, 1.892653139836618791, {102.9802142875056637, 1046.413008350430934, 7959.303585513717165, 53179.94726212436744, 302479.4156959063016, 1.065276709153258211*10^6}, {0, 0, 0, 0, 0}}, {1.911362899904175121, 1.902892394206830599, {112.449944625404601, 1193.828153187928057, 9492.489921252075218, 66678.28151499924858, 410471.6257256575545, 1.659102391875430563*10^6}, {0, 0, 0, 0, 0}}, {1.919833405601519643, 1.911362899904175121, {123.2868370634842107, 1370.295513014037026, 11405.89802646315528, 83551.48893125727568, 525647.611353048516, 2.083245232151669973*10^6}, {0, 0, 0, 0, 0}}, {1.928303911298864165, 1.919833405601519643, {135.7673509183388262, 1583.338328022039805, 13829.45266511939995, 106240.7976884248333, 699501.1428997805224, 2.891913158875731744*10^6}, {0, 0, 0, 0, 0}}, {1.936774416996208687, 1.928303911298864165, {150.2415888683586735, 1842.947141608227, 16931.62309648475509, 136628.7426376946648, 938667.3572410826554, 3.993961929687330982*10^6}, {0, 0, 0, 0, 0}}, {1.943784433624958706, 1.936774416996208687, {164.0436778985076966, 2102.456671473738755, 20191.15361475192737, 171282.8673016927882, 1.273413591752250809*10^6, 6.216581898991255648*10^6}, {0, 0, 0, 0, 0}}, {1.950794450253708726, 1.943784433624958706, {179.8374428133170925, 2413.078401454265716, 24258.56992454713295, 214601.7110762150069, 1.630617982858442189*10^6, 7.806451778674634705*10^6}, {0, 0, 0, 0, 0}}, {1.957804466882458745, 1.950794450253708726, {198.0253752779862586, 2788.039566930063063, 29409.68903063321667, 272839.279347945941, 2.16953315399193355*10^6, 1.083410094167613087*10^7}, {0, 0, 0, 0, 0}}, {1.964814483511208765, 1.957804466882458745, {219.1171111239541135, 3244.902397106876473, 36002.16048814232903, 350823.9622019071642, 2.910800398128477639*10^6, 1.495998108707008381*10^7}, {0, 0, 0, 0, 0}}, {1.970617419880287391, 1.964814483511208765, {239.2336546031607809, 3701.671384174683302, 42930.04074196074167, 439760.17323984828, 3.948020327434092678*10^6, 2.327523115067808756*10^7}, {0, 0, 0, 0, 0}}, {1.976420356249366017, 1.970617419880287391, {262.2520492117822683, 4248.365600997197248, 51574.33739545247168, 550934.3591234787841, 5.055244251825910951*10^6, 2.922946494139581698*10^7}, {0, 0, 0, 0, 0}}, {1.982223292618444644, 1.976420356249366017, {288.7584629559145734, 4908.246109016651893, 62520.68253062366353, 700372.7821090704765, 6.725127198949581218*10^6, 4.055889223916204761*10^7}, {0, 0, 0, 0, 0}}, {1.98802622898752327, 1.982223292618444644, {319.4950300537266447, 5712.193715392951235, 76528.47092236827316, 900458.7689376413538, 9.021790301624658735*10^6, 5.599741752538039997*10^7}, {0, 0, 0, 0, 0}}, {1.992830861292320716, 1.98802622898752327, {348.8147955016125649, 6516.076374963465209, 91250.44188091038455, 1.128649170599341994*10^6, 1.223478271417720594*10^7, 8.709669485487289126*10^7}, {0, 0, 0, 0, 0}}, {1.997635493597118161, 1.992830861292320716, {382.3629276928122513, 7478.174009582021058, 109618.8440568686647, 1.413898912533465765*10^6, 1.566553365693044027*10^7, 1.093820709526489407*10^8}, {0, 0, 0, 0, 0}}, {2.002440125901915607, 1.997635493597118161, {420.993285700396429, 8639.399365985206588, 132877.2828776588647, 1.797284788011139729*10^6, 2.083841734879465103*10^7, 1.517608483004866981*10^8}, {0, 0, 0, 0, 0}}, {2.007244758206713052, 2.002440125901915607, {465.7868473670511677, 10054.06270902089088, 162638.3704675187011, 2.310564999741016759*10^6, 2.795241971376458092*10^7, 2.095089009831775447*10^8}, {0, 0, 0, 0, 0}}, {2.011223364388067067, 2.007244758206713052, {508.5200346836801153, 11468.73531563664581, 193919.0564635138817, 2.895952412380773447*10^6, 3.790345360625522818*10^7, 3.257961953043396816*10^8}, {0, 0, 0, 0, 0}}, {2.015201970569421081, 2.011223364388067067, {557.4149023013887588, 13161.77664215423915, 232946.0520134767906, 3.627719957723027406*10^6, 4.853087926734805052*10^7, 4.091691493409091863*10^8}, {0, 0, 0, 0, 0}}, {2.019180576750775096, 2.015201970569421081, {613.7154488755353548, 15205.1541773687456, 282360.4209052047522, 4.611166997325266178*10^6, 6.455215062366970995*10^7, 5.67649912967608592*10^8}, {0, 0, 0, 0, 0}}, {2.02315918293212911, 2.019180576750775096, {678.9964904772493209, 17694.39681314524862, 345586.9185630446101, 5.927738340425434183*10^6, 8.658433153662208061*10^7, 7.836030012706553965*10^8}, {0, 0, 0, 0, 0}}, {2.026454084762477995, 2.02315918293212911, {741.2792246671818718, 20183.80752562906334, 412045.0816521483468, 7.429285759244428372*10^6, 1.173999776843380893*10^8, 1.218363664960648941*10^9}, {0, 0, 0, 0, 0}}, {2.02974898659282688, 2.026454084762477995, {812.5413326123326552, 23162.99513884085704, 494958.6678165842603, 9.306311281806186822*10^6, 1.503144726184335812*10^8, 1.530179973835345847*10^9}, {0, 0, 0, 0, 0}}, {2.033043888423175766, 2.02974898659282688, {894.5954161772796733, 26758.56389619971897, 599936.8972873033695, 1.182877601091562087*10^7, 1.999284699437076348*10^8, 2.122732580233902929*10^9}, {0, 0, 0, 0, 0}}, {2.036338790253524651, 2.033043888423175766, {989.7360279927868347, 31138.56026934377241, 734253.4736649663031, 1.520554384541619017*10^7, 2.681545395400112853*10^8, 2.930164036193557992*10^9}, {0, 0, 0, 0, 0}}, {2.039067656892265345, 2.036338790253524651, {1080.511376626735802, 35519.03826638856988, 875440.2326685019221, 1.905677818131820309*10^7, 3.63573821264503727*10^8, 4.555429163200112066*10^9}, {0, 0, 0, 0, 0}}, {2.04179652353100604, 2.039067656892265345, {1184.37273372031557, 40761.2633177622077, 1.051582422674381577*10^6, 2.387106597616700139*10^7, 4.655012409619518051*10^8, 5.721382113477978259*10^9}, {0, 0, 0, 0, 0}}, {2.044525390169746734, 2.04179652353100604, {1303.961407002804654, 47087.96820019187689, 1.274593707534941074*10^6, 3.034057179477791423*10^7, 6.191298401597715685*10^8, 7.936635999183492439*10^9}, {0, 0, 0, 0, 0}}, {2.047254256808487428, 2.044525390169746734, {1442.620922366934368, 54794.78619754532758, 1.55992308101308273*10^6, 3.900091742433155443*10^7, 8.303854593169034624*10^8, 1.095519356987215689*10^10}, {0, 0, 0, 0, 0}}, {2.049514430270179751, 2.047254256808487428, {1574.922933779846067, 62502.67870878398647, 1.859854087370380091*10^6, 4.887818540147403351*10^7, 1.125829131105863847*10^9, 1.703049657918387944*10^10}, {0, 0, 0, 0, 0}}, {2.051774603731872073, 2.049514430270179751, {1726.296157063060355, 71726.79717961389498, 2.234038162432082439*10^6, 6.122541818480007448*10^7, 1.441443388368964191*10^9, 2.138962661276354058*10^10}, {0, 0, 0, 0, 0}}, {2.054034777193564396, 2.051774603731872073, {1900.589693085426437, 82859.00682690889323, 2.707780035082811114*10^6, 7.781737946858500214*10^7, 1.917121033450996088*10^9, 2.967063041778920552*10^10}, {0, 0, 0, 0, 0}}, {2.056294950655256718, 2.054034777193564396, {2102.675887965302262, 96419.42059494185562, 3.313893600551269356*10^6, 1.000276354719866833*10^8, 2.571217923682244229*10^9, 4.095447347938178283*10^10}, {0, 0, 0, 0, 0}}, {2.058166989320154775, 2.056294950655256718, {2295.501011799226347, 109982.0018241561357, 3.951035527232206085*10^6, 1.253589181345217152*10^8, 3.485952570233959782*10^9, 6.366310091303276029*10^10}, {0, 0, 0, 0, 0}}, {2.060039027985052831, 2.058166989320154775, {2516.120471620622652, 126212.3623897746288, 4.74590594493814727*10^6, 1.570247187100253929*10^8, 4.463180269042433628*10^9, 7.995886547286225724*10^10}, {0, 0, 0, 0, 0}}, {2.061911066649950888, 2.060039027985052831, {2770.143662669076422, 145799.9493592192002, 5.752253491200596437*10^6, 1.995758378848345187*10^8, 5.935949411023089651*10^9, 1.109128715723975478*10^11}, {0, 0, 0, 0, 0}}, {2.063783105314848944, 2.061911066649950888, {3064.671104938813076, 169659.8366608252919, 7.039776827240116676*10^6, 2.565346749871572598*10^8, 7.961109182496967945*10^9, 1.530912248249730225*10^11}, {0, 0, 0, 0, 0}}, {2.065333696263844118, 2.063783105314848944, {3345.705692818337529, 193523.8745458711448, 8.393227214243651916*10^6, 3.214976831060372622*10^8, 1.079317345826959798*10^10, 2.379700867281871182*10^11}, {0, 0, 0, 0, 0}}, {2.066884287212839291, 2.065333696263844118, {3667.248123463986637, 222081.848718607887, 1.008172261126627954*10^7, 4.027058605863713837*10^8, 1.381880950151699281*10^10, 2.98884397156782428*10^11}, {0, 0, 0, 0, 0}}, {2.068434878161834465, 2.066884287212839291, {4037.473329706101117, 256546.7938398246927, 1.221942980866675152*10^7, 5.118285483136761634*10^8, 1.837858755970273488*10^10, 4.145843297278086169*10^11}, {0, 0, 0, 0, 0}}, {2.069985469110829638, 2.068434878161834465, {4466.729278842702594, 298528.7049516393106, 1.495439504742951608*10^7, 6.578986202930317718*10^8, 2.4648551803041513*10^10, 5.722383234629383289*10^11}, {0, 0, 0, 0, 0}}, {2.071269827283936612, 2.069985469110829638, {4876.324778681090879, 340518.328494730174, 1.782942605160701394*10^7, 8.244956391181705934*10^8, 3.341659166348087229*10^10, 8.89485965347449552*10^11}, {0, 0, 0, 0, 0}}, {2.072554185457043585, 2.071269827283936612, {5344.957410646554648, 390766.9126705154155, 2.141615266869443178*10^7, 1.032753356975919593*10^9, 4.278412028191030389*10^10, 1.117175458679167369*10^12}, {0, 0, 0, 0, 0}}, {2.073838543630150558, 2.072554185457043585, {5884.541246992223898, 451408.7359331685321, 2.595707765455441373*10^7, 1.312595291798940879*10^9, 5.690116690629125499*10^10, 1.54962675545973245*10^12}, {0, 0, 0, 0, 0}}, {2.075122901803257531, 2.073838543630150558, {6510.15724256422302, 525276.4925565493103, 3.176666773797598192*10^7, 1.687185371467110692*10^9, 7.631283993617418906*10^10, 2.138888803058054728*10^12}, {0, 0, 0, 0, 0}}, {2.076186749676962032, 2.075122901803257531, {7107.123843435709644, 599158.3162727002543, 3.787381821162946804*10^7, 2.114416536989879663*10^9, 1.034582268712027965*10^11, 3.324631674658890777*10^12}, {0, 0, 0, 0, 0}}, {2.077250597550666532, 2.076186749676962032, {7790.133076517669882, 687571.767066127927, 4.549273318560510359*10^7, 2.648485050124826725*10^9, 1.324600106828626142*10^11, 4.175676069385641693*10^12}, {0, 0, 0, 0, 0}}, {2.078314445424371033, 2.077250597550666532, {8576.548619341448967, 794272.0426978773119, 5.513851879315621954*10^7, 3.366124301959749076*10^9, 1.761656907294496873*10^11, 5.792016904529070007*10^12}, {0, 0, 0, 0, 0}}, {2.079378293298075534, 2.078314445424371033, {9488.349514809416453, 924243.1608754150816, 6.747914209430458955*10^7, 4.326735831254184859*10^9, 2.362630595996973489*10^11, 7.994455448795148065*10^12}, {0, 0, 0, 0, 0}}, {2.080259496331346176, 2.079378293298075534, {10358.40009184079386, 1.054239632929496587*10^6, 8.045188725481323998*10^7, 5.4223431223688587*10^9, 3.203029565615153786*10^11, 1.242623365786526825*10^13}, {0, 0, 0, 0, 0}}, {2.081140699364616818, 2.080259496331346176, {11353.85245157039652, 1.209804504269600378*10^6, 9.663587504523748544*10^7, 6.791928401867955036*10^9, 4.100909840753419483*10^11, 1.560714450213035953*10^13}, {0, 0, 0, 0, 0}}, {2.08202190239788746, 2.081140699364616818, {12500.01279483722328, 1.397544971258372918*10^6, 1.1712526070961542*10^8, 8.63226212255836523*10^9, 5.454003044028892259*10^11, 2.164834067919864839*10^13}, {0, 0, 0, 0, 0}}, {2.082903105431158101, 2.08202190239788746, {13828.91377783078662, 1.626230288851597451*10^6, 1.433388975020747199*10^8, 1.109567331065136992*10^10, 7.314565394887011287*10^11, 2.988011604114597282*10^13}, {0, 0, 0, 0, 0}}, {2.08363302424087885, 2.082903105431158101, {15096.97051573718851, 1.854960947111443304*10^6, 1.708953439912688573*10^8, 1.390527237472716176*10^10, 9.916355192112793102*10^11, 4.644400605571253579*10^13}, {0, 0, 0, 0, 0}}, {2.084362943050599598, 2.08363302424087885, {16547.79300988103889, 2.128679238660835081*10^6, 2.052730017020176405*10^8, 1.741746718484815708*10^10, 1.269611997918048119*10^12, 5.833296786000135993*10^13}, {0, 0, 0, 0, 0}}, {2.085092861860320346, 2.084362943050599598, {18218.26328696593725, 2.459010444373344981*10^6, 2.48796012740685044*10^8, 2.213684696559384767*10^10, 1.688516139535048085*10^12, 8.091219026492190591*10^13}, {0, 0, 0, 0, 0}}, {2.085822780670041095, 2.085092861860320346, {20155.06663570674676, 2.861383929386796772*10^6, 3.044782251964747387*10^8, 2.84540432335765148*10^10, 2.264526694140537856*10^12, 1.116787799531676467*10^14}, {0, 0, 0, 0, 0}}, {2.086427389638417625, 2.085822780670041095, {22003.19731166964684, 3.263838076012304373*10^6, 3.630128994399151218*10^8, 3.565901082442421786*10^10, 3.070010831562998616*10^12, 1.735864528073900728*10^14}, {0, 0, 0, 0, 0}}, {2.087031998606794156, 2.086427389638417625, {24117.69883946590913, 3.745448063820228912*10^6, 4.360369423885374832*10^8, 4.466572405721100746*10^10, 3.93059796073558437*10^12, 2.180221149900729385*10^14}, {0, 0, 0, 0, 0}}, {2.087636607575170686, 2.087031998606794156, {26552.32442710962364, 4.32666849147443367*10^6, 5.284871758457412062*10^8, 5.676813398780798505*10^10, 5.22747741693528886*10^12, 3.024123717572102919*10^14}, {0, 0, 0, 0, 0}}, {2.088241216543547216, 2.087636607575170686, {29375.11483473006152, 5.034647178894419908*10^6, 6.467654606772497055*10^8, 7.296797285153191555*10^10, 7.010738356822722796*10^12, 4.174030284997125442*10^14}, {0, 0, 0, 0, 0}}, {2.088742029570233808, 2.088241216543547216, {32068.67404586399141, 5.742768861322971124*10^6, 7.711030041205703839*10^8, 9.144442190627922899*10^10, 9.50441689216775249*10^12, 6.487826592849208544*10^14}, {0, 0, 0, 0, 0}}, {2.089242842596920399, 2.088742029570233808, {35150.45431679133477, 6.590165470790065908*10^6, 9.26218317437173939*10^8, 1.145412771044145211*10^11, 1.216869591201324739*10^13, 8.148622024522108995*10^14}, {0, 0, 0, 0, 0}}, {2.08974365562360699, 2.089242842596920399, {38698.79775050501301, 7.612826799885088494*10^6, 1.122597958085890822*10^9, 1.455767109577731868*10^11, 1.618367422189334972*10^13, 1.130270975779152757*10^15}, {0, 0, 0, 0, 0}}, {2.090244468650293581, 2.08974365562360699, {42812.8696284203902, 8.858519294112542806*10^6, 1.373840450624998079*10^9, 1.871195563477940275*10^11, 2.170442504235928769*10^13, 1.560048722813647141*10^15}, {0, 0, 0, 0, 0}}, {2.090659305509732816, 2.090244468650293581, {46738.59831218619379, 1.010446468382538772*10^7, 1.637954029683922264*10^9, 2.345005493743236881*10^11, 2.942452710275211034*10^13, 2.424826940011324991*10^15}, {0, 0, 0, 0, 0}}, {2.09107414236917205, 2.090659305509732816, {51230.13858643940524, 1.15954647607414506*10^7, 1.967444556234537474*10^9, 2.937301123573670822*10^11, 3.767280397793943479*10^13, 3.045550743030872408*10^15}, {0, 0, 0, 0, 0}}, {2.091488979228611285, 2.09107414236917205, {56401.66962772590369, 1.33948435227246151*10^7, 2.384587092391458041*10^9, 3.733172923231200256*10^11, 5.010265317030718073*10^13, 4.224388259662758397*10^15}, {0, 0, 0, 0, 0}}, {2.091903816088050519, 2.091488979228611285, {62397.7191364373646, 1.558664591933551487*10^7, 2.918267000561087543*10^9, 4.798495788183421444*10^11, 6.719416836358268112*10^13, 5.830678580360401577*10^15}, {0, 0, 0, 0, 0}}, {2.092247436957327942, 2.091903816088050519, {68119.27269992830587, 1.77788948529360439*10^7, 3.4792875203002061*10^9, 6.013532051838888567*10^11, 9.109455895986721576*10^13, 9.062770138518434977*10^15}, {0, 0, 0, 0, 0}}, {2.092591057826605366, 2.092247436957327942, {74665.46709400530191, 2.040231837641015495*10^7, 4.17917917909889852*10^9, 7.532412627957282154*10^11, 1.166301456974294209*10^14, 1.138272282200255618*10^16}, {0, 0, 0, 0, 0}}, {2.092934678695882789, 2.092591057826605366, {82202.71222185527048, 2.356833509574229829*10^7, 5.065257674435970582*10^9, 9.57334190065538297*10^11, 1.551112806343504058*10^14, 1.578860874447599462*10^16}, {0, 0, 0, 0, 0}}, {2.093278299565160212, 2.092934678695882789, {90941.64922080773503, 2.742482207498388868*10^7, 6.198880014702238162*10^9, 1.230524876748567356*10^12, 2.080242843615526435*10^14, 2.179209193783083382*10^16}, {0, 0, 0, 0, 0}}, {2.093562930468994313, 2.093278299565160212, {99280.52698846945084, 3.128209663160503343*10^7, 7.390578713738396357*10^9, 1.542108003490183651*10^12, 2.820165850103275701*10^14, 3.387195703928794326*10^16}, {0, 0, 0, 0, 0}}, {2.093847561372828414, 2.093562930468994313, {108821.2761487159864, 3.589802449145929099*10^7, 8.877261959645973006*10^9, 1.9316087839763479*10^12, 3.610713082990952892*10^14, 4.254274974369136325*10^16}, {0, 0, 0, 0, 0}}, {2.094132192276662514, 2.093847561372828414, {119806.4302540316798, 4.146864687583750581*10^7, 1.07594357093077821*10^10, 2.454983187520450463*10^12, 4.80203585545759034*10^14, 5.90096533446124051*10^16}, {0, 0, 0, 0, 0}}, {2.094416823180496615, 2.094132192276662514, {132542.9874409187312, 4.825415364247683509*10^7, 1.316743187139905397*10^10, 3.155551159725710107*10^12, 6.440148926408919723*10^14, 8.144754078064240745*10^16}, {0, 0, 0, 0, 0}}, {2.094652591145546851, 2.094416823180496615, {144696.4832427778215, 5.504104844368576822*10^7, 1.56987922642499401*10^10, 3.954572455525350353*10^12, 8.730846587843337533*10^14, 1.265957139428784721*10^17}, {0, 0, 0, 0, 0}}, {2.094888359110597087, 2.094652591145546851, {158601.6449544733333, 6.316279667255568692*10^7, 1.885674700209505112*10^10, 4.9534051840956305*10^12, 1.117827147955274693*10^15, 1.590026339749938784*10^17}, {0, 0, 0, 0, 0}}, {2.095124127075647323, 2.094888359110597087, {174611.9525075921512, 7.296433333683931983*10^7, 2.285478656788302618*10^10, 6.295541993973488108*10^12, 1.486643961604853476*10^15, 2.205472721912579858*10^17}, {0, 0, 0, 0, 0}}, {2.095359895040697559, 2.095124127075647323, {193174.8395045363941, 8.490346302926270838*10^7, 2.796975647398724953*10^10, 8.092072080338625282*10^12, 1.993780692942757579*10^15, 3.044083085201507941*10^17}, {0, 0, 0, 0, 0}}, {2.09555518849701145, 2.095359895040697559, {210887.9487095562889, 9.684503774029453705*10^7, 3.334677281264273793*10^10, 1.0141075078248729*10^13, 2.702948175969376145*10^15, 4.731483113010800438*10^17}, {0, 0, 0, 0, 0}}, {2.095750481953325341, 2.09555518849701145, {231154.0216032716827, 1.111352923568999292*10^8, 4.005477560038428083*10^10, 1.270247274638838156*10^13, 3.460636554629024548*10^15, 5.942684098133713518*10^17}, {0, 0, 0, 0, 0}}, {2.095945775409639232, 2.095750481953325341, {254488.2368688313878, 1.283811410552517678*10^8, 4.854725236483699258*10^10, 1.614423564214296635*10^13, 4.602441109870959784*10^15, 8.242897969862620416*10^17}, {0, 0, 0, 0, 0}}, {2.096141068865953123, 2.095945775409639232, {281542.705716771405, 1.493880922654846529*10^8, 5.941226674387579809*10^10, 2.075123966719415857*10^13, 6.172464326055972871*10^15, 1.137718096464610219*10^18}, {0, 0, 0, 0, 0}}, {2.096302836149830943, 2.096141068865953123, {307358.6710636750314, 1.703993488381425036*10^8, 7.08339111680721699*10^10, 2.600568293069268042*10^13, 8.367945504634247099*10^15, 1.768378792046461475*10^18}, {0, 0, 0, 0, 0}}, {2.096464603433708763, 2.096302836149830943, {336895.4511973776534, 1.955431171813163582*10^8, 8.508278316356934449*10^10, 3.257410614217760051*10^13, 1.071364122764322339*10^16, 2.221061945665018006*10^18}, {0, 0, 0, 0, 0}}, {2.096626370717586582, 2.096464603433708763, {370903.892575786158, 2.258872648268456199*10^8, 1.03122162080338199*10^11, 4.140012817903739833*10^13, 1.424850505495632682*10^16, 3.080760146323688496*10^18}, {0, 0, 0, 0, 0}}, {2.096788138001464402, 2.096626370717586582, {410334.4136998731515, 2.628490864212320314*10^8, 1.262011882673169786*10^11, 5.321428161894405523*10^13, 1.910907229371119818*10^16, 4.252189214661067015*10^18}, {0, 0, 0, 0, 0}}, {2.09692213459810224, 2.096788138001464402, {447959.8832090964857, 2.998184873561168197*10^8, 1.504625877774726121*10^11, 6.668872188543510709*10^13, 2.590596678778111264*10^16, 6.609264052683680617*10^18}, {0, 0, 0, 0, 0}}, {2.097056131194740077, 2.09692213459810224, {491008.2515788382662, 3.440590596093217657*10^8, 1.807294694438872786*10^11, 8.353271892846273288*10^13, 3.316790561330246947*10^16, 8.301154414035782857*10^18}, {0, 0, 0, 0, 0}}, {2.097190127791377915, 2.097056131194740077, {540573.8391624546274, 3.974497199642244988*10^8, 2.190479914537536378*10^11, 1.06166077138172985*10^14, 4.411133669252602777*10^16, 1.151425027827750381*10^19}, {0, 0, 0, 0, 0}}, {2.097324124388015753, 2.097190127791377915, {598041.8322911178846, 4.62484203303970932*10^8, 2.680715261460330048*10^11, 1.364621660386889072*10^14, 5.915895440890404519*10^16, 1.589243070957361007*10^19}, {0, 0, 0, 0, 0}}, {2.097435117720740425, 2.097324124388015753, {652879.0585045039439, 5.275320274017822651*10^8, 3.196066136563510225*10^11, 1.710158773512603768*10^14, 8.020116071098279077*10^16, 2.470192349929997697*10^19}, {0, 0, 0, 0, 0}}, {2.097546111053465097, 2.097435117720740425, {715619.8852698746839, 6.053735073184475515*10^8, 3.838983024218988609*10^11, 2.14210444421009156*10^14, 1.026830808261121964*10^17, 3.102531307975772745*10^19}, {0, 0, 0, 0, 0}}, {2.097657104386189769, 2.097546111053465097, {787859.2288197259401, 6.993146042586526046*10^8, 4.652929574636144346*10^11, 2.722511840977855493*10^14, 1.365623675758112059*10^17, 4.303415855034847958*10^19}, {0, 0, 0, 0, 0}}, {2.097768097718914442, 2.097657104386189769, {871615.9276697333821, 8.137430539972378781*10^8, 5.69426763161917134*10^11, 3.499421440243488848*10^14, 1.83147623323183767*10^17, 5.939747104672184736*10^19}, {0, 0, 0, 0, 0}}, {2.097860036776959901, 2.097768097718914442, {951538.4212005997066, 9.281949827456121133*10^8, 6.788955122268150461*10^11, 4.385513054932353349*10^14, 2.482912563824778496*10^17, 9.232266838689425241*10^19}, {0, 0, 0, 0, 0}}, {2.09795197583500536, 2.097860036776959901, {1.042980012882886612*10^6, 1.065157401757615015*10^9, 8.154613149185629894*10^11, 5.493189838298459515*10^14, 3.178920431134146828*10^17, 1.159561416633644879*10^20}, {0, 0, 0, 0, 0}}, {2.098043914893050819, 2.09795197583500536, {1.148265212194963666*10^6, 1.230447162707677175*10^9, 9.883565414823765304*10^11, 6.981580193969601103*10^14, 4.227774250639918947*10^17, 1.608388201258697601*10^20}, {0, 0, 0, 0, 0}}, {2.098135853951096278, 2.098043914893050819, {1.270336373752619422*10^6, 1.431784503608224143*10^9, 1.209553343591610255*10^12, 8.973878575352546757*10^14, 5.669986492978996153*10^17, 2.219961803429632196*10^20}, {0, 0, 0, 0, 0}}, {2.098212009794353808, 2.098135853951096278, {1.386819379214459657*10^6, 1.633163163038303862*10^9, 1.442082422578058691*10^12, 1.124616212801072304*10^15, 7.686739189915441792*10^17, 3.450530417608485968*10^20}, {0, 0, 0, 0, 0}}, {2.098288165637611337, 2.098212009794353808, {1.520090888229075989*10^6, 1.874149123402630797*10^9, 1.732169960091449304*10^12, 1.408667624661427209*10^15, 9.84147908080940361*10^17, 4.333824028954252297*10^20}, {0, 0, 0, 0, 0}}, {2.098364321480868866, 2.098288165637611337, {1.673538755633154095*10^6, 2.164977158463717189*10^9, 2.099426978962691223*10^12, 1.790348793487615769*10^15, 1.308857888703332366*10^18, 6.011299711076404695*10^20}, {0, 0, 0, 0, 0}}, {2.098440477324126396, 2.098364321480868866, {1.851451314180199254*10^6, 2.519231057548063616*10^9, 2.569284233641412085*10^12, 2.30125156503986694*10^15, 1.755345942548662619*10^18, 8.297036382119667221*10^20}, {0, 0, 0, 0, 0}}, {2.098503559465709941, 2.098440477324126396, {2.021219421836598742*10^6, 2.873557665348499906*10^9, 3.063213060058239422*10^12, 2.883953424485464189*10^15, 2.379703389946211352*10^18, 1.289624657255867115*10^21}, {0, 0, 0, 0, 0}}, {2.098566641607293487, 2.098503559465709941, {2.215455925652793431*10^6, 3.297573483724281947*10^9, 3.679405220330002321*10^12, 3.612371697456910651*10^15, 3.046779709624289639*10^18, 1.619752819743932804*10^21}, {0, 0, 0, 0, 0}}, {2.098629723748877032, 2.098566641607293487, {2.439098452694733009*10^6, 3.809286638586607877*10^9, 4.459517647239905967*10^12, 4.59115061049924568*10^15, 4.05203482024152913*10^18, 2.246703921504272894*10^21}, {0, 0, 0, 0, 0}}, {2.098692805890460578, 2.098629723748877032, {2.698397030966388643*10^6, 4.432597861937735168*10^9, 5.457569309642104704*10^12, 5.901303933702078516*10^15, 5.43429720535575954*10^18, 3.100990594519500672*10^21}, {0, 0, 0, 0, 0}}, {2.098745058698879693, 2.098692805890460578, {2.945825487612610585*10^6, 5.056037026952489268*10^9, 6.506752839700853022*10^12, 7.395578036477909911*10^15, 7.3672174382440993*10^18, 4.819930386858900424*10^21}, {0, 0, 0, 0, 0}}, {2.098797311507298809, 2.098745058698879693, {3.228915396553785528*10^6, 5.802094648030965317*10^9, 7.815643163215301459*10^12, 9.263525675131302912*10^15, 9.432389185202086033*10^18, 6.053773735532368968*10^21}, {0, 0, 0, 0, 0}}, {2.098849564315717924, 2.098797311507298809, {3.554863099716362892*10^6, 6.702456096395056254*10^9, 9.472726235030602071*10^12, 1.177349529234076706*10^16, 1.254451342835803167*10^19, 8.396983057110308305*10^21}, {0, 0, 0, 0, 0}}, {2.098901817124137039, 2.098849564315717924, {3.932777696992628524*10^6, 7.799174807352389607*10^9, 1.159274694220451906*10^13, 1.513323767818444021*10^16, 1.682379755870210411*10^19, 1.158985166422225887*10^22}, {0, 0, 0, 0, 0}}, {2.098945099675532507, 2.098901817124137039, {4.293392195454153195*10^6, 8.896118644727983223*10^9, 1.382137990191773586*10^13, 1.896513732206175547*10^16, 2.28078385239043278*10^19, 1.80143328494113136*10^22}, {0, 0, 0, 0, 0}}, {2.098988382226927975, 2.098945099675532507, {4.705981460999878171*10^6, 1.020881016647637553*10^10, 1.660167145063948697*10^13, 2.375528116716298741*10^16, 2.920131116746480532*10^19, 2.262578226923126375*10^22}, {0, 0, 0, 0, 0}}, {2.099031664778323442, 2.098988382226927975, {5.181033798545907582*10^6, 1.179299991375472869*10^10, 2.012157984117790824*10^13, 3.019181886711530231*10^16, 3.883599690456421091*10^19, 3.138345050214835929*10^22}, {0, 0, 0, 0, 0}}, {2.09907494732971891, 2.099031664778323442, {5.7318252610628756*10^6, 1.372268107864571236*10^10, 2.462484147841600984*10^13, 3.880750418225683608*10^16, 5.208404046225552409*10^19, 4.331669251844159991*10^22}, {0, 0, 0, 0, 0}}, {2.099110799551529839, 2.09907494732971891, {6.257402706875822076*10^6, 1.565275836953557821*10^10, 2.935881286933225083*10^13, 4.863398423936560171*10^16, 7.060976392868494595*10^19, 6.732798014628799629*10^22}, {0, 0, 0, 0, 0}}, {2.099146651773340768, 2.099110799551529839, {6.858730753307702799*10^6, 1.796244461075296181*10^10, 3.526459495403490277*10^13, 6.091777488148475874*10^16, 9.040302885253446676*10^19, 8.456312183017057427*10^22}, {0, 0, 0, 0, 0}}, {2.099182503995151697, 2.099146651773340768, {7.551095575300131707*10^6, 2.074983311009191516*10^10, 4.274144098311383756*10^13, 7.742355917558375092*10^16, 1.202306194297776197*10^20, 1.172946198114135843*10^23}, {0, 0, 0, 0, 0}}, {2.099218356216962626, 2.099182503995151697, {8.353846349772922578*10^6, 2.414511519447241688*10^10, 5.230708588209111587*10^13, 9.951752479531496212*10^16, 1.612446419269661537*10^20, 1.618947206789334947*10^23}, {0, 0, 0, 0, 0}}, {2.099248053676513364, 2.099218356216962626, {9.119848971360938466*10^6, 2.754109428246562974*10^10, 6.236279508496648583*10^13, 1.247164387385836207*10^17, 2.185975959414013124*10^20, 2.51636119234094333*10^23}, {0, 0, 0, 0, 0}}, {2.099277751136064102, 2.099248053676513364, {9.996254271798216804*10^6, 3.160499690237584361*10^10, 7.490761680474149713*10^13, 1.562168520697242675*10^17, 2.798746752352690016*10^20, 3.160518969964110844*10^23}, {0, 0, 0, 0, 0}}, {2.09930744859561484, 2.099277751136064102, {1.100534107960545303*10^7, 3.650941863629701151*10^10, 9.078962850898612958*10^13, 1.985440978209890151*10^17, 3.722165713842856744*10^20, 4.383847960418808742*10^23}, {0, 0, 0, 0, 0}}, {2.099337146055165578, 2.09930744859561484, {1.217530984355718131*10^7, 4.248343166338645423*10^10, 1.111085816063997263*10^14, 2.55201612093771194*10^17, 4.991900386400223522*10^20, 6.050762085768965873*10^23}, {0, 0, 0, 0, 0}}, {2.099361745342578812, 2.099337146055165578, {1.329172003287109302*10^7, 4.845867109329469935*10^10, 1.324685093932848952*10^14, 3.198214206065532067*10^17, 6.767464680066532436*10^20, 9.404817341944678994*10^23}, {0, 0, 0, 0, 0}}, {2.099386344629992045, 2.099361745342578812, {1.456903655735944369*10^7, 5.560912476535135315*10^10, 1.59115708532952436*10^14, 4.006007225467686872*10^17, 8.664514217087126223*10^20, 1.181233590219380849*10^24}, {0, 0, 0, 0, 0}}, {2.099410943917405279, 2.099386344629992045, {1.603972968545631119*10^7, 6.423847532391873099*10^10, 1.928516305924462259*10^14, 5.091442301598134551*10^17, 1.152328542669525243*10^21, 1.638448779128690201*10^24}, {0, 0, 0, 0, 0}}, {2.099435543204818513, 2.099410943917405279, {1.774490014824596816*10^7, 7.474977621978899839*10^10, 2.360123226607492608*10^14, 6.544361150510200888*10^17, 1.545419985465062916*10^21, 2.261452453761110372*10^24}, {0, 0, 0, 0, 0}}, {2.099455919524972813, 2.099435543204818513, {1.937201169453525646*10^7, 8.526323500316511685*10^10, 2.813842108342711716*10^14, 8.201464167861890923*10^17, 2.09510894208515252*10^21, 3.515019567526291219*10^24}, {0, 0, 0, 0, 0}}, {2.099476295845127114, 2.099455919524972813, {2.123363610791490664*10^7, 9.784448815186203415*10^10, 3.379871052954930125*10^14, 1.027295939643163031*10^18, 2.682407971436974504*10^21, 4.414821719567865054*10^24}, {0, 0, 0, 0, 0}}, {2.099496672165281414, 2.099476295845127114, {2.337709716648219138*10^7, 1.130278665431819271*10^11, 4.096475760000497173*10^14, 1.305643675056876854*10^18, 3.567442081302433514*10^21, 6.123648446510465063*10^24}, {0, 0, 0, 0, 0}}, {2.099517048485435714, 2.099496672165281414, {2.586229711215539017*10^7, 1.315225444009919189*10^11, 5.013277589118639372*10^14, 1.678228530273478491*10^18, 4.784396182218414352*10^21, 8.452104183886247081*10^24}, {0, 0, 0, 0, 0}}, {2.099533926796467893, 2.099517048485435714, {2.823373012875116744*10^7, 1.500210191030262574*10^11, 5.977048746029023409*10^14, 2.103174141319089686*10^18, 6.486153471818341873*10^21, 1.313726999819221292*10^25}, {0, 0, 0, 0, 0}}, {2.099550805107500072, 2.099533926796467893, {3.094695382032133451*10^7, 1.721577866249017055*10^11, 7.179384360342455639*10^14, 2.634386019252031174*10^18, 8.304346098748277745*10^21, 1.650025094983460443*10^25}, {0, 0, 0, 0, 0}}, {2.099567683418532251, 2.099550805107500072, {3.407094020615282994*10^7, 1.988730043723882142*10^11, 8.70156687073929222*10^14, 3.3481777818013836*10^18, 1.104428334934959754*10^22, 2.288693459291130304*10^25}, {0, 0, 0, 0, 0}}, {2.099584561729564431, 2.099567683418532251, {3.769299378194057328*10^7, 2.314144673469381754*10^11, 1.064899994603077551*10^15, 4.303630140042441047*10^18, 1.481179675158496366*10^22, 3.158946126432243915*10^25}, {0, 0, 0, 0, 0}}, {2.099598542535797333, 2.099584561729564431, {4.114923780127201338*10^7, 2.639626109235692243*10^11, 1.269620335489907218*10^15, 5.393355824343905708*10^18, 2.008019050588824757*10^22, 4.910011419024719604*10^25}, {0, 0, 0, 0, 0}}, {2.099612523342030235, 2.099598542535797333, {4.51036244899572485*10^7, 3.029123459101525687*10^11, 1.525015565918670219*10^15, 6.755589513043960356*10^18, 2.570905119150390076*10^22, 6.166914482546294174*10^25}, {0, 0, 0, 0, 0}}, {2.099626504148263137, 2.099612523342030235, {4.965667708697693518*10^7, 3.499178831834660709*10^11, 1.848351370100294124*10^15, 8.586028976238106386*10^18, 3.419149953453292155*10^22, 8.553916463272627011*10^25}, {0, 0, 0, 0, 0}}, {2.09964048495449604, 2.099626504148263137, {5.493563749085862727*10^7, 4.071747232513735078*10^11, 2.262017165603302492*10^15, 1.103618011578297107*10^19, 4.585517460200714161*10^22, 1.180645714941695643*10^26}, {0, 0, 0, 0, 0}}, {2.09965206567147614, 2.09964048495449604, {5.997293883367609772*10^7, 4.644433179134016977*10^11, 2.69687576896321587*10^15, 1.383066024309177799*10^19, 6.216535753762951907*10^22, 1.835100599740112644*10^26}, {0, 0, 0, 0, 0}}, {2.099663646388456241, 2.09965206567147614, {6.573625799196190017*10^7, 5.329755393963128637*10^11, 3.239375906906913605*10^15, 1.732395679180314063*10^19, 7.959149384050105998*10^22, 2.304863981524180233*10^26}, {0, 0, 0, 0, 0}}, {2.099675227105436341, 2.099663646388456241, {7.237210251609824239*10^7, 6.156819786405665253*10^11, 3.926192641893137717*10^15, 2.20179148902127917*10^19, 1.0585192362035619*10^23, 3.196998109538332518*10^26}, {0, 0, 0, 0, 0}}, {2.099686807822416442, 2.099675227105436341, {8.006592105497772369*10^7, 7.164256279492439754*10^11, 4.804884661882442049*10^15, 2.830105454552619475*10^19, 1.419609699201350932*10^23, 4.412624477665783931*10^26}, {0, 0, 0, 0, 0}}, {2.099696400474203028, 2.099686807822416442, {8.74075337053359535*10^7, 8.171899595719441256*10^11, 5.728593580838545334*10^15, 3.546718753332754427*10^19, 1.92454930604143805*10^23, 6.85862804764099792*10^26}, {0, 0, 0, 0, 0}}, {2.099705993125989615, 2.099696400474203028, {9.580728070362401898*10^7, 9.377726896290517461*10^11, 6.880950259455212672*10^15, 4.442535738757409493*10^19, 2.464037211152403276*10^23, 8.614353215788185813*10^26}, {0, 0, 0, 0, 0}}, {2.099715585777776201, 2.099705993125989615, {1.054786894148494364*10^8, 1.083295015029595465*10^12, 8.3398583701703391*10^15, 5.646249002949713172*10^19, 3.277022028195456872*10^23, 1.194867512893015204*10^27}, {0, 0, 0, 0, 0}}, {2.099725178429562788, 2.099715585777776201, {1.166920418908743942*10^8, 1.260553886853212682*10^12, 1.020634013899506612*10^16, 7.257490173541290147*10^19, 4.394905727629853795*10^23, 1.649203863207980496*10^27}, {0, 0, 0, 0, 0}}, {2.099733124307914782, 2.099725178429562788, {1.273920720528458067*10^8, 1.437849149363038569*10^12, 1.216844497010734916*10^16, 9.095165147892533138*10^19, 5.958125511047765509*10^23, 2.563389637980777286*10^27}, {0, 0, 0, 0, 0}}, {2.099741070186266775, 2.099733124307914782, {1.396342796583412581*10^8, 1.650014966693803049*10^12, 1.461623405118368728*10^16, 1.139238801349464256*10^20, 7.628301816182215914*10^23, 3.219586135993448012*10^27}, {0, 0, 0, 0, 0}}, {2.099749016064618769, 2.099741070186266775, {1.537298700720057637*10^8, 1.90606210618830422*10^12, 1.771518718716546944*10^16, 1.447917658552001503*10^20, 1.014518488990852001*10^24, 4.465777965141956551*10^27}, {0, 0, 0, 0, 0}}, {2.099756961942970763, 2.099749016064618769, {1.700727657519132903*10^8, 2.217949831646015057*10^12, 2.167989167198406919*10^16, 1.861102507377693203*10^20, 1.360599067859456084*10^24, 6.163845104930215971*10^27}, {0, 0, 0, 0, 0}}, {2.099763543749984586, 2.099756961942970763, {1.856675200535438253*10^8, 2.529901586750564567*10^12, 2.584771476847827937*10^16, 2.332353782713695739*10^20, 1.844549238709078553*10^24, 9.580584313970713868*10^27}, {0, 0, 0, 0, 0}}, {2.09977012555699841, 2.099763543749984586, {2.035099201975640083*10^8, 2.903208228710346856*10^12, 3.104720854911584768*10^16, 2.921450995372655318*10^20, 2.361611597593368142*10^24, 1.20330971061495352*10^28}, {0, 0, 0, 0, 0}}, {2.099776707364012234, 2.09977012555699841, {2.240535323066502598*10^8, 3.353724240291207454*10^12, 3.762987846921715317*10^16, 3.713023537450215953*10^20, 3.140802090522112524*10^24, 1.669069800471801078*10^28}, {0, 0, 0, 0, 0}}, {2.099783289171026057, 2.099776707364012234, {2.478724784950626063*10^8, 3.902491996083018988*10^12, 4.605154211019753883*10^16, 4.772590052767575334*10^20, 4.212217364515441975*10^24, 2.303716798697502617*10^28}, {0, 0, 0, 0, 0}}, {2.099788741077242105, 2.099783289171026057, {2.706010463623128001*10^8, 4.45137241240543615*10^12, 5.490466202706475171*10^16, 5.981061450223203581*10^20, 5.710456897213627714*10^24, 3.580711818743740146*10^28}, {0, 0, 0, 0, 0}}, {2.099794192983458153, 2.099788741077242105, {2.966054446826370622*10^8, 5.108207008422095458*10^12, 6.5949214753454219*10^16, 7.491735625734882897*10^20, 7.311206961804748429*10^24, 4.497330393917511668*10^28}, {0, 0, 0, 0, 0}}, {2.099799644889674202, 2.099794192983458153, {3.265467232035043914*10^8, 5.90089181276970051*10^12, 7.993185384741447766*10^16, 9.521635227162036385*10^20, 9.723467707570551701*10^24, 6.238093381751521416*10^28}, {0, 0, 0, 0, 0}}, {2.09980509679589025, 2.099799644889674202, {3.612616359496034714*10^8, 6.866450971410348273*10^12, 9.782080843267650762*10^16, 1.223877551759792527*10^21, 1.304041398845936131*10^25, 8.610065624293380684*10^28}, {0, 0, 0, 0, 0}}, {2.099809612771720564, 2.09980509679589025, {3.943873772911822275*10^8, 7.832208356845365386*10^12, 1.166262448521908469*10^17, 1.533776579002873533*10^21, 1.767874626313456623*10^25, 1.33827924289914403*10^29}, {0, 0, 0, 0, 0}}, {2.099814128747550878, 2.099809612771720564, {4.322874762988870666*10^8, 8.987911572370377978*10^12, 1.400866335081219815*10^17, 1.921172142076640219*10^21, 2.263443627677065391*10^25, 1.680862414949382276*10^29}, {0, 0, 0, 0, 0}}, {2.099818644723381193, 2.099814128747550878, {4.759253796387786669*10^8, 1.038264379687694456*10^13, 1.697879854491884108*10^17, 2.441717281288683414*10^21, 3.010244564915908314*10^25, 2.331466845156913591*10^29}, {0, 0, 0, 0, 0}}, {2.099823160699211507, 2.099818644723381193, {5.265206140990197804*10^8, 1.208154916980831152*10^13, 2.07786973507650598*10^17, 3.138497639114230735*10^21, 4.037123021370561371*10^25, 3.217983654215077504*10^29}, {0, 0, 0, 0, 0}}, {2.099826901416108399, 2.099823160699211507, {5.747997113926318618*10^8, 1.378080332375745291*10^13, 2.477327149194153306*10^17, 3.933199170929169072*10^21, 5.473083414693757348*10^25, 5.001774568847884331*10^29}, {0, 0, 0, 0, 0}}, {2.09983064213300529, 2.099826901416108399, {6.300371941864012847*10^8, 1.581426795914865588*10^13, 2.975663161041956448*10^17, 4.926631935573333992*10^21, 7.007293161007405232*10^25, 6.282167885122851813*10^29}, {0, 0, 0, 0, 0}}, {2.099834382849902181, 2.09983064213300529, {6.936372374036917057*10^8, 1.826830513424298915*10^13, 3.606567170741012812*10^17, 6.261511954924238854*10^21, 9.319280539409493119*10^25, 8.713780502474428832*10^29}, {0, 0, 0, 0, 0}}, {2.099838123566799073, 2.099834382849902181, {7.673772398300877868*10^8, 2.125753623446643947*10^13, 4.413726184142154077*10^17, 8.048327559225574012*10^21, 1.24983472919880516*10^26, 1.202710786129280859*10^30}, {0, 0, 0, 0, 0}}, {2.099841222113697842, 2.099838123566799073, {8.377415891564739486*10^8, 2.424738101652267796*10^13, 5.262237338687929838*10^17, 1.008625110554940264*10^22, 1.69438723834349904*10^26, 1.8693967618641616*10^30}, {0, 0, 0, 0, 0}}, {2.099844320660596612, 2.099841222113697842, {9.18247434398548895*10^8, 2.782527053667260215*10^13, 6.320782379561321244*10^17, 1.263379875924712309*10^22, 2.169356322124197249*10^26, 2.347939544358992785*10^30}, {0, 0, 0, 0, 0}}, {2.099847419207495381, 2.099844320660596612, {1.010941289686338621*10^9, 3.214315919713921823*10^13, 7.660922957074263976*10^17, 1.605694985927738512*10^22, 2.885114079071743974*10^26, 3.256746746609100921*10^30}, {0, 0, 0, 0, 0}}, {2.099850517754394151, 2.099847419207495381, {1.118413624105108571*10^9, 3.740272380431687848*10^13, 9.375457228055162714*10^17, 2.063903941977815546*10^22, 3.869307033237170228*10^26, 4.4950919277434017*10^30}, {0, 0, 0, 0, 0}}, {2.099853084372812252, 2.099850517754394151, {1.220966114388199155*10^9, 4.266336818745420792*10^13, 1.117783003152108943*10^18, 2.586506732345121257*10^22, 5.245577119027931123*10^26, 6.986808790718550341*10^30}, {0, 0, 0, 0, 0}}, {2.099855650991230353, 2.099853084372812252, {1.338299323475802038*10^9, 4.895867974353854735*10^13, 1.342634825389278199*10^18, 3.239796947682681693*10^22, 6.716012508079810889*10^26, 8.775346669835115485*10^30}, {0, 0, 0, 0, 0}}, {2.099858217609648453, 2.099855650991230353, {1.473395942494944808*10^9, 5.65560228779710599*10^13, 1.627302023539555494*10^18, 4.117625912314682244*10^22, 8.931894702653693153*10^26, 1.217198363772277689*10^31}, {0, 0, 0, 0, 0}}, {2.099860784228066554, 2.099858217609648453, {1.630031449485058268*10^9, 6.581024877396610984*10^13, 1.991496403764519923*10^18, 5.292651734168630613*10^22, 1.197881333112262132*10^27, 1.680025794145798197*10^31}, {0, 0, 0, 0, 0}}, {2.099862910234326788, 2.099860784228066554, {1.779496531787073692*10^9, 7.506637454052775863*10^13, 2.374349086978612778*10^18, 6.632808370459629819*10^22, 1.623954588796568838*10^27, 2.61129675991118758*10^31}, {0, 0, 0, 0, 0}}, {2.099865036240587022, 2.099862910234326788, {1.950503766272465249*10^9, 8.61430015197207651*10^13, 2.851970161278804702*10^18, 8.308098349096632214*10^22, 2.079180056523838873*10^27, 3.279756897983471369*10^31}, {0, 0, 0, 0, 0}}, {2.099867162246847255, 2.099865036240587022, {2.147400274824821205*10^9, 9.951055849960513077*10^13, 3.456648618601470004*10^18, 1.055919293592017334*10^23, 2.765185042469093376*10^27, 4.549238770723650313*10^31}, {0, 0, 0, 0, 0}}, {2.099869288253107489, 2.099867162246847255, {2.375688626267731279*10^9, 1.157934076192165936*10^14, 4.230255474001511516*10^18, 1.357241575434933293*10^23, 3.708466854104873713*10^27, 6.279041038727869476*10^31}, {0, 0, 0, 0, 0}}, {2.099871049287231926, 2.099869288253107489, {2.593526445376581911*10^9, 1.320795995693339708*10^14, 5.043495535982698959*10^18, 1.700909815030536513*10^23, 5.027527851484017645*10^27, 9.75963558190196055*10^31}, {0, 0, 0, 0, 0}}, {2.099872810321356362, 2.099871049287231926, {2.842760864802126656*10^9, 1.515689710073701975*10^14, 6.058038750891095658*10^18, 2.130519266776728408*10^23, 6.43683986885586534*10^27, 1.225798331815811423*10^32}, {0, 0, 0, 0, 0}}, {2.099874571355480799, 2.099872810321356362, {3.129727595439872769*10^9, 1.75089243350875756*10^14, 7.342472079070035699*10^18, 2.707787395632546989*10^23, 8.560611799853581255*10^27, 1.700262998003543805*10^32}, {0, 0, 0, 0, 0}}, {2.099876332389605236, 2.099874571355480799, {3.462446353824608032*10^9, 2.037389843914021936*10^14, 8.985736223740311803*10^18, 3.480494819114882217*10^23, 1.148087546498221352*10^28, 2.346770894871551838*10^32}, {0, 0, 0, 0, 0}}, {2.099877791106470515, 2.099876332389605236, {3.77993398841521554*10^9, 2.32394607156539071*10^14, 1.071318761012493412*10^19, 4.361793733776211952*10^23, 1.556449698205595351*10^28, 3.647631634544827506*10^32}, {0, 0, 0, 0, 0}}, {2.099879249823335794, 2.099877791106470515, {4.143180584462659701*10^9, 2.666862376104732569*10^14, 1.286823894744043032*10^19, 5.463479312862563403*10^23, 1.992752256616662782*10^28, 4.581380867349815172*10^32}, {0, 0, 0, 0, 0}}, {2.099880708540201073, 2.099879249823335794, {4.561420121051808404*10^9, 3.080702550447634963*10^14, 1.559657986076010535*10^19, 6.943819119714371212*10^23, 2.650241240979935461*10^28, 6.354676920537716683*10^32}, {0, 0, 0, 0, 0}}, {2.099882167257066352, 2.099880708540201073, {5.046340930552879034*10^9, 3.58479594077328411*10^14, 1.908713456601578623*10^19, 8.925341225028987514*10^23, 3.554312513050760695*10^28, 8.77097887844840554*10^32}, {0, 0, 0, 0, 0}}, {2.099883375555567529, 2.099882167257066352, {5.509063145318365333*10^9, 4.088992820293628706*10^14, 2.275651637809174004*10^19, 1.118533411201951574*10^24, 4.818542501470341011*10^28, 1.363290302100051042*10^33}, {0, 0, 0, 0, 0}}, {2.099884583854068706, 2.099883375555567529, {6.038476738529362721*10^9, 4.692355490516780011*10^14, 2.733418857398256662*10^19, 1.401048404811507849*10^24, 6.169271936290885864*10^28, 1.712276000556953745*10^33}, {0, 0, 0, 0, 0}}, {2.099885792152569883, 2.099884583854068706, {6.648039768981082965*10^9, 5.420509005910741281*10^14, 3.312961911593587354*10^19, 1.780665056793477875*10^24, 8.204762462564222775*10^28, 2.375039556258397526*10^33}, {0, 0, 0, 0, 0}}, {2.099887000451071061, 2.099885792152569883, {7.354787391595352451*10^9, 6.307463431816363692*10^14, 4.054411312155551031*10^19, 2.288804325873377293*10^24, 1.100363598460439012*10^29, 3.278124449721191254*10^33}, {0, 0, 0, 0, 0}}, {2.099888001320604218, 2.099887000451071061, {8.029181681984845233*10^9, 7.194599947397747653*10^14, 4.833846437728555144*10^19, 2.868354324655981197*10^24, 1.491750865110303115*10^29, 5.09525257471507157*10^33}, {0, 0, 0, 0, 0}}, {2.099889002190137375, 2.099888001320604218, {8.8007752928436056*10^9, 8.256219085940655843*10^14, 5.806216903806730698*10^19, 3.592832552640911855*10^24, 1.9099171056893467*10^29, 6.399575121336202105*10^33}, {0, 0, 0, 0, 0}}, {2.099890003059670532, 2.099889002190137375, {9.689182666101034662*10^9, 9.537408237817872235*10^14, 7.03725863332223014*10^19, 4.566317166063404992*10^24, 2.540075447658916901*10^29, 8.876632068306607518*10^33}, {0, 0, 0, 0, 0}}, {2.099891003929203689, 2.099890003059670532, {1.071923168087817827*10^10, 1.109800825505707333*10^15, 8.612215223355369046*10^19, 5.86938371317212766*10^24, 3.406566092179294027*10^29, 1.225188209497187316*10^34}, {0, 0, 0, 0, 0}}, {2.099891832979162315, 2.099891003929203689, {1.170212734569947056*10^10, 1.265892865984792129*10^15, 1.0267859541900034*10^20, 7.355575121206200863*10^24, 4.61824429865716021*10^29, 1.904333857557255953*10^34}, {0, 0, 0, 0, 0}}, {2.099892662029120941, 2.099891832979162315, {1.282668611780588122*10^10, 1.45268519685615775*10^15, 1.233332924535560471*10^20, 9.213418827531708889*10^24, 5.912826324117218724*10^29, 2.39182011075084863*10^34}, {0, 0, 0, 0, 0}}, {2.099893491079079567, 2.099892662029120941, {1.412149505704453697*10^10, 1.678110963289027303*10^15, 1.494825790135789183*10^20, 1.170981166914370156*10^25, 7.863705145830132354*10^29, 3.317611981121201941*10^34}, {0, 0, 0, 0, 0}}, {2.099894320129038193, 2.099893491079079567, {1.562273954502678594*10^10, 1.952699188193337478*10^15, 1.829371648369887625*10^20, 1.505138066313238196*10^25, 1.05462344960250056*10^30, 4.579100554879725043*10^34}, {0, 0, 0, 0, 0}}, {2.099895006855740456, 2.099894320129038193, {1.705526040365668525*10^10, 2.22734378542198229*10^15, 2.181056864955827947*10^20, 1.886255296223064118*10^25, 1.429741446826047287*10^30, 7.11738503208147593*10^34}, {0, 0, 0, 0, 0}}, {2.099895693582442719, 2.099895006855740456, {1.869424809630181536*10^10, 2.556005671832419556*10^15, 2.619795519070324151*10^20, 2.362678617696131003*10^25, 1.83052526388156727*10^30, 8.939348837468814145*10^34}, {0, 0, 0, 0, 0}}, {2.099896380309144983, 2.099895693582442719, {2.058136682088578251*10^10, 2.952643249486925642*10^15, 3.175248003906439637*10^20, 3.002850751256156856*10^25, 2.434489049410410761*10^30, 1.239946544191355061*10^35}, {0, 0, 0, 0, 0}}, {2.099897067035847246, 2.099896380309144983, {2.276935494607806341*10^10, 3.435782378175602234*10^15, 3.885876677545084068*10^20, 3.859758893539801467*10^25, 3.26496122589912004*10^30, 1.711423741180825038*10^35}, {0, 0, 0, 0, 0}}, {2.099897635871969479, 2.099897067035847246, {2.485718184760573202*10^10, 3.9190206942053712*10^15, 4.632912077476158381*10^20, 4.837091571877346225*10^25, 4.426272134093871558*10^30, 2.660099199174070624*10^35}, {0, 0, 0, 0, 0}}, {2.099898204708091713, 2.099897635871969479, {2.724592374644843067*10^10, 4.497302656183336992*10^15, 5.564862840499720887*10^20, 6.058826104603591162*10^25, 5.667040697642930851*10^30, 3.34105216684480562*10^35}, {0, 0, 0, 0, 0}}, {2.099898773544213947, 2.099898204708091713, {2.999630410972403966*10^10, 5.195188130842879845*10^15, 6.744732364671434752*10^20, 7.700476223745052778*10^25, 7.536824972140316733*10^30, 4.634259344339296855*10^35}, {0, 0, 0, 0, 0}}, {2.09989934238033618, 2.099898773544213947, {3.318518644988082956*10^10, 6.045273445867902073*10^15, 8.25422082303209738*10^20, 9.897921692120092808*10^25, 1.010784636979720081*10^31, 6.396389829734761324*10^35}, {0, 0, 0, 0, 0}}, {2.099899813564189803, 2.09989934238033618, {3.622808885823406032*10^10, 6.895533281435015586*10^15, 9.84104296519271529*10^20, 1.240418246749906768*10^26, 1.37030964923471129*10^31, 9.942033088713793068*10^35}, {0, 0, 0, 0, 0}}, {2.099900284748043427, 2.099899813564189803, {3.970955969836998523*10^10, 7.913022809049938325*10^15, 1.182065478319340335*10^21, 1.553718457125188261*10^26, 1.75443359904779732*10^31, 1.248707236339783554*10^36}, {0, 0, 0, 0, 0}}, {2.09990075593189705, 2.099900284748043427, {4.371810036099307207*10^10, 9.140955216817675301*10^15, 1.432688552672510319*10^21, 1.974701341632299341*10^26, 2.333291689038491094*10^31, 1.732039156937053382*10^36}, {0, 0, 0, 0, 0}}, {2.099901227115750673, 2.09990075593189705, {4.83657355388451198*10^10, 1.063668387945427009*10^16, 1.753327937269096365*10^21, 2.53821175169861246*10^26, 3.129242620849548496*10^31, 2.390629618443134482*10^36}, {0, 0, 0, 0, 0}}, {2.099901617411330082, 2.099901227115750673, {5.280061232867144389*10^10, 1.213271961171508341*10^16, 2.09039422771267116*10^21, 3.180914406937469772*10^26, 4.242279909353339696*10^31, 3.715802101191480516*10^36}, {0, 0, 0, 0, 0}}, {2.09990200770690949, 2.099901617411330082, {5.787468048839522068*10^10, 1.392299668566069483*10^16, 2.510895299813261873*10^21, 3.984337893723893124*10^26, 5.431471940440660658*10^31, 4.667002142482589829*10^36}, {0, 0, 0, 0, 0}}, {2.099902398002488898, 2.09990200770690949, {6.371692633135448978*10^10, 1.608354888626531091*10^16, 3.043258617208679823*10^21, 5.063901602100290112*10^26, 7.223532623147546688*10^31, 6.473439266658103563*10^36}, {0, 0, 0, 0, 0}}, {2.099902788298068307, 2.099902398002488898, {7.049062019719663524*10^10, 1.871528971590940349*10^16, 3.724347726469362034*10^21, 6.508961271715569578*10^26, 9.68768125461042884*10^31, 8.934899411525249344*10^36}, {0, 0, 0, 0, 0}}, {2.099903111591487923, 2.099902788298068307, {7.695422944307487242*10^10, 2.13475708358415905*10^16, 4.44033019945524189*10^21, 8.157100631787321264*10^26, 1.313348325271948025*10^32, 1.388768789238595151*10^37}, {0, 0, 0, 0, 0}}, {2.09990343488490754, 2.099903111591487923, {8.434942787263155937*10^10, 2.449757082552885011*10^16, 5.333541434252728332*10^21, 1.021739065950894026*10^27, 1.681504928755526531*10^32, 1.744276669823841827*10^37}, {0, 0, 0, 0, 0}}, {2.099903758178327156, 2.09990343488490754, {9.286420653206522934*10^10, 2.829907144722998138*10^16, 6.464365890219239985*10^21, 1.298581152252529521*10^27, 2.236300922113978403*10^32, 2.419426591550767938*10^37}, {0, 0, 0, 0, 0}}, {2.099904081471746773, 2.099903758178327156, {1.027365237067875444*10^11, 3.292963042990378081*10^16, 7.911107610164004651*10^21, 1.669150606062847854*10^27, 2.999165595708545453*10^32, 3.339389208516632315*10^37}, {0, 0, 0, 0, 0}}, {2.09990434926528757, 2.099904081471746773, {1.12156908187194871*10^11, 3.756114005559835938*10^16, 9.431968390837296965*10^21, 2.091797584113063436*10^27, 4.065935912642177674*10^32, 5.190477580442762056*10^37}, {0, 0, 0, 0, 0}}, {2.099904617058828368, 2.09990434926528757, {1.229350369176320832*10^11, 4.310357819516447401*10^16, 1.132929128226903075*10^22, 2.620136009381699233*10^27, 5.20569535556804394*10^32, 6.519176567738964238*10^37}, {0, 0, 0, 0, 0}}, {2.099904884852369165, 2.099904617058828368, {1.353448973665077867*10^11, 4.979233441810931282*10^16, 1.373134249133386748*10^22, 3.330066698539985224*10^27, 6.923263277327155693*10^32, 9.042527149427951187*10^37}, {0, 0, 0, 0, 0}}, {2.099905152645909963, 2.099904884852369165, {1.497333017332600611*10^11, 5.793982229020293378*10^16, 1.680445227354741817*10^22, 4.280350780122355037*10^27, 9.284981652539752892*10^32, 1.248085711133498674*10^38}, {0, 0, 0, 0, 0}}, {2.099905374467252872, 2.099905152645909963, {1.634630369915112839*10^11, 6.608898282266494313*10^16, 2.003500274295091993*10^22, 5.364181871002349238*10^27, 1.258754781773009008*10^33, 1.939923889549394779*10^38}, {0, 0, 0, 0, 0}}, {2.09990559628859578, 2.099905374467252872, {1.791716160156492879*10^11, 7.584092588027777138*10^16, 2.406521868080324319*10^22, 6.719046903882581164*10^27, 1.611607772985339114*10^33, 2.436520757088020227*10^38}, {0, 0, 0, 0, 0}}, {2.099905818109938689, 2.09990559628859578, {1.972583617221800013*10^11, 8.760982039382299275*10^16, 2.916755793472106513*10^22, 8.539585067503406617*10^27, 2.143341888077999039*10^33, 3.379614720843249765*10^38}, {0, 0, 0, 0, 0}}, {2.099906039931281598, 2.099905818109938689, {2.182287354001317722*10^11, 1.01945359337239574*10^17, 3.569533245268769834*10^22, 1.097648272979902201*10^28, 2.874495640096942441*10^33, 4.664679212477516298*10^38}, {0, 0, 0, 0, 0}}, {2.09990622367248769, 2.099906039931281598, {2.382391320727638*10^11, 1.162838413335640257*10^17, 4.255753606000269913*10^22, 1.37558468198413478*10^28, 3.896922220807118702*10^33, 7.250401603546123146*10^38}, {0, 0, 0, 0, 0}}, {2.099906407413693782, 2.09990622367248769, {2.611335937301699499*10^11, 1.334424258777940345*10^17, 5.111835645544841113*10^22, 1.723024726002794155*10^28, 4.989303899942804394*10^33, 9.106416029738640296*10^38}, {0, 0, 0, 0, 0}}, {2.099906591154899874, 2.099906407413693782, {2.874941133831000952*10^11, 1.54149844933643734*10^17, 6.195653749164743346*10^22, 2.189881456640606952*10^28, 6.635475591736352993*10^33, 1.263119863793136642*10^39}, {0, 0, 0, 0, 0}}, {2.099906774896105966, 2.099906591154899874, {3.180573753671118249*10^11, 1.793732855848531451*10^17, 7.582257000504337708*10^22, 2.814796714256194491*10^28, 8.899021553447647734*10^33, 1.743408482382383732*10^39}, {0, 0, 0, 0, 0}}, {2.099906927094403811, 2.099906774896105966, {3.472215192828099369*10^11, 2.046019045499510503*10^17, 9.039898315637016284*10^22, 3.527533672073372757*10^28, 1.206430594338849228*10^34, 2.70981370433468728*10^39}, {0, 0, 0, 0, 0}}, {2.099907079292701655, 2.099906927094403811, {3.805890424545120065*10^11, 2.347925057277982906*10^17, 1.085835288415629486*10^23, 4.418504958940506367*10^28, 1.544616117100304055*10^34, 3.403492979298050168*10^39}, {0, 0, 0, 0, 0}}, {2.099907231490999499, 2.099907079292701655, {4.190081703422681674*10^11, 2.712272960524993465*10^17, 1.31605551158721418*10^23, 5.615707035211727215*10^28, 2.054246995004280121*10^34, 4.720868862560237477*10^39}, {0, 0, 0, 0, 0}}, {2.099907383689297344, 2.099907231490999499, {4.635525832100989326*10^11, 3.15608045237882931*10^17, 1.610592121473714088*10^23, 7.218232595652441955*10^28, 2.755007991802858992*10^34, 6.515931745769380044*10^39}, {0, 0, 0, 0, 0}}, {2.099907509759667509, 2.099907383689297344, {5.060578520586072612*10^11, 3.599979056881869863*10^17, 1.92021834727041053*10^23, 9.04596712261995913*10^28, 3.734934126180430337*10^34, 1.012783941320717545*10^40}, {0, 0, 0, 0, 0}}, {2.099907635830037674, 2.099907509759667509, {5.546893341731419094*10^11, 4.131183945682715184*10^17, 2.30648705342471518*10^23, 1.133076373051721597*10^29, 4.781907450521461001*10^34, 1.272044284194470913*10^40}, {0, 0, 0, 0, 0}}, {2.09990776190040784, 2.099907635830037674, {6.10683275381037348*10^11, 4.772255603345353463*10^17, 2.795511466101956824*10^23, 1.440085508267522687*10^29, 6.359650726073491202*10^34, 1.764409178916437475*10^40}, {0, 0, 0, 0, 0}}, {2.099907887970778005, 2.09990776190040784, {6.756045105154854653*10^11, 5.5531367390683643*10^17, 3.421154125453964999*10^23, 1.851035335555179303*10^29, 8.52910512611923074*10^34, 2.435308015565693503*10^40}, {0, 0, 0, 0, 0}}, {2.099907992398609714, 2.099907887970778005, {7.375537960870557129*10^11, 6.334178187878292355*10^17, 4.078849531764343091*10^23, 2.319737493403095959*10^29, 1.156281429894309555*10^35, 3.785246602583797366*10^40}, {0, 0, 0, 0, 0}}, {2.099908096826441423, 2.099907992398609714, {8.084317285151360467*10^11, 7.268835408592931248*10^17, 4.899345770367666184*10^23, 2.905648130076258952*10^29, 1.480409184663636089*10^35, 4.754223589687332472*10^40}, {0, 0, 0, 0, 0}}, {2.099908201254273132, 2.099908096826441423, {8.900400737423707636*10^11, 8.396803668038886089*10^17, 5.938111491726867193*10^23, 3.692938855460793805*10^29, 1.968855617459682162*10^35, 6.594421156946393676*10^40}, {0, 0, 0, 0, 0}}, {2.09990830568210484, 2.099908201254273132, {9.846594996148853402*10^11, 9.770767288123243433*10^17, 7.267076123158852301*10^23, 4.746773906312025047*10^29, 2.64048723157336179*10^35, 9.101883448253973471*10^40}, {0, 0, 0, 0, 0}}, {2.099908392182779195, 2.09990830568210484, {1.074947458891317533*10^12, 1.114501297975373024*10^18, 8.664125892986074508*10^23, 5.948708375076264695*10^29, 3.579679587242167286*10^35, 1.414723442759675865*10^41}, {0, 0, 0, 0, 0}}, {2.099908478683453549, 2.099908392182779195, {1.17824847064020798*10^12, 1.278954626371133376*10^18, 1.040699055387121609*10^24, 7.451210930359110979*10^29, 4.583132100971803063*10^35, 1.776875398252987063*10^41}, {0, 0, 0, 0, 0}}, {2.099908565184127904, 2.099908478683453549, {1.297188517849966685*10^12, 1.477421112778657696*10^18, 1.261349435183809278*10^24, 9.470130288705832708*10^29, 6.09529140729295864*10^35, 2.464643174316319198*10^41}, {0, 0, 0, 0, 0}}, {2.099908651684802258, 2.099908565184127904, {1.435091558879663035*10^12, 1.71917058564400189*10^18, 1.543642684404751936*10^24, 1.21725728757547505*10^30, 8.174565463790306032*10^35, 3.401798941902745569*10^41}, {0, 0, 0, 0, 0}}, {2.099908723335879766, 2.099908651684802258, {1.56668170580532451*10^12, 1.960969689115719928*10^18, 1.840398301161053547*10^24, 1.525479992125567946*10^30, 1.108216876620434659*10^36, 5.28748224257651907*10^41}, {0, 0, 0, 0, 0}}, {2.099908794986957274, 2.099908723335879766, {1.717237720389587541*10^12, 2.250326007357877265*10^18, 2.210610507292902318*10^24, 1.910780034031223229*10^30, 1.418871219697864485*10^36, 6.641013240868537734*10^41}, {0, 0, 0, 0, 0}}, {2.099908866638034782, 2.099908794986957274, {1.89058684039525442*10^12, 2.599528619196399678*10^18, 2.679307048806771736*10^24, 2.428509412021313104*10^30, 1.887013806921624436*10^36, 9.21152263728963518*10^41}, {0, 0, 0, 0, 0}}, {2.09990893828911229, 2.099908866638034782, {2.091573567485115908*10^12, 3.024887826502659563*10^18, 3.278942860557831471*10^24, 3.121520707327565611*10^30, 2.530726894747001333*10^36, 1.271411143300137926*10^42}, {0, 0, 0, 0, 0}}, {2.09990899763982772, 2.09990893828911229, {2.283359569812413336*10^12, 3.450334359068143174*10^18, 3.909299043840408698*10^24, 3.911923496073992961*10^30, 3.430878702114427592*10^36, 1.976179062320845746*10^42}, {0, 0, 0, 0, 0}}, {2.099909056990543149, 2.09990899763982772, {2.502787367698814414*10^12, 3.959458009671083309*10^18, 4.695688719670988132*10^24, 4.899982529787527143*10^30, 4.392619487576796126*10^36, 2.482056812129223091*10^42}, {0, 0, 0, 0, 0}}, {2.099909116341258578, 2.099909056990543149, {2.755434967154894448*10^12, 4.573881463837792816*10^18, 5.691274805810820908*10^24, 6.227641842804808264*10^30, 5.841921033097942911*10^36, 3.442776227468705892*10^42}, {0, 0, 0, 0, 0}}, {2.099909175691974008, 2.099909116341258578, {3.048362985019232763*10^12, 5.322302765839897*10^18, 6.964996751789472226*10^24, 8.004792105769232438*10^30, 7.834763381815000139*10^36, 4.751857246458825811*10^42}, {0, 0, 0, 0, 0}}, {2.099909224853934225, 2.099909175691974008, {3.327881410585434647*10^12, 6.070877717000383784*10^18, 8.303973658598534843*10^24, 1.003169200391274411*10^31, 1.062150280955617386*10^37, 7.385904116912724206*10^42}, {0, 0, 0, 0, 0}}, {2.099909274015894442, 2.099909224853934225, {3.647686359050828625*10^12, 6.966682906871290849*10^18, 9.974390549263316396*10^24, 1.256545932268698896*10^31, 1.359891277993992976*10^37, 9.276605534716411127*10^42}, {0, 0, 0, 0, 0}}, {2.09990932317785466, 2.099909274015894442, {4.015907492846220649*10^12, 8.047763540955205099*10^18, 1.208917392640049547*10^25, 1.597009372509329687*10^31, 1.808574014231776063*10^37, 1.286726268732301969*10^43}, {0, 0, 0, 0, 0}}, {2.099909372339814877, 2.09990932317785466, {4.442835304907991322*10^12, 9.364613948021217745*10^18, 1.479476215824739549*10^25, 2.052739759379690118*10^31, 2.425529099028403422*10^37, 1.775990985269467655*10^43}, {0, 0, 0, 0, 0}}, {2.099909413062126562, 2.099909372339814877, {4.850219312514935311*10^12, 1.068173470142323783*10^19, 1.763896231764243645*10^25, 2.572515657894654688*10^31, 3.288263203938860269*10^37, 2.760457322129391689*10^43}, {0, 0, 0, 0, 0}}, {2.099909453784438246, 2.099909413062126562, {5.316318895375913788*10^12, 1.22579076748243356*10^19, 2.118719377893561338*10^25, 3.222272059752503635*10^31, 4.210026143157375697*10^37, 3.467100745889329264*10^43}, {0, 0, 0, 0, 0}}, {2.09990949450674993, 2.099909453784438246, {5.852982626460113168*10^12, 1.416007356622304364*10^19, 2.567933041531244432*10^25, 4.095352623448108606*10^31, 5.599082812695549902*10^37, 4.809097023023715638*10^43}, {0, 0, 0, 0, 0}}, {2.099909535229061615, 2.09990949450674993, {6.475208380215995009*10^12, 1.647707735800592072*10^19, 3.142643063873218654*10^25, 5.264022430640255044*10^31, 7.509086265309152614*10^37, 6.637707776488509106*10^43}, {0, 0, 0, 0, 0}}, {2.099909568960561775, 2.099909535229061615, {7.068950024680814602*10^12, 1.879455682529625655*10^19, 3.746796466785959778*10^25, 6.596929817554091657*10^31, 1.017998591371647759*10^38, 1.031711826565518804*10^44}, {0, 0, 0, 0, 0}}, {2.099909602692061935, 2.099909568960561775, {7.748266658728101149*10^12, 2.156783975574908639*10^19, 4.500497328724690559*10^25, 8.263157725014394494*10^31, 1.30336302709535833*10^38, 1.295817477326148464*10^44}, {0, 0, 0, 0, 0}}, {2.099909636423562094, 2.099909602692061935, {8.530426979871561516*10^12, 2.491470858710747965*10^19, 5.454698679938064158*10^25, 1.050207556642571517*10^32, 1.733394823586388291*10^38, 1.797384163116556849*10^44}, {0, 0, 0, 0, 0}}, {2.099909670155062254, 2.099909636423562094, {9.437289633694303328*10^12, 2.899148643699053168*10^19, 6.675474280203167884*10^25, 1.349899909312273712*10^32, 2.324704187735393013*10^38, 2.48082140571059747*10^44}, {0, 0, 0, 0, 0}}, {2.099909698095865612, 2.099909670155062254, {1.030263813483605562*10^13, 3.306910123991590839*10^19, 7.958792309158906939*10^25, 1.691709159638318056*10^32, 3.151575977231027799*10^38, 3.855988949881844832*10^44}, {0, 0, 0, 0, 0}}, {2.099909726036668969, 2.099909698095865612, {1.129270786727556679*10^13, 3.794870414018962805*10^19, 9.559772953978932411*10^25, 2.118994744152944986*10^32, 4.035022877851157196*10^38, 4.843075115526094723*10^44}, {0, 0, 0, 0, 0}}, {2.099909753977472326, 2.099909726036668969, {1.243266708668340878*10^13, 4.38375338290037725*10^19, 1.158664856431611516*10^26, 2.693140282265927655*10^32, 5.366338943269823359*10^38, 6.717664073641440644*10^44}, {0, 0, 0, 0, 0}}, {2.099909781918275683, 2.099909753977472326, {1.375437366654490949*10^13, 5.101064148477864362*10^19, 1.417977032706109802*10^26, 3.461667933925653069*10^32, 7.196946964694259257*10^38, 9.271988243941013062*10^44}, {0, 0, 0, 0, 0}}, {2.099909805062472904, 2.099909781918275683, {1.50155754626615376*10^13, 5.818522176292743086*10^19, 1.690574216716458384*10^26, 4.338199677657410141*10^32, 9.756822086440020482*10^38, 1.441163161917764172*10^45}, {0, 0, 0, 0, 0}}, {2.099909828206670125, 2.099909805062472904, {1.645855216301509124*10^13, 6.677090344830512472*10^19, 2.03064799857405064*10^26, 5.433925958057332088*10^32, 1.249184554595381006*10^39, 1.810083363208414315*10^45}, {0, 0, 0, 0, 0}}, {2.099909851350867346, 2.099909828206670125, {1.811998523087148686*10^13, 7.713232388371059407*10^19, 2.461188652761513872*10^26, 6.906258228754900805*10^32, 1.661340697583942992*10^39, 2.510704808261205046*10^45}, {0, 0, 0, 0, 0}}, {2.099909874495064566, 2.099909851350867346, {2.004630591006732647*10^13, 8.97534367664769161*10^19, 3.012009006228710912*10^26, 8.877061774805181498*10^32, 2.228070387874951723*10^39, 3.46537504867885503*10^45}, {0, 0, 0, 0, 0}}, {2.099909893666090472, 2.099909874495064566, {2.188444391854495092*10^13, 1.023771407344613291*10^20, 3.591048831538714968*10^26, 1.112482978294583952*10^33, 3.020570594337416844*10^39, 5.386299821560485426*10^45}, {0, 0, 0, 0, 0}}, {2.099909912837116378, 2.099909893666090472, {2.398750968203694449*10^13, 1.174836835227063109*10^20, 4.31341969517851126*10^26, 1.393469776134458152*10^33, 3.867294185629668579*10^39, 6.765126915459722702*10^45}, {0, 0, 0, 0, 0}}, {2.099909932008142284, 2.099909912837116378, {2.640896458320488064*10^13, 1.357146460589749172*10^20, 5.227956600959964539*10^26, 1.771032984665535157*10^33, 5.143269820685002648*10^39, 9.383676476112700433*10^45}, {0, 0, 0, 0, 0}}, {2.09990995117916819, 2.099909932008142284, {2.921647981815690019*10^13, 1.579215468952235352*10^20, 6.39798674051096391*10^26, 2.276423598618888712*10^33, 6.897782737150014217*10^39, 1.295172503681032648*10^46}, {0, 0, 0, 0, 0}}, {2.099909967059098298, 2.09990995117916819, {3.1895473258075642*10^13, 1.801330067567372268*10^20, 7.627959531727759895*10^26, 2.852838663395681338*10^33, 9.351248423455260669*10^39, 2.013111806794525654*10^46}, {0, 0, 0, 0, 0}}, {2.099909982939028407, 2.099909967059098298, {3.496058553916002983*10^13, 2.067130318934418576*10^20, 9.16239027139071025*10^26, 3.57339800355765751*10^33, 1.197258184404102625*10^40, 2.528443888968489443*10^46}, {0, 0, 0, 0, 0}}, {2.099909998818958515, 2.099909982939028407, {3.848973393028693448*10^13, 2.387904866276523127*10^20, 1.110501228374120472*10^27, 4.541616789991968469*10^33, 1.592281732870316357*10^40, 3.507118157364450177*10^46}, {0, 0, 0, 0, 0}}, {2.099910014698888624, 2.099909998818958515, {4.258154578675233842*10^13, 2.778636214083716566*10^20, 1.359034260757666814*10^27, 5.837634717217875788*10^33, 2.135453482432580989*10^40, 4.84066454778353574*10^46}, {0, 0, 0, 0, 0}}, {2.099910027852706343, 2.099910014698888624, {4.648604360901953948*10^13, 3.169447778130867732*10^20, 1.620300066839947184*10^27, 7.315786936211702156*10^33, 2.895010871161611451*10^40, 7.523939032198090324*10^46}, {0, 0, 0, 0, 0}}, {2.099910041006524062, 2.099910027852706343, {5.095329016818297692*10^13, 3.63712443067216459*10^20, 1.946237589147955413*10^27, 9.163581091261319885*10^33, 3.706537675486416773*10^40, 9.449975705633001769*10^46}, {0, 0, 0, 0, 0}}, {2.099910054160341781, 2.099910041006524062, {5.609684595383308708*10^13, 4.201528586611965766*10^20, 2.358881437527581671*10^27, 1.164647030615988704*10^34, 4.929473282999649743*10^40, 1.310773852980405543*10^47}, {0, 0, 0, 0, 0}}, {2.0999100673141595, 2.099910054160341781, {6.206045536199228164*10^13, 4.889022025183151766*10^20, 2.886805172974788336*10^27, 1.496996389966356081*10^34, 6.611054232069860141*10^40, 1.809182421459072195*10^47}, {0, 0, 0, 0, 0}}, {2.099910078209857366, 2.0999100673141595, {6.775106401258746373*10^13, 5.576656604563615887*10^20, 3.441775347236080025*10^27, 1.876052059401780039*10^34, 8.962533733059394647*10^40, 2.812047416798446949*10^47}, {0, 0, 0, 0, 0}}, {2.099910089105555231, 2.099910078209857366, {7.426185056468642966*10^13, 6.399535628218857501*10^20, 4.134118544633303146*10^27, 2.349898285400055406*10^34, 1.147490300652077925*10^41, 3.531897275896759302*10^47}, {0, 0, 0, 0, 0}}, {2.099910100001253096, 2.099910089105555231, {8.175832370438543856*10^13, 7.392607098139398008*10^20, 5.010639785116528392*10^27, 2.986607564318567869*10^34, 1.526093425941840741*10^41, 4.898974076619519833*10^47}, {0, 0, 0, 0, 0}}, {2.099910110896950962, 2.099910100001253096, {9.044998363906448074*10^13, 8.602254674999963609*10^20, 6.132033862095504036*10^27, 3.838880471507662999*10^34, 2.046686496283744676*10^41, 6.761759675363669647*10^47}, {0, 0, 0, 0, 0}}, {2.09991011992218109, 2.099910110896950962, {9.874375873852794567*10^13, 9.812150589704022511*10^20, 7.310878881801660892*10^27, 4.810926507665850602*10^34, 2.774670441358169883*10^41, 1.050993454423631706*10^48}, {0, 0, 0, 0, 0}}, {2.099910128947411217, 2.09991011992218109, {1.082329017633381752*10^14, 1.126000966903238162*10^21, 8.781526076969460095*10^27, 6.026052366134531798*10^34, 3.552463526268562211*10^41, 1.320034966867768582*10^48}, {0, 0, 0, 0, 0}}, {2.099910137972641345, 2.099910128947411217, {1.191586332759646185*10^14, 1.300732306846692156*10^21, 1.064339676287739291*10^28, 7.658822380311371565*10^34, 4.724563885425361528*10^41, 1.830975415692061451*10^48}, {0, 0, 0, 0, 0}}, {2.099910146997871473, 2.099910137972641345, {1.318262892624127243*10^14, 1.513570303271170143*10^21, 1.302541634534282883*10^28, 9.844381304656417019*10^34, 6.336244518688055218*10^41, 2.527185394079807701*10^48}, {0, 0, 0, 0, 0}}, {2.099910154473737623, 2.099910146997871473, {1.439140481690606993*10^14, 1.726451994842941436*10^21, 1.55294708782477207*10^28, 1.233708507510302819*10^35, 8.589977217880727269*10^41, 3.928053398540902738*10^48}, {0, 0, 0, 0, 0}}, {2.099910161949603774, 2.099910154473737623, {1.57743995537904423*10^14, 1.981203404628765735*10^21, 1.865335969637389812*10^28, 1.545313996993433091*10^35, 1.099791178914293286*10^42, 4.933587184557148971*10^48}, {0, 0, 0, 0, 0}}, {2.099910169425469924, 2.099910161949603774, {1.736676981726597738*10^14, 2.288643927120843968*10^21, 2.260826950452884895*10^28, 1.964019677507972815*10^35, 1.462656448682981405*10^42, 6.843210273082230154*10^48}, {0, 0, 0, 0, 0}}, {2.099910176901336075, 2.099910169425469924, {1.921301678731519312*10^14, 2.663133270864699253*10^21, 2.766805839385000516*10^28, 2.524481915776035088*10^35, 1.961609395161545879*10^42, 9.445272122462599371*10^48}, {0, 0, 0, 0, 0}}, {2.099910183093818029, 2.099910176901336075, {2.09747466827243414*10^14, 3.037699496402734743*10^21, 3.298706894989791028*10^28, 3.163708028127322636*10^35, 2.659332348226259029*10^42, 1.468097012102748802*10^49}, {0, 0, 0, 0, 0}}, {2.099910189286299984, 2.099910183093818029, {2.299039175968125553*10^14, 3.485935666030309727*10^21, 3.962270622583907344*10^28, 3.96278559198053679*10^35, 3.404793964170983554*10^42, 1.843911950710013435*10^49}, {0, 0, 0, 0, 0}}, {2.099910195478781938, 2.099910189286299984, {2.5311191106682238*10^14, 4.026878549549605314*10^21, 4.802356441058076812*10^28, 5.036509664403141938*10^35, 4.528172205425309637*10^42, 2.557627286542192479*10^49}, {0, 0, 0, 0, 0}}, {2.099910201671263893, 2.099910195478781938, {2.800200294911186989*10^14, 4.685794114127692326*10^21, 5.87713616969489426*10^28, 6.473752637015176421*10^35, 6.072858154127468753*10^42, 3.530139327188202993*10^49}, {0, 0, 0, 0, 0}}, {2.099910206800680603, 2.099910201671263893, {3.056963541791577284*10^14, 5.344844952543770079*10^21, 7.006978708009265851*10^28, 8.112976790146417678*10^35, 8.232907211443575102*10^42, 5.486964198973639234*10^49}, {0, 0, 0, 0, 0}}, {2.099910211930097314, 2.099910206800680603, {3.350733645748253976*10^14, 6.133518365308441117*10^21, 8.416493726673438865*10^28, 1.016212218265127534*10^36, 1.054074824449792265*10^43, 6.891560146365202469*10^49}, {0, 0, 0, 0, 0}}, {2.099910217059514024, 2.099910211930097314, {3.688978445502570256*10^14, 7.085309628406184186*10^21, 1.020096977451192651*10^29, 1.291556794981401582*10^36, 1.401856433234801764*10^43, 9.559047692273746851*10^49}, {0, 0, 0, 0, 0}}, {2.099910222188930734, 2.099910217059514024, {4.081150700288527288*10^14, 8.244674316604670811*10^21, 1.248397305855524108*10^29, 1.660121743925324502*10^36, 1.880068797137626233*10^43, 1.319377939331600281*10^50}, {0, 0, 0, 0, 0}}, {2.099910226437778932, 2.099910222188930734, {4.455370182630058667*10^14, 9.404277019686169432*10^21, 1.488393851817102654*10^29, 2.080482516473383622*10^36, 2.548788653567378735*10^43, 2.050734786095282021*10^50}, {0, 0, 0, 0, 0}}, {2.099910230686627129, 2.099910226437778932, {4.883525292700375753*10^14, 1.079195118377401447*10^22, 1.7877972859142606*10^29, 2.605963024194827374*10^36, 3.263262761949217863*10^43, 2.575697892336023747*10^50}, {0, 0, 0, 0, 0}}, {2.099910234935475326, 2.099910230686627129, {5.376500028791557741*10^14, 1.246663188687434504*10^22, 2.166848413225635027*10^29, 3.312053516848187287*10^36, 4.339944176697248771*10^43, 3.572662571437376026*10^50}, {0, 0, 0, 0, 0}}, {2.099910239184323523, 2.099910234935475326, {5.948071310732379641*10^14, 1.450653889848404611*10^22, 2.651794663706501541*10^29, 4.257197269008370252*10^36, 5.82042029018603489*10^43, 4.93113156579407898*10^50}, {0, 0, 0, 0, 0}}, {2.099910242703770669, 2.099910239184323523, {6.493477332292771269*10^14, 1.654686469827458056*10^22, 3.161585542702963488*10^29, 5.335165640567959889*10^36, 7.890679967246779275*10^43, 7.664553677401656137*10^50}, {0, 0, 0, 0, 0}}, {2.099910246223217815, 2.099910242703770669, {7.117491810996695357*10^14, 1.898848318637170803*10^22, 3.797566111637419787*10^29, 6.682701862278617175*10^36, 1.010258817165367746*10^44, 9.626585985878981158*10^50}, {0, 0, 0, 0, 0}}, {2.099910249742664961, 2.099910246223217815, {7.835977625414795812*10^14, 2.193509087870200491*10^22, 4.602731063501353364*10^29, 8.493392269771914747*10^36, 1.343583765805896413*10^44, 1.335270861726767682*10^51}, {0, 0, 0, 0, 0}}, {2.099910253262112107, 2.099910249742664961, {8.669013941351462472*10^14, 2.552431578642313764*10^22, 5.632834118977227455*10^29, 1.09171081299128349*10^37, 1.801917696096376845*10^44, 1.842994171290253031*10^51}, {0, 0, 0, 0, 0}}, {2.0999102561773747, 2.099910253262112107, {9.463915709942042201*10^14, 2.91142775536977563*10^22, 6.715711121505383129*10^29, 1.36814379293828305*10^37, 2.442840062802534677*10^44, 2.864601677022568135*10^51}, {0, 0, 0, 0, 0}}, {2.099910259092637294, 2.0999102561773747, {1.037338534016128493*10^15, 3.341031548226750376*10^22, 8.066635119026870836*10^29, 1.713704444977691743*10^37, 3.127614758949767794*10^44, 3.59790478608776138*10^51}, {0, 0, 0, 0, 0}}, {2.099910262007899887, 2.099910259092637294, {1.142054217747345072*10^15, 3.859488402505073656*10^22, 9.776933685630280825*10^29, 2.178035828263688988*10^37, 4.159540450842717649*10^44, 4.990530839466387308*10^51}, {0, 0, 0, 0, 0}}, {2.099910264923162481, 2.099910262007899887, {1.263465059333536537*10^15, 4.491014024255847112*10^22, 1.196503660187831371*10^30, 2.79957075956618925*10^37, 5.578475817253221904*10^44, 6.888129976030950059*10^51}, {0, 0, 0, 0, 0}}, {2.099910267337961066, 2.099910264923162481, {1.379317982977592464*10^15, 5.122669296752859484*10^22, 1.426523978502023872*10^30, 3.508452341052862302*10^37, 7.562678498181607626*10^44, 1.070635435980384276*10^52}, {0, 0, 0, 0, 0}}, {2.099910269752759651, 2.099910267337961066, {1.511868594625113975*10^15, 5.878558964761307495*10^22, 1.713481746745972708*10^30, 4.394604136559464132*10^37, 9.682641630238260866*10^44, 1.344705056262167284*10^52}, {0, 0, 0, 0, 0}}, {2.099910272167558236, 2.099910269752759651, {1.664486422273907205*10^15, 6.790785965484317671*10^22, 2.076776395892608909*10^30, 5.585330240878812787*10^37, 1.287733389054392984*10^45, 1.865194454064327332*10^52}, {0, 0, 0, 0, 0}}, {2.099910274582356821, 2.099910272167558236, {1.841436600467439629*10^15, 7.901957934869024298*10^22, 2.541564297126577605*10^30, 7.179187331069051132*10^37, 1.72701519670378632*10^45, 2.57441587747827889*10^52}, {0, 0, 0, 0, 0}}, {2.099910276582606205, 2.099910274582356821, {2.010286393576758515*10^15, 9.013358025283259152*10^22, 3.030164080055164716*10^30, 8.997035174938502334*10^37, 2.341295565672259594*10^45, 4.001464657272884722*10^52}, {0, 0, 0, 0, 0}}, {2.099910278582855589, 2.099910276582606205, {2.203472224794630825*10^15, 1.034334905353316003*10^23, 3.639708072956479221*10^30, 1.126947273414871031*10^38, 2.997605401091772346*10^45, 5.025790830621606136*10^52}, {0, 0, 0, 0, 0}}, {2.099910280583104972, 2.099910278582855589, {2.425905011233978253*10^15, 1.194841627172320432*10^23, 4.411403756246948684*10^30, 1.43229571776807473*10^38, 3.986635785569913266*10^45, 6.971102801249134468*10^52}, {0, 0, 0, 0, 0}}, {2.099910282583354356, 2.099910280583104972, {2.683800971377646273*10^15, 1.390352799327660363*10^23, 5.398687268047635706*10^30, 1.841022612429640165*10^38, 5.346588543811960784*10^45, 9.621794497599408557*10^52}, {0, 0, 0, 0, 0}}, {2.099910284240220325, 2.099910282583354356, {2.929891028808174366*10^15, 1.585904109473437878*10^23, 6.436551008205475897*10^30, 2.307189440537988595*10^38, 7.248311464191406847*10^45, 1.495534228113830902*10^53}, {0, 0, 0, 0, 0}}, {2.099910285897086294, 2.099910284240220325, {3.211449634381299858*10^15, 1.819916586437932451*10^23, 7.731319508656832106*10^30, 2.889930736859270227*10^38, 9.280151516289786688*10^45, 1.8783727595530432*10^53}, {0, 0, 0, 0, 0}}, {2.099910287553952264, 2.099910285897086294, {3.535634202104471637*10^15, 2.102328833923100221*10^23, 9.370524019397622248*10^30, 3.672962805533199526*10^38, 1.234204612684407516*10^46, 2.605426697451804909*10^53}, {0, 0, 0, 0, 0}}, {2.099910289210818233, 2.099910287553952264, {3.911504556898255498*10^15, 2.446331557990396129*10^23, 1.146767140659447503*10^31, 4.721097393307006961*10^38, 1.655226260393138187*10^46, 3.596113983134556044*10^53}, {0, 0, 0, 0, 0}}, {2.099910290583249521, 2.099910289210818233, {4.270168403924418705*10^15, 2.790404905019520931*10^23, 1.367225925286425617*10^31, 5.916530291398388822*10^38, 2.24397209187233098*10^46, 5.589509889572525419*10^53}, {0, 0, 0, 0, 0}}, {2.09991029195568081, 2.099910290583249521, {4.680525870993918535*10^15, 3.202150835720400716*10^23, 1.642255371771750897*10^31, 7.410905426423981567*10^38, 2.873000299970388826*10^46, 7.020356283698429665*10^53}, {0, 0, 0, 0, 0}}, {2.099910293328112098, 2.09991029195568081, {5.15300852803474871*10^15, 3.699056364820673264*10^23, 1.990448511401058389*10^31, 9.418903934065107759*10^38, 3.820918458327940825*10^46, 9.737696415233475176*10^53}, {0, 0, 0, 0, 0}}, {2.099910294700543387, 2.099910293328112098, {5.700820612931696288*10^15, 4.304330594733709028*10^23, 2.435916009952213358*10^31, 1.210672831860285951*10^39, 5.124340410047088992*10^46, 1.344035749560267142*10^54}, {0, 0, 0, 0, 0}}, {2.099910295837368983, 2.099910294700543387, {6.223555080576421276*10^15, 4.909729086043078791*10^23, 2.904205572817302591*10^31, 1.517228281041023176*10^39, 6.947012106168588102*10^46, 2.089060899999029769*10^54}, {0, 0, 0, 0, 0}}, {2.099910296974194578, 2.099910295837368983, {6.821630392239949778*10^15, 5.634197770994676641*10^23, 3.488411910920645807*10^31, 1.900444136563914948*10^39, 8.894392197305429044*10^46, 2.623835024193640046*10^54}, {0, 0, 0, 0, 0}}, {2.099910298111020173, 2.099910296974194578, {7.510250034970728892*10^15, 6.508505125045918376*10^23, 4.22802958333739504*10^31, 2.415372984052527094*10^39, 1.18290093191574202*10^47, 3.639431942874732827*10^54}, {0, 0, 0, 0, 0}}, {2.099910299247845769, 2.099910298111020173, {8.308658519523295082*10^15, 7.573487660838713754*10^23, 5.17427348339379202*10^31, 3.104635604176548817*10^39, 1.586421461909680832*10^47, 5.023289318881649131*10^54}, {0, 0, 0, 0, 0}}, {2.099910300189512172, 2.099910299247845769, {9.07051764173330961*10^15, 8.638688835077428507*10^23, 6.168995082079158647*10^31, 3.8907629022661828*10^39, 2.150694181004019691*10^47, 7.807796265010884665*10^54}, {0, 0, 0, 0, 0}}, {2.099910301131178575, 2.099910300189512172, {9.942182244246451055*10^15, 9.913394512391821761*10^23, 7.409942369148423294*10^31, 4.873477272186623899*10^39, 2.753574810288145528*10^47, 9.806496929751634675*10^54}, {0, 0, 0, 0, 0}}, {2.099910302072844977, 2.099910301131178575, {1.094581064264013029*10^16, 1.145174195387068499*10^24, 8.981008076915008899*10^31, 6.193954936721584376*10^39, 3.66208970431546212*10^47, 1.360225694251112194*10^55}, {0, 0, 0, 0, 0}}, {2.09991030301451138, 2.099910302072844977, {1.210945074073227139*10^16, 1.332558317408362415*10^24, 1.099098079390583199*10^32, 7.961492139796487911*10^39, 4.911330734143258373*10^47, 1.877437827784372524*10^55}, {0, 0, 0, 0, 0}}, {2.099910303794521628, 2.09991030301451138, {1.321982198659602624*10^16, 1.519980908955536254*10^24, 1.310392786203473553*10^32, 9.97742801845498623*10^39, 6.658237224169425808*10^47, 2.918138122060117035*10^55}, {0, 0, 0, 0, 0}}, {2.099910304574531875, 2.099910303794521628, {1.449022918190561517*10^16, 1.744265905329956741*10^24, 1.573989749955023926*10^32, 1.249748954234568855*10^40, 8.52466820402916312*10^47, 3.665145908431636244*10^55}, {0, 0, 0, 0, 0}}, {2.099910305354542123, 2.099910304574531875, {1.595296695404905147*10^16, 2.01493878023360188*10^24, 1.907709122837891691*10^32, 1.588370740727933014*10^40, 1.133729853499553277*10^48, 5.083798703595050152*10^55}, {0, 0, 0, 0, 0}}, {2.099910306134552371, 2.099910305354542123, {1.764891370823047879*10^16, 2.344641925642940259*10^24, 2.334659333328709909*10^32, 2.041635965482415233*10^40, 1.520476755975299883*10^48, 7.01686200702562792*10^55}, {0, 0, 0, 0, 0}}, {2.099910306780658024, 2.099910306134552371, {1.926722379693107684*10^16, 2.674412758343760961*10^24, 2.783482935692925564*10^32, 2.558600263343391211*10^40, 2.061293666243995821*10^48, 1.090644505874285258*10^56}, {0, 0, 0, 0, 0}}, {2.099910307426763677, 2.099910306780658024, {2.111877821045342299*10^16, 3.069043146314237218*10^24, 3.343404860041023529*10^32, 3.204841966790612596*10^40, 2.639113624851211701*10^48, 1.369836204133017192*10^56}, {0, 0, 0, 0, 0}}, {2.09991030807286933, 2.099910307426763677, {2.325064473941937776*10^16, 3.545293200321381303*10^24, 4.052277947186806078*10^32, 4.073199814617926029*10^40, 3.509863177850241447*10^48, 1.90005301090158003*10^56}, {0, 0, 0, 0, 0}}, {2.099910308718974983, 2.09991030807286933, {2.572240159769055573*10^16, 4.125407261855695738*10^24, 4.959188178839424114*10^32, 5.235547988191429496*10^40, 4.707175489912183944*10^48, 2.622529049803121372*10^56}, {0, 0, 0, 0, 0}}, {2.099910309254163484, 2.099910308718974983, {2.808100693166857863*10^16, 4.705640419462090177*10^24, 5.912560977797293898*10^32, 6.561245338450097617*10^40, 6.381466198101347674*10^48, 4.07624789656668015*10^56}, {0, 0, 0, 0, 0}}, {2.099910309789351985, 2.099910309254163484, {3.077955410527659996*10^16, 5.399994235487055298*10^24, 7.101924303169908197*10^32, 8.218460193385770896*10^40, 8.170312976619238525*10^48, 5.119717667547110231*10^56}, {0, 0, 0, 0, 0}}, {2.099910310324540486, 2.099910309789351985, {3.388664204945770876*10^16, 6.237958194832970885*10^24, 8.607683616267824696*10^32, 1.044526715607961336*10^41, 1.086602728966037779*10^49, 7.101385508602282417*10^56}, {0, 0, 0, 0, 0}}, {2.099910310859728987, 2.099910310324540486, {3.748910300605729293*10^16, 7.258671309268103986*10^24, 1.053410535835023266*10^33, 1.342597955761326847*10^41, 1.457273253652414456*10^49, 9.801615893507937201*10^56}, {0, 0, 0, 0, 0}}, {2.099910311303041516, 2.099910310859728987, {4.09266513228551238*10^16, 8.279593973739559683*10^24, 1.25592209917638105*10^33, 1.682558272509435598*10^41, 1.975609371163128192*10^49, 1.523484217338358302*10^57}, {0, 0, 0, 0, 0}}, {2.099910311746354046, 2.099910311303041516, {4.4859647725771867*10^16, 9.50131241338620699*10^24, 1.508561808076581022*10^33, 2.107532560112629064*10^41, 2.529410386401081856*10^49, 1.913477605301274278*10^57}, {0, 0, 0, 0, 0}}, {2.099910312189666575, 2.099910311746354046, {4.938807169683465335*10^16, 1.097571350007284177*10^25, 1.828409062838403594*10^33, 2.678572398297863741*10^41, 3.363964436128268854*10^49, 2.654119429955094703*10^57}, {0, 0, 0, 0, 0}}, {2.099910312632979105, 2.099910312189666575, {5.463847684910428613*10^16, 1.277166248849134672*10^25, 2.237611715851302318*10^33, 3.442942887506958935*10^41, 4.511506614448129613*10^49, 3.663321637221823582*10^57}, {0, 0, 0, 0, 0}}, {2.099910313000188039, 2.099910312632979105, {5.964853014631675186*10^16, 1.456798018107404126*10^25, 2.667778522915544266*10^33, 4.314733247055660657*10^41, 6.116200049118675027*10^49, 5.693972053157326142*10^57}, {0, 0, 0, 0, 0}}, {2.099910313367396973, 2.099910313000188039, {6.538067404086805314*10^16, 1.671759887881150694*10^25, 3.20442549320261737*10^33, 5.40453246401264079*10^41, 7.830687662935783847*10^49, 7.151559487739526458*10^57}, {0, 0, 0, 0, 0}}, {2.099910313734605907, 2.099910313367396973, {7.198062358529604697*10^16, 1.931181374948391725*10^25, 3.883831992560065643*10^33, 6.86890051323114915*10^41, 1.041434594803922322*10^50, 9.919683898208392827*10^57}, {0, 0, 0, 0, 0}}, {2.099910314101814841, 2.099910313734605907, {7.963282428784017791*10^16, 2.247179349637526148*10^25, 4.753043586132443408*10^33, 8.82904347929902007*10^41, 1.396697008004238979*10^50, 1.369154388780570689*10^58}, {0, 0, 0, 0, 0}}, {2.099910314405984907, 2.099910314101814841, {8.693472428390822604*10^16, 2.563242197978363637*10^25, 5.666786381095382672*10^33, 1.10646527359087542*10^42, 1.893486819148617935*10^50, 2.128103289365067847*10^58}, {0, 0, 0, 0, 0}}, {2.099910314710154972, 2.099910314405984907, {9.528903490658635539*10^16, 2.941468505751786169*10^25, 6.806709997901256885*10^33, 1.385932142040343392*10^42, 2.424267315581896663*10^50, 2.672871789300380264*10^58}, {0, 0, 0, 0, 0}}, {2.099910315014325038, 2.099910314710154972, {1.049081284957347532*10^17, 3.397921695863165278*10^25, 8.249877586483128182*10^33, 1.761453014697299526*10^42, 3.224130444442856298*10^50, 3.707449164864464122*10^58}, {0, 0, 0, 0, 0}}, {2.099910315318495104, 2.099910315014325038, {1.16060825077008186*10^17, 3.953921452268094644*10^25, 1.009622141841530255*10^34, 2.264109841676703318*10^42, 4.3239713445629474*10^50, 5.117169405137729952*10^58}, {0, 0, 0, 0, 0}}, {2.099910315570448202, 2.099910315318495104, {1.267029760461890569*10^17, 4.510035354134162048*10^25, 1.203715661293853202*10^34, 2.837406930076081362*10^42, 5.861960540035430579*10^50, 7.953715908555414336*10^58}, {0, 0, 0, 0, 0}}, {2.099910315822401301, 2.099910315570448202, {1.388789624247819334*10^17, 5.175526122531747898*10^25, 1.445853588851078077*10^34, 3.554068580641690074*10^42, 7.505179966781231595*10^50, 9.989770223243956858*10^58}, {0, 0, 0, 0, 0}}, {2.0999103160743544, 2.099910315822401301, {1.528983061870246515*10^17, 5.978657417160575328*10^25, 1.752405364658772658*10^34, 4.517050024250030224*10^42, 9.981440192833537704*10^50, 1.385646906806838144*10^59}, {0, 0, 0, 0, 0}}, {2.099910316326307499, 2.0999103160743544, {1.691527989622325277*10^17, 6.95694131099389886*10^25, 2.144598194451028267*10^34, 5.806057459334473927*10^42, 1.338638808664555447*10^51, 1.912525200624015449*10^59}, {0, 0, 0, 0, 0}}, {2.099910316535007733, 2.099910316326307499, {1.846631972574467115*10^17, 7.935426044242900137*10^25, 2.55688373586443369*10^34, 7.276213975261688695*10^42, 1.814777954904506946*10^51, 2.97267510793044225*10^59}, {0, 0, 0, 0, 0}}, {2.099910316743707967, 2.099910316535007733, {2.024090833020997914*10^17, 9.10635983102676446*10^25, 3.071223250348700009*10^34, 9.114012939557489443*10^42, 2.32349485437223767*10^51, 3.733643697864379247*10^59}, {0, 0, 0, 0, 0}}, {2.099910316952408201, 2.099910316743707967, {2.228415697627431777*10^17, 1.051947269864587854*10^26, 3.72238803532835414*10^34, 1.158347157223687794*10^43, 3.090109101969938219*10^51, 5.178809647720555533*10^59}, {0, 0, 0, 0, 0}}, {2.099910317161108436, 2.099910316952408201, {2.465316731788912693*10^17, 1.224076729618649375*10^26, 4.555468055854616459*10^34, 1.488898753963680238*10^43, 4.144231580803837613*10^51, 7.147999906646564076*10^59}, {0, 0, 0, 0, 0}}, {2.099910317333981038, 2.099910317161108436, {2.691372964192372977*10^17, 1.396241527151793265*10^26, 5.431228195287300678*10^34, 1.86590401442255877*10^43, 5.618289313130452154*10^51, 1.111027524606914244*10^60}, {0, 0, 0, 0, 0}}, {2.09991031750685364, 2.099910317333981038, {2.950010303064142412*10^17, 1.602267816041331946*10^26, 6.523767223884525133*10^34, 2.337187085101899902*10^43, 7.193203044016670474*10^51, 1.39543702718682402*10^60}, {0, 0, 0, 0, 0}}, {2.099910317679726242, 2.09991031750685364, {3.247803487998210572*10^17, 1.850905615363250585*10^26, 7.906944914114574484*10^34, 2.970452240831633836*10^43, 9.56652955645948818*10^51, 1.935563038142863119*10^60}, {0, 0, 0, 0, 0}}, {2.099910317852598844, 2.099910317679726242, {3.593074797062866606*10^17, 2.153768118793913127*10^26, 9.676539531557417677*10^34, 3.818114986083393651*10^43, 1.282993984946968255*10^52, 2.671541407598102905*10^60}, {0, 0, 0, 0, 0}}, {2.099910317995794354, 2.099910317852598844, {3.922540354528366652*10^17, 2.456692799194474731*10^26, 1.153679351764157642*10^35, 4.784902976843870483*10^43, 1.739340877528880223*10^52, 4.15242875732091443*10^60}, {0, 0, 0, 0, 0}}, {2.099910318138989865, 2.099910317995794354, {4.299491231426537048*10^17, 2.819196915077760792*10^26, 1.385752038266775284*10^35, 5.993455909041490069*10^43, 2.226911324339059614*10^52, 5.215399899989880405*10^60}, {0, 0, 0, 0, 0}}, {2.099910318282185375, 2.099910318138989865, {4.733509779115238917*10^17, 3.256676161557235762*10^26, 1.67956100442729859*10^35, 7.617393852987884075*10^43, 2.961658787266475315*10^52, 7.234103065120172341*10^60}, {0, 0, 0, 0, 0}}, {2.099910318425380885, 2.099910318282185375, {5.236725298140621743*10^17, 3.789564001415354462*10^26, 2.055451078961131832*10^35, 9.791130530632579313*10^43, 3.97196327790838506*10^52, 9.984797965476827114*10^60}, {0, 0, 0, 0, 0}}, {2.099910318543993979, 2.099910318425380885, {5.716904731381460234*10^17, 4.322561241911727608*10^26, 2.450598646990859597*10^35, 1.227035062942116711*10^44, 5.384747063794870025*10^52, 1.551956562977692946*10^61}, {0, 0, 0, 0, 0}}, {2.099910318662607073, 2.099910318543993979, {6.266291622748866306*10^17, 4.960388748006245069*10^26, 2.94355798675644596*10^35, 1.536954998707695265*10^44, 6.894194444566039784*10^52, 1.949238524338837948*10^61}, {0, 0, 0, 0, 0}}, {2.099910318781220167, 2.099910318662607073, {6.898851766056095112*10^17, 5.730135309559638322*10^26, 3.56765501496949034*10^35, 1.953395793203950835*10^44, 9.168866013976956999*10^52, 2.703722179309292912*10^61}, {0, 0, 0, 0, 0}}, {2.099910318899833261, 2.099910318781220167, {7.63226300510163762*10^17, 6.667753689689235734*10^26, 4.366105387389967546*10^35, 2.510826348009615591*10^44, 1.229662217138521635*10^53, 3.731785332911019017*10^61}, {0, 0, 0, 0, 0}}, {2.09991031899808401, 2.099910318899833261, {8.33210031095306435*10^17, 7.605564560698818075*10^26, 5.205461742424516382*10^35, 3.146594722976954895*10^44, 1.667039584686922345*10^53, 5.800386506627181831*10^61}, {0, 0, 0, 0, 0}}, {2.099910319096334758, 2.09991031899808401, {9.132803996510158814*10^17, 8.727824721909615062*10^26, 6.252585875489540185*10^35, 3.941349872098020543*10^44, 2.13434259909708898*10^53, 7.285214744077641825*10^61}, {0, 0, 0, 0, 0}}, {2.099910319194585507, 2.099910319096334758, {1.005472850188373472*10^18, 1.008219701223281861*10^27, 7.578267340266737382*10^35, 5.009265896642849822*10^44, 2.838547922661087808*10^53, 1.010507253917258544*10^62}, {0, 0, 0, 0, 0}}, {2.099910319292836255, 2.099910319194585507, {1.112363839281893371*10^18, 1.173194046854986392*10^27, 9.274303070949540926*10^35, 6.438734454755575753*10^44, 3.806855860596646562*10^53, 1.394742469410048918*10^62}, {0, 0, 0, 0, 0}}, {2.099910319374220268, 2.099910319292836255, {1.214361596944230773*10^18, 1.338202261337425685*10^27, 1.105722962228762905*10^36, 8.069091625569572772*10^44, 5.160912748526962536*10^53, 2.167875340641755151*10^62}, {0, 0, 0, 0, 0}}, {2.099910319455604281, 2.099910319374220268, {1.33106012072388632*10^18, 1.535664405476161643*10^27, 1.328148801765255216*10^36, 1.010715266702572862*10^45, 6.60761509839775459*10^53, 2.722825000871892543*10^62}, {0, 0, 0, 0, 0}}, {2.099910319536988293, 2.099910319455604281, {1.465425967608343658*10^18, 1.773966775686625065*10^27, 1.609744654109844752*10^36, 1.284570434244251324*10^45, 8.78773263450571356*10^53, 3.776737558443509702*10^62}, {0, 0, 0, 0, 0}}, {2.099910319618372306, 2.099910319536988293, {1.621214193110042327*10^18, 2.064239825931721054*10^27, 1.970009649795493237*10^36, 1.651141721199486901*10^45, 1.178547355637459583*10^54, 5.21280401318961406*10^62}, {0, 0, 0, 0, 0}}, {2.099910319685785101, 2.099910319618372306, {1.769870780593444468*10^18, 2.354572468561163857*10^27, 2.348731639377083984*10^36, 2.069228654913530208*10^45, 1.59774372741780001*10^54, 8.102362639442300622*10^62}, {0, 0, 0, 0, 0}}, {2.099910319753197896, 2.099910319685785101, {1.939952993252125433*10^18, 2.702007935982553851*10^27, 2.821199540090078638*10^36, 2.591866704292040258*10^45, 2.04562179038383799*10^54, 1.017646870519546413*10^63}, {0, 0, 0, 0, 0}}, {2.09991031982061069, 2.099910319753197896, {2.135784438275512778*10^18, 3.121301951768822788*10^27, 3.41935396982712641*10^36, 3.294137773042473065*10^45, 2.720554556752372141*10^54, 1.411543215554707233*10^63}, {0, 0, 0, 0, 0}}, {2.099910319888023485, 2.09991031982061069, {2.362837919684827992*10^18, 3.632038596160167357*10^27, 4.184614186745623593*10^36, 4.234169001133499929*10^45, 3.648611663648217317*10^54, 1.948268320202449237*10^63}, {0, 0, 0, 0, 0}}, {2.099910319943863505, 2.099910319888023485, {2.579497398370308178*10^18, 4.142880093600678084*10^27, 4.989079997661907231*10^36, 5.306306366316760434*10^45, 4.946382825851196536*10^54, 3.028231333707738209*10^63}, {0, 0, 0, 0, 0}}, {2.099910319999703525, 2.099910319943863505, {2.827383645136312524*10^18, 4.754194249783980927*10^27, 5.992677051265542468*10^36, 6.64655342026660868*10^45, 6.33294834365850318*10^54, 3.803421640195560525*10^63}, {0, 0, 0, 0, 0}}, {2.099910320055543545, 2.099910319999703525, {3.112798099398075379*10^18, 5.491943821972045864*10^27, 7.263252305961469919*10^36, 8.447449340657863323*10^45, 8.422442288701311066*10^54, 5.27559624820672162*10^63}, {0, 0, 0, 0, 0}}, {2.099910320111383565, 2.099910320055543545, {3.443717096992836395*10^18, 6.390587081151183094*10^27, 8.888786861389429551*10^36, 1.085805470237624051*10^46, 1.129557247609222682*10^55, 7.281588638092626406*10^63}, {0, 0, 0, 0, 0}}, {2.099910320157637512, 2.099910320111383565, {3.759487359844496216*10^18, 7.289414829708321047*10^27, 1.059760034129372851*10^37, 1.360743153558834677*10^46, 1.531328375134151293*10^55, 1.131791480895723942*10^64}, {0, 0, 0, 0, 0}}, {2.099910320203891459, 2.099910320157637512, {4.120769062235384509*10^18, 8.365024641002738205*10^27, 1.272940028893451299*10^37, 1.704434579729839102*10^46, 1.960588947183722826*10^55, 1.42151630316741934*10^64}, {0, 0, 0, 0, 0}}, {2.099910320250145405, 2.099910320203891459, {4.53674623429686212*10^18, 9.663098094884610616*10^27, 1.542830444743974898*10^37, 2.166254275912483517*10^46, 2.607465964262230859*10^55, 1.971736711097038726*10^64}, {0, 0, 0, 0, 0}}, {2.099910320296399352, 2.099910320250145405, {5.019043983221098743*10^18, 1.124426466308827834*10^28, 1.888119868194018607*10^37, 2.784427165950009247*10^46, 3.496945395254166263*10^55, 2.721469755710553718*10^64}, {0, 0, 0, 0, 0}}, {2.09991032033471287, 2.099910320296399352, {5.479263215291506593*10^18, 1.282575584112316045*10^28, 2.251099061278276253*10^37, 3.489474225821061023*10^46, 4.740770528790395163*10^55, 4.230033359636967275*10^64}, {0, 0, 0, 0, 0}}, {2.099910320373026388, 2.09991032033471287, {6.005813075097440477*10^18, 1.471829579697183211*10^28, 2.70392731545090378*10^37, 4.370832599826327474*10^46, 6.069698995205105779*10^55, 5.312870334478224971*10^64}, {0, 0, 0, 0, 0}}, {2.099910320411339906, 2.099910320373026388, {6.612078823354067872*10^18, 1.700226146119492993*10^28, 3.277217534182584977*10^37, 5.555117762379736496*10^46, 8.072336409958809447*10^55, 7.369300975618370891*10^64}, {0, 0, 0, 0, 0}}, {2.099910320449653424, 2.099910320411339906, {7.315003467475706047*10^18, 1.978433064256137183*10^28, 4.010667251067105098*10^37, 7.140353272288930105*10^46, 1.082603570847957691*10^56, 1.017140352106913818*10^65}, {0, 0, 0, 0, 0}}, {2.099910320481389649, 2.099910320449653424, {7.985749786824256136*10^18, 2.256697097628172847*10^28, 4.781692855450079541*10^37, 8.948367912654048838*10^46, 1.467673790389922245*10^56, 1.58096102733349645*10^65}, {0, 0, 0, 0, 0}}, {2.099910320513125873, 2.099910320481389649, {8.753169650677952705*10^18, 2.589690293383179509*10^28, 5.743572172521819138*10^37, 1.120851327642784022*10^47, 1.879090767359176889*10^56, 1.985667777997629224*10^65}, {0, 0, 0, 0, 0}}, {2.099910320544862098, 2.099910320513125873, {9.636771401436632212*10^18, 2.991555006027148278*10^28, 6.961331883839036994*10^37, 1.424548064234433765*10^47, 2.49907826252239239*10^56, 2.754251952789173487*10^65}, {0, 0, 0, 0, 0}}, {2.099910320576598323, 2.099910320544862098, {1.066124861787735426*10^19, 3.481061240572826044*10^28, 8.519295871912968489*10^37, 1.831064050680309088*10^47, 3.351583622676380012*10^56, 3.801528544321623863*10^65}, {0, 0, 0, 0, 0}}, {2.09991032060288638, 2.099910320576598323, {1.16388275488916792*10^19, 3.970667969613743642*10^28, 1.015707702835553469*10^38, 2.294709263295258644*10^47, 4.543705167579859201*10^56, 5.908789736263250513*10^65}, {0, 0, 0, 0, 0}}, {2.099910320629174438, 2.09991032060288638, {1.275730329524223006*10^19, 4.556570888473953366*10^28, 1.220026186076150019*10^38, 2.874298363036156177*10^47, 5.817392451856159482*10^56, 7.421367879036197961*10^65}, {0, 0, 0, 0, 0}}, {2.099910320655462495, 2.099910320629174438, {1.404510828206346818*10^19, 5.263653528980069891*10^28, 1.47869773951520034*10^38, 3.653094811161506327*10^47, 7.736783807110541622*10^56, 1.029392590225443413*10^66}, {0, 0, 0, 0, 0}}, {2.099910320681750553, 2.099910320655462495, {1.553823215498958924*10^19, 6.124941793355272751*10^28, 1.809634098512712487*10^38, 4.695559771118965328*10^47, 1.037601674544091226*10^57, 1.420808764823575698*10^66}, {0, 0, 0, 0, 0}}, {2.099910320703525731, 2.099910320681750553, {1.696300414224594665*10^19, 6.986406878214633976*10^28, 2.157524895024579785*10^38, 5.88452626719417619*10^47, 1.406665213010762489*10^57, 2.208390690455863963*10^66}, {0, 0, 0, 0, 0}}, {2.09991032072530091, 2.099910320703525731, {1.859312613165138483*10^19, 8.017305511295055901*10^28, 2.591529887676114939*10^38, 7.370817945254973637*10^47, 1.80098032126853848*10^57, 2.77371178634572082*10^66}, {0, 0, 0, 0, 0}}, {2.099910320747076089, 2.09991032072530091, {2.0470036948835372*10^19, 9.261420370785228153*10^28, 3.140989456232515329*10^38, 9.367954675862010679*10^47, 2.395196043902676106*10^57, 3.847320880495224562*10^66}, {0, 0, 0, 0, 0}}, {2.099910320768851267, 2.099910320747076089, {2.264618968715343005*10^19, 1.077686066959768617*10^29, 3.843950978738099744*10^38, 1.204123993148088995*10^48, 3.21226427928711253*10^57, 5.310225933236304628*10^66}, {0, 0, 0, 0, 0}}, {2.099910320786888295, 2.099910320768851267, {2.472272299947038617*10^19, 1.229261208479061747*10^29, 4.582926426230414566*10^38, 1.509021205569731729*10^48, 4.354831461365603593*10^57, 8.253787424117045654*10^66}, {0, 0, 0, 0, 0}}, {2.099910320804925322, 2.099910320786888295, {2.70985435829864812*10^19, 1.410648253581094094*10^29, 5.504822138546642342*10^38, 1.890164148606505793*10^48, 5.575573840753392712*10^57, 1.036665638883855653*10^67}, {0, 0, 0, 0, 0}}, {2.099910320822962349, 2.099910320804925322, {2.983404643606814757*10^19, 1.629550782781410187*10^29, 6.671961754265256007*10^38, 2.402307614378696082*10^48, 7.415179526477869622*10^57, 1.437923499551658761*10^67}, {0, 0, 0, 0, 0}}, {2.099910320840999376, 2.099910320822962349, {3.300567929678227452*10^19, 1.89619313636448068*10^29, 8.165163962751177727*10^38, 3.087841836862383291*10^48, 9.944704266709859303*10^57, 1.984679441748518647*10^67}, {0, 0, 0, 0, 0}}, {2.099910320855939982, 2.099910320840999376, {3.603212186845676874*10^19, 2.162890231004641643*10^29, 9.734865482514797676*10^38, 3.869716771516623676*10^48, 1.348192653197791109*10^58, 3.084825847932508577*10^67}, {0, 0, 0, 0, 0}}, {2.099910320870880587, 2.099910320855939982, {3.949476054319627787*10^19, 2.482041494524446865*10^29, 1.169311877171002494*10^39, 4.847115388295981449*10^48, 1.726116786872903945*10^58, 3.874503660159841893*10^67}, {0, 0, 0, 0, 0}}, {2.099910320885821192, 2.099910320870880587, {4.348161798506701416*10^19, 2.867201409019238287*10^29, 1.417230916265852376*10^39, 6.160450251720226763*10^48, 2.295632023519211378*10^58, 5.374191690235751463*10^67}, {0, 0, 0, 0, 0}}, {2.099910320900761798, 2.099910320885821192, {4.810411291662040656*10^19, 3.336359743927123004*10^29, 1.734410842057511834*10^39, 7.918426394402777503*10^48, 3.078736192100135502*10^58, 7.417674004877525617*10^67}, {0, 0, 0, 0, 0}}, {2.099910320913137545, 2.099910320900761798, {5.2515000324645664*10^19, 3.805614395953624462*10^29, 2.067840439686173453*10^39, 9.92345756075909877*10^48, 4.17380889768453882*10^58, 1.152943494069904173*10^68}, {0, 0, 0, 0, 0}}, {2.099910320925513292, 2.099910320913137545, {5.756162155311299523*10^19, 4.36716237722755378*10^29, 2.483804620169157322*10^39, 1.242988742791274824*10^49, 5.343807197290717429*10^58, 1.448082973865547525*10^68}, {0, 0, 0, 0, 0}}, {2.099910320937889039, 2.099910320925513292, {6.337226519543049328*10^19, 5.044852855613416424*10^29, 3.010424136103169913*10^39, 1.579778837513061685*10^49, 7.106943761225435859*10^58, 2.008586432616461296*10^68}, {0, 0, 0, 0, 0}}, {2.099910320950264786, 2.099910320937889039, {7.010931842025619114*10^19, 5.87033890558173098*10^29, 3.684164804001152436*10^39, 2.030592234843439935*10^49, 9.531320677153933154*10^58, 2.77233121305278322*10^68}, {0, 0, 0, 0, 0}}, {2.099910320960515985, 2.099910320950264786, {7.653796435207422816*10^19, 6.695994425922589806*10^29, 4.392422362365211422*10^39, 2.544760140716778484*10^49, 1.292150693231437663*10^59, 4.309088311772902251*10^68}, {0, 0, 0, 0, 0}}, {2.099910320970767184, 2.099910320960515985, {8.389316026362386232*10^19, 7.68404044458816901*10^29, 5.275996516942488738*10^39, 3.187506157655144377*10^49, 1.654365195853853308*10^59, 5.412162390660289596*10^68}, {0, 0, 0, 0, 0}}, {2.099910320981018383, 2.099910320970767184, {9.236188030949609813*10^19, 8.876439672055238733*10^29, 6.394620224000666817*10^39, 4.051166835991030037*10^49, 2.20020670158592443*10^59, 7.507025595348777416*10^68}, {0, 0, 0, 0, 0}}, {2.099910320991269581, 2.099910320981018383, {1.021807955979295216*10^20, 1.032888582507115956*10^30, 7.825752684375216045*10^39, 5.207227571277474245*10^49, 2.950758628941600772*10^59, 1.036149654165543815*10^69}, {0, 0, 0, 0, 0}}, {2.099910320999760954, 2.099910320991269581, {1.115502228114847781*10^20, 1.17816301619154277*10^30, 9.330204516328289243*10^39, 6.525753885811569259*10^49, 4.000311118567981415*10^59, 1.610507555154601979*10^69}, {0, 0, 0, 0, 0}}, {2.099910321008252326, 2.099910320999760954, {1.222700498894732606*10^20, 1.352010125887529857*10^30, 1.120705671482877419*10^40, 8.174004442126854209*10^49, 5.121674679131739515*10^59, 2.022777856760954197*10^69}, {0, 0, 0, 0, 0}}, {2.099910321016743699, 2.099910321008252326, {1.346127822320735435*10^20, 1.561813268031499593*10^30, 1.358319159044807574*10^40, 1.038876603694090239*10^50, 6.811520806053174128*10^59, 2.805726075517341578*10^69}, {0, 0, 0, 0, 0}}, {2.099910321025235071, 2.099910321016743699, {1.489233560429140911*10^20, 1.817371775348694906*10^30, 1.662314481982296409*10^40, 1.335335500342976738*10^50, 9.135120704881411116*10^59, 3.872575184280263571*10^69}, {0, 0, 0, 0, 0}}, {2.099910321032268727, 2.099910321025235071, {1.625788236547822979*10^20, 2.072982748235040015*10^30, 1.981884006929536682*10^40, 1.673456884867336976*10^50, 1.238438297418633476*10^60, 6.019218910235937845*10^69}, {0, 0, 0, 0, 0}}, {2.099910321039302383, 2.099910321032268727, {1.782024309609490434*10^20, 2.37886746391322604*10^30, 2.380557299574835377*10^40, 2.096132377954707836*10^50, 1.585596190284984419*10^60, 7.560065575385237958*10^69}, {0, 0, 0, 0, 0}}, {2.099910321046336039, 2.099910321039302383, {1.961913408382243454*10^20, 2.748016968873788207*10^30, 2.885286183068869464*10^40, 2.664083315736722612*10^50, 2.108748039802425372*10^60, 1.048630873952948812*10^70}, {0, 0, 0, 0, 0}}, {2.099910321053369695, 2.099910321046336039, {2.170482804063615467*10^20, 3.197673229979095529*10^30, 3.531020655080506871*10^40, 3.424319129649199861*10^50, 2.828100864443974406*10^60, 1.447362212361192093*10^70}, {0, 0, 0, 0, 0}}, {2.099910321059195881, 2.099910321053369695, {2.369504357301149702*10^20, 3.647421804472467534*10^30, 4.209837212088021825*10^40, 4.291393752373492302*10^50, 3.834025332165199387*10^60, 2.249663230289225462*10^70}, {0, 0, 0, 0, 0}}, {2.099910321065022068, 2.099910321059195881, {2.597210553941689693*10^20, 4.185627239404025966*10^30, 5.056682767617788663*10^40, 5.37529796688826218*10^50, 4.908775812899570512*10^60, 2.825549593253082986*10^70}, {0, 0, 0, 0, 0}}, {2.099910321070848254, 2.099910321065022068, {2.859389842603598086*10^20, 4.835147335338119098*10^30, 6.128807285661957241*10^40, 6.831744875136845651*10^50, 6.528378055336417166*10^60, 3.919223331894760842*10^70}, {0, 0, 0, 0, 0}}, {2.09991032107667444, 2.099910321070848254, {3.163369217504266588*10^20, 5.626319404989643995*10^30, 7.500450126462772854*10^40, 8.781284927023604301*10^50, 8.755390057621100034*10^60, 5.409468568291902965*10^70}, {0, 0, 0, 0, 0}}, {2.099910321081500443, 2.09991032107667444, {3.453433093593405216*10^20, 6.417653900433095615*10^30, 8.942364583555079578*10^40, 1.100480120189645775*10^51, 1.186958629939298662*10^61, 8.408042181533445488*10^70}, {0, 0, 0, 0, 0}}, {2.099910321086326446, 2.099910321081500443, {3.785303390717658082*10^20, 7.364628611306284301*10^30, 1.074119938927303878*10^41, 1.378435280935175001*10^51, 1.519685789417625777*10^61, 1.05603984837475098*10^71}, {0, 0, 0, 0, 0}}}][t]}}\ \>", "\<\ {{y[t] -> InterpolatingFunction[{1., 2.09991}, <>][t]}}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["Plot[y[t]/.%, {t,1,2.1}]"], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.842812 0.866622 0.0147151 4.29491e-05 [ [(1.2)] .19713 .01472 0 2 Msboxa [(1.4)] .37046 .01472 0 2 Msboxa [(1.6)] .54378 .01472 0 2 Msboxa [(1.8)] .71711 .01472 0 2 Msboxa [(2)] .89043 .01472 0 2 Msboxa [(2000)] .01131 .10061 1 0 Msboxa [(4000)] .01131 .18651 1 0 Msboxa [(6000)] .01131 .27241 1 0 Msboxa [(8000)] .01131 .35831 1 0 Msboxa [(10000)] .01131 .44421 1 0 Msboxa [(12000)] .01131 .5301 1 0 Msboxa [(14000)] .01131 .616 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .19713 .01472 m .19713 .02097 L s P [(1.2)] .19713 .01472 0 2 Mshowa p .002 w .37046 .01472 m .37046 .02097 L s P [(1.4)] .37046 .01472 0 2 Mshowa p .002 w .54378 .01472 m .54378 .02097 L s P [(1.6)] .54378 .01472 0 2 Mshowa p .002 w .71711 .01472 m .71711 .02097 L s P [(1.8)] .71711 .01472 0 2 Mshowa p .002 w .89043 .01472 m .89043 .02097 L s P [(2)] .89043 .01472 0 2 Mshowa p .001 w .05847 .01472 m .05847 .01847 L s P p .001 w .09314 .01472 m .09314 .01847 L s P p .001 w .1278 .01472 m .1278 .01847 L s P p .001 w .16247 .01472 m .16247 .01847 L s P p .001 w .2318 .01472 m .2318 .01847 L s P p .001 w .26646 .01472 m .26646 .01847 L s P p .001 w .30113 .01472 m .30113 .01847 L s P p .001 w .33579 .01472 m .33579 .01847 L s P p .001 w .40512 .01472 m .40512 .01847 L s P p .001 w .43979 .01472 m .43979 .01847 L s P p .001 w .47445 .01472 m .47445 .01847 L s P p .001 w .50912 .01472 m .50912 .01847 L s P p .001 w .57845 .01472 m .57845 .01847 L s P p .001 w .61311 .01472 m .61311 .01847 L s P p .001 w .64778 .01472 m .64778 .01847 L s P p .001 w .68244 .01472 m .68244 .01847 L s P p .001 w .75177 .01472 m .75177 .01847 L s P p .001 w .78644 .01472 m .78644 .01847 L s P p .001 w .8211 .01472 m .8211 .01847 L s P p .001 w .85577 .01472 m .85577 .01847 L s P p .001 w .9251 .01472 m .9251 .01847 L s P p .001 w .95976 .01472 m .95976 .01847 L s P p .001 w .99443 .01472 m .99443 .01847 L s P p .002 w 0 .01472 m 1 .01472 L s P p .002 w .02381 .10061 m .03006 .10061 L s P [(2000)] .01131 .10061 1 0 Mshowa p .002 w .02381 .18651 m .03006 .18651 L s P [(4000)] .01131 .18651 1 0 Mshowa p .002 w .02381 .27241 m .03006 .27241 L s P [(6000)] .01131 .27241 1 0 Mshowa p .002 w .02381 .35831 m .03006 .35831 L s P [(8000)] .01131 .35831 1 0 Mshowa p .002 w .02381 .44421 m .03006 .44421 L s P [(10000)] .01131 .44421 1 0 Mshowa p .002 w .02381 .5301 m .03006 .5301 L s P [(12000)] .01131 .5301 1 0 Mshowa p .002 w .02381 .616 m .03006 .616 L s P [(14000)] .01131 .616 1 0 Mshowa p .001 w .02381 .03189 m .02756 .03189 L s P p .001 w .02381 .04907 m .02756 .04907 L s P p .001 w .02381 .06625 m .02756 .06625 L s P p .001 w .02381 .08343 m .02756 .08343 L s P p .001 w .02381 .11779 m .02756 .11779 L s P p .001 w .02381 .13497 m .02756 .13497 L s P p .001 w .02381 .15215 m .02756 .15215 L s P p .001 w .02381 .16933 m .02756 .16933 L s P p .001 w .02381 .20369 m .02756 .20369 L s P p .001 w .02381 .22087 m .02756 .22087 L s P p .001 w .02381 .23805 m .02756 .23805 L s P p .001 w .02381 .25523 m .02756 .25523 L s P p .001 w .02381 .28959 m .02756 .28959 L s P p .001 w .02381 .30677 m .02756 .30677 L s P p .001 w .02381 .32395 m .02756 .32395 L s P p .001 w .02381 .34113 m .02756 .34113 L s P p .001 w .02381 .37549 m .02756 .37549 L s P p .001 w .02381 .39267 m .02756 .39267 L s P p .001 w .02381 .40985 m .02756 .40985 L s P p .001 w .02381 .42703 m .02756 .42703 L s P p .001 w .02381 .46139 m .02756 .46139 L s P p .001 w .02381 .47857 m .02756 .47857 L s P p .001 w .02381 .49574 m .02756 .49574 L s P p .001 w .02381 .51292 m .02756 .51292 L s P p .001 w .02381 .54728 m .02756 .54728 L s P p .001 w .02381 .56446 m .02756 .56446 L s P p .001 w .02381 .58164 m .02756 .58164 L s P p .001 w .02381 .59882 m .02756 .59882 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p .004 w .02381 .01484 m .09603 .01487 L .16825 .0149 L .24046 .01494 L .31268 .015 L .34879 .01503 L .3849 .01507 L .42101 .01512 L .45712 .01518 L .49323 .01526 L .52934 .01535 L .56545 .01547 L .60156 .01562 L .63767 .01583 L .65572 .01596 L .67378 .01611 L .70988 .01652 L .72794 .01679 L .74599 .01713 L .76405 .01756 L .7821 .01811 L .80016 .01884 L .81821 .01983 L .82724 .02046 L .83627 .02123 L .85432 .02328 L .86335 .0247 L .87238 .0265 L .8814 .02883 L .89043 .03192 L .89946 .03616 L .90397 .0389 L .90849 .04219 L .913 .0462 L .91751 .05116 L .92203 .05738 L .92654 .06536 L .93105 .07579 L .93557 .08982 L .94008 .1093 L .94234 .12201 L .94459 .13747 L .94685 .15652 L .94911 .18038 L .95137 .21082 L .95362 .25048 L .95588 .30352 L .95814 .37669 L .96039 .48165 L s .96234 .61803 m .96039 .48165 L s s s s s s s P P % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, Inherited}, {Inherited, Inherited}}, ImageCacheValid->False], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["DSolve[{y'[t] == y[t]^(3/2),y[1]==3},y[t],t]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {{y[t] -> (1/2 - 3^(-1/2) - t/2)^(-2)}, {y[t] -> (1/2 + 3^(-1/2) - t/2)^(-2)}}\ \>", "\<\ 1 1 t -2 1 1 t -2 {{y[t] -> (- - ------- - -) }, {y[t] -> (- + ------- - -) }} 2 Sqrt[3] 2 2 Sqrt[3] 2\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["N[1+2/Sqrt[3]]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ 2.154700538379251529\ \>", "\<\ 2.1547\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 1024}, {0, 748}}, WindowToolbars->{"RulerBar", "EditBar"}, CellGrouping->Automatic, WindowSize->{520, 653}, WindowMargins->{{124, Automatic}, {Automatic, 1}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, 128}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, CharacterEncoding->"MacintoshAutomaticEncoding", MacintoshSystemPageSetup->"\<\ 00<0001804P000000]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:001 0000I00000400`<300000BL?00400@0000000000000006P801T1T00000000000 00000000000000000000000000000000\>" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 97, 2, 44, "Subsection"], Cell[CellGroupData[{ Cell[1853, 57, 138, 3, 41, "Subsubsection"], Cell[1994, 62, 253, 7, 47, "Text"], Cell[2250, 71, 546, 20, 82, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[2833, 96, 91, 2, 41, "Subsubsection"], Cell[2927, 100, 92, 1, 27, "Input"], Cell[3022, 103, 84, 1, 42, "Input"], Cell[CellGroupData[{ Cell[3131, 108, 66, 1, 27, "Input"], Cell[3200, 111, 122, 6, 25, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3359, 122, 62, 1, 27, "Input"], Cell[3424, 125, 124, 6, 25, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3585, 136, 62, 1, 27, "Input"], Cell[3650, 139, 131, 7, 25, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3818, 151, 86, 1, 27, "Input"], Cell[3907, 154, 599, 25, 67, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4543, 184, 147, 3, 42, "Input"], Cell[4693, 189, 3660, 391, 70, 3502, 386, "GraphicsData", "PostScript", "Graphics"], Cell[8356, 582, 131, 7, 70, "Output"] }, Open ]], Cell[8502, 592, 62, 1, 70, "Input"], Cell[CellGroupData[{ Cell[8589, 597, 86, 1, 70, "Input"], Cell[8678, 600, 1297, 54, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10012, 659, 147, 3, 70, "Input"], Cell[10162, 664, 3818, 401, 70, 3660, 396, "GraphicsData", "PostScript", "Graphics"], Cell[13983, 1067, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14151, 1079, 129, 3, 70, "Input"], Cell[14283, 1084, 5099, 195, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19419, 1284, 108, 2, 70, "Input"], Cell[19530, 1288, 4340, 435, 70, 4182, 430, "GraphicsData", "PostScript", "Graphics"], Cell[23873, 1725, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24041, 1737, 66, 1, 70, "Input"], Cell[24110, 1740, 4886, 479, 70, 4728, 474, "GraphicsData", "PostScript", "Graphics"], Cell[28999, 2221, 131, 7, 70, "Output"] }, Open ]], Cell[29145, 2231, 74, 1, 70, "Input"], Cell[CellGroupData[{ Cell[29244, 2236, 57, 1, 70, "Input"], Cell[29304, 2239, 136, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[29477, 2251, 64, 1, 70, "Input"], Cell[29544, 2254, 144, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[29725, 2266, 64, 1, 70, "Input"], Cell[29792, 2269, 144, 7, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[29985, 2282, 138, 3, 70, "Subsubsection"], Cell[30126, 2287, 692, 24, 70, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[30855, 2316, 91, 2, 70, "Subsubsection"], Cell[30949, 2320, 92, 1, 70, "Input"], Cell[31044, 2323, 82, 1, 70, "Input"], Cell[31129, 2326, 61, 1, 70, "Input"], Cell[CellGroupData[{ Cell[31215, 2331, 66, 1, 70, "Input"], Cell[31284, 2334, 144, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[31465, 2346, 62, 1, 70, "Input"], Cell[31530, 2349, 144, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[31711, 2361, 62, 1, 70, "Input"], Cell[31776, 2364, 144, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[31957, 2376, 86, 1, 70, "Input"], Cell[32046, 2379, 620, 29, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[32703, 2413, 149, 3, 70, "Input"], Cell[32855, 2418, 3659, 391, 70, 3501, 386, "GraphicsData", "PostScript", "Graphics"], Cell[36517, 2811, 131, 7, 70, "Output"] }, Open ]], Cell[36663, 2821, 62, 1, 70, "Input"], Cell[CellGroupData[{ Cell[36750, 2826, 86, 1, 70, "Input"], Cell[36839, 2829, 1271, 57, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38147, 2891, 149, 3, 70, "Input"], Cell[38299, 2896, 3814, 401, 70, 3656, 396, "GraphicsData", "PostScript", "Graphics"], Cell[42116, 3299, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[42284, 3311, 131, 3, 70, "Input"], Cell[42418, 3316, 12646, 441, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[55101, 3762, 73, 1, 70, "Input"], Cell[55177, 3765, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[55345, 3777, 114, 2, 70, "Input"], Cell[55462, 3781, 3958, 420, 70, 3800, 415, "GraphicsData", "PostScript", "Graphics"], Cell[59423, 4203, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[59591, 4215, 66, 1, 70, "Input"], Cell[59660, 4218, 4501, 463, 70, 4343, 458, "GraphicsData", "PostScript", "Graphics"], Cell[64164, 4683, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[64332, 4695, 68, 1, 70, "Input"], Cell[64403, 4698, 108, 6, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[64548, 4709, 86, 1, 70, "Input"], Cell[64637, 4712, 2492, 111, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[67166, 4828, 149, 3, 70, "Input"], Cell[67318, 4833, 5005, 517, 70, 4847, 512, "GraphicsData", "PostScript", "Graphics"], Cell[72326, 5352, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[72494, 5364, 85, 1, 70, "Input"], Cell[72582, 5367, 5941, 589, 70, 5783, 584, "GraphicsData", "PostScript", "Graphics"], Cell[78526, 5958, 131, 7, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[78706, 5971, 147, 4, 70, "Subsubsection"], Cell[78856, 5977, 703, 24, 70, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[79596, 6006, 91, 2, 70, "Subsubsection"], Cell[79690, 6010, 741, 20, 70, "Text"], Cell[80434, 6032, 231, 4, 70, "Input"], Cell[80668, 6038, 82, 1, 70, "Input"], Cell[80753, 6041, 61, 1, 70, "Input"], Cell[CellGroupData[{ Cell[80839, 6046, 66, 1, 70, "Input"], Cell[80908, 6049, 141, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[81086, 6061, 62, 1, 70, "Input"], Cell[81151, 6064, 141, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[81329, 6076, 62, 1, 70, "Input"], Cell[81394, 6079, 141, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[81572, 6091, 88, 1, 70, "Input"], Cell[81663, 6094, 631, 24, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[82331, 6123, 149, 3, 70, "Input"], Cell[82483, 6128, 4536, 487, 70, 4378, 482, "GraphicsData", "PostScript", "Graphics"], Cell[87022, 6617, 131, 7, 70, "Output"] }, Open ]], Cell[87168, 6627, 62, 1, 70, "Input"], Cell[CellGroupData[{ Cell[87255, 6632, 88, 1, 70, "Input"], Cell[87346, 6635, 1176, 46, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[88559, 6686, 149, 3, 70, "Input"], Cell[88711, 6691, 4693, 497, 70, 4535, 492, "GraphicsData", "PostScript", "Graphics"], Cell[93407, 7190, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[93575, 7202, 66, 1, 70, "Input"], Cell[93644, 7205, 5490, 560, 70, 5332, 555, "GraphicsData", "PostScript", "Graphics"], Cell[99137, 7767, 131, 7, 70, "Output"] }, Open ]], Cell[99283, 7777, 63, 1, 70, "Input"], Cell[CellGroupData[{ Cell[99371, 7782, 88, 1, 70, "Input"], Cell[99462, 7785, 2589, 108, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[102088, 7898, 149, 3, 70, "Input"], Cell[102240, 7903, 5030, 520, 70, 4872, 515, "GraphicsData", "PostScript", "Graphics"], Cell[107273, 8425, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[107441, 8437, 63, 1, 70, "Input"], Cell[107507, 8440, 5634, 567, 70, 5476, 562, "GraphicsData", "PostScript", "Graphics"], Cell[113144, 9009, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[113312, 9021, 131, 3, 70, "Input"], Cell[113446, 9026, 157, 4, 70, "Message"], Cell[113606, 9032, 140678, 4960, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[254321, 13997, 77, 1, 70, "Input"], Cell[254401, 14000, 5153, 513, 70, 4995, 508, "GraphicsData", "PostScript", "Graphics"], Cell[259557, 14515, 131, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[259725, 14527, 97, 1, 70, "Input"], Cell[259825, 14530, 367, 11, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[260229, 14546, 67, 1, 70, "Input"], Cell[260299, 14549, 129, 7, 70, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)