{VERSION 6 0 "IBM INTEL LINUX" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Assignment 12" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 45 "restart; interface(warnlevel=0): with(plots)
:" }}}{PARA 0 "" 0 "" {TEXT 257 3 "43." }{TEXT -1 19 " Graph the surfa
ce " }{TEXT 256 0 "" }{XPPEDIT 18 0 "x^2-y^2+z = 4;" "6#/,(*$%\"xG\"\"
#\"\"\"*$%\"yGF'!\"\"%\"zGF(\"\"%" }{TEXT -1 67 " along with its tange
nt plane and normal line at the point (1,1,4)." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 9 "Solution.
" }}{PARA 0 "" 0 "" {TEXT -1 9 "Gradient:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "grad := proc(f) <diff(f,x),diff(f,y),diff(f,z)> end:
" }}}{PARA 0 "" 0 "" {TEXT -1 15 "Tangent  Plane:" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 21 "g := grad(x^2-y^2+z);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 27 "n := eval(g,\{x=1,y=1,z=4\});" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "n.<x,y,z> = n.<1,1,4>;" }}}{PARA 0 
"" 0 "" {TEXT -1 12 "Normal Line:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "r := <1,1,4> + t*n;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "graph := plot3d(4-x^2+y^2,x=-1..2,y=-1..2):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 65 "tplane := plot3d(4-2*x+2*y,x=0.25..1.75,y
=0.25..1.75,color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "nline :
= spacecurve([1+2*t,1-2*t,4+t],t=-1..1,color=black):" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 105 "display(graph, tplane, nline, scaling=constrain
ed, axes=boxed, orientation=[-20,100], style=patchnogrid);" }{TEXT -1 
0 "" }}}}{MARK "1 0 0" 32 }{VIEWOPTS 0 0 0 3 4 1802 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }