\magnification1200\footline{\ifnum\pageno=1 \hfil\else\hfil\number\pageno\hfil\fi}
\def\ans#1#2#3#4#5{\par\noindent\hbox to\hsize{%
(a)\ #1\hfil (b)\ #2\hfil (c)\ #3\hfil (d)\ #4\hfil (e)\ #5}\par}
\def\ansA#1#2#3#4#5{\par\noindent\hbox to\hsize{%
(a)\ #1\hfil }\par\hbox to\hsize{(b)\ #2\hfil }%
\par\hbox to\hsize{(c)\ #3\hfil }
\par\hbox to\hsize{(d)\ #4\hfil }\par\hbox to\hsize{(e)\ #5\hfil}\par}

\long\def\boxit#1#2{\vbox{\hrule\hbox{\vrule\kern#2
\vbox{\kern#2#1\kern#2}\kern#2\vrule}\hrule}}
\newcount\pc
\def\pr{\vskip10pt\noindent\number\pc.\global\advance\pc by 1}
\def\dd#1#2{{{\textstyle d\> #1}\over{\textstyle d#2}}}

\def\rhs#1#2{\par\noindent\hbox to\hsize{\hfill\hbox to#1{#2\hfill}}}
\def\ul#1{\vrule width#1 height -3pt depth3.1pt}
\def\UL#1#2{\hbox to0pt{\qquad #2\hss}\ul{#1}}
\newif\ifnotmarkanswers\notmarkanswerstrue
\newcount\ansmark
\def\ll#1#2{\tabalign {#1.}&
\global\ansmark=#2 \relax%
\ifnotmarkanswers \global\ansmark=0 \fi%
\ifnum\ansmark=1 \relax($\bullet$)\else(a)\fi&
\ifnum\ansmark=2 \relax($\bullet$)\else(b)\fi&
\ifnum\ansmark=3 \relax($\bullet$)\else(c)\fi&
\ifnum\ansmark=4 \relax($\bullet$)\else(d)\fi&
\ifnum\ansmark=5 \relax($\bullet$)\else(e)\fi&
(f)\qquad\cr}

\def\marked{\pageno=1 %
\global\notmarkanswersfalse
\headline{\vbox{\rhs{3in}{Name:\ \ul{3in}\hss}\vskip10pt%
\rhs{3in}{Instructor-section:\ \UL{2.3in}{Bullwinkle}\hss}%
}}
\answersheet}


\def\+{\tabalign}
\long\def\exam#1{%
\pc=1 \pageno=1 %
\headline{\vbox{\rhs{3in}{Name:\ \ul{3in}\hss}\vskip10pt%
\rhs{3in}{Instructor-section:\ \UL{2.3in}{#1}\hss}%
}}
\long\gdef\answersheet{
\null\vskip10pt
\centerline{\bf Math 125, Test I}
\centerline{September 24, 1998}
\vskip10pt

\itemitem{$\bullet$}
The Honor Code is in effect for this examination.
All work is to be your own.
\itemitem{$\bullet$} No calculators.
\itemitem{$\bullet$} The exam lasts for one hour.
\itemitem{$\bullet$} Be sure that your name is on every page in case
pages become detached. 
\itemitem{$\bullet$} Be sure that you have all 11 pages of the test.
\vskip10pt
\centerline{Good Luck!}
\vskip20pt
\def\HH{\hskip.75in}

\settabs\+9.\qquad &\HH&\HH&\HH&\HH&\HH&\cr
\boxit{\vbox{{\obeylines\baselineskip20pt
\ll 1 2
\ll 2 3
\ll 3 1
\ll 4 5
\ll 5 2
\ll 6 3
\ll 7 1
\ll 8 5
}}}{10pt}
%%\vskip10pt
\settabs\+Total multiple choice: &\hskip 2in\cr
\hfill{{\vbox to0pt{\boxit{\vbox{\obeylines\hsize=3in\baselineskip26pt
\null
\tabalign Total multiple choice: &\quad\ul{1in}\cr
\tabalign\hfill9.&\quad\ul{1in}\cr
\tabalign\hfill10.&\quad\ul{1in}\cr
\tabalign\hfill11.&\quad\ul{1in}\cr
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\tabalign\hfill13.&\quad\ul{1in}\cr
\tabalign\hfill14.&\quad\ul{1in}\cr

\tabalign\hfil {\bf Total:}&\quad\ul{1in}\cr
}}{10pt}\vss}}}}
\answersheet
\vfill\eject\null\vskip10pt
\centerline{\bf Multiple Choice}


\pr(5pts) $$\lim_{z\to0}\ {{1-\cos{(9z)}}\over{z}}=\ ?$$
\ans{-1}{0}{1}{9}{Does not exist.} %% (b)

\vskip2in
\pr(5pts)
$$\lim_{u\to 4}\ {{u^2+x^2}\over{2u+x^2}}=\ ?$$
\ans{$-2$}{$1$}{$\displaystyle{{16+x^2}\over{8+x^2}}$}
{$\displaystyle{{u^2+16}\over{2u+16}}$}
{Does not exist.}%% (c)

\vfill\eject\null\vskip10pt
\pr(5pts)
$$\lim_{t\to3^-}{{\sqrt t+\sqrt 3}\over{t-3}}=\ ?$$
\ans{$-\infty$}{$+\infty$}{${{1}\over{\sqrt3}}$}{$\sqrt 3$}{Does not exist.}
%%a

\vskip2in
\pr(5pts)
$$\dd{\sin(x^2)}{x}=\ ?$$
\ans{$\cos(x^2)$}{$\cos(2x)$}{$x^2\cos(x)$}{$2\sin(x)$}{$2x\cos(x^2)$}%% (e)

\vfill\eject\null\vskip10pt
\pr(5pts)
If $y$ is defined implicitly as a function of $x$ by the equation
$$x^2-y^2=2xy-2$$
then
$\dd{y}{x}$ evaluated at the point $(1,1)$ is
\ans{$-1$}{$0$}{$1$}{$2$}{$2/3$}
%%(b)

\vskip2in
\pr(5pts)
Suppose $f$ and $g$ are two functions which are differentiable at $3$.
If $f(3)=1$, $f^\prime(3)=2$, $g(3)=4$ and $g^\prime(3)=-1$, 
$$\biggl({{\textstyle f}\over{\textstyle g}}\biggr)^\prime(3)=\ ?$$
\ans{${{1}\over{4}}$}
{${{5}\over{16}}$}
{${{9}\over{16}}$}
{${{8}\over{3}}$}
{\hfuzz=12pt\vtop{\hsize =1.2in\noindent Can not be determined from the information given.}}
%%(c)

\vfill\eject\null\vskip10pt
\pr(5pts)
$$\dd{(x^2+2)(x^3+2x+1)^{45}}{x}=\ ?$$
\ansA{$\bigl(2x(x^3+2x+1)+45(x^2+2)(3x^2+2)\bigr)(x^3+2x+1)^{44}$}
{$\bigl(2(x+1)(x^3+2x+1)+45(x^2+2)\bigr)(x^3+2x+1)^{44}$}
{$90x(x^3+2x+1)^{44}$}
{$\bigl(2x+45(x^3+2x+1)^{44}\bigr)(x^2+2)(x^3+2x+1)^{45}$}
{$45(x^2+2)^{44}+(3x^2+2)$}
%%(a)
\vskip2in
\pr(5pts)
The derivative of $$\dd{(x+\tan x)}{x}$$ evaluated at $x=0$ is
\ans{$-2$}
{$0$}
{$4/\pi$}
{$\pi/4$}
{$2$}%%(e)



\vfill\eject\null\vskip10pt

\centerline{\bf Partial Credit}

\pr(10pts)
 Is the function
$$f(x)= \cases{%
{{\textstyle\sin 2x \cos 4x }\over {\textstyle x}}& $ 0< x\le \pi/4$\cr\noalign{\vskip4pt}
\hfill 2\hfill&$x=0$\cr}$$
continuous on the entire interval $[0,\pi/4]$? Why or why not?

\vfill\eject\null\vskip10pt
\pr(10pts)
Write an equation for the line tangent to the ellipse $9x^2 + 5y^2=270$ at
the point $(5,3)$.

\vfill\eject\null\vskip10pt
\pr(10pts)
Use the {\bf definition of derivative} to find $f'(3)$, where
$$f(x)=\sqrt{2x+3}\ .$$


\vfill\eject\null\vskip10pt
\pr(10pts)
The function
$$f(x)= \cases{x^2 + ax +1&$ x\le 1$\cr
x^3 -1&$x>1$} $$
is continuous on $(-\infty, \infty)$ for a unique 
number $a$.  Find $a$.


\vfill\eject\null\vskip10pt
\pr(10pts)
The position of a particle moving along the $x$-axis is given by
$$ x(t)= t^5 - 5t +1  \ .$$
Find the particle's acceleration at each time when the instantaneous
velocity of the particle is $0$.

\vfill\eject\null\vskip10pt
\pr(10pts)
If
$$ x^4 - y^4 = 4xy-4\ ,$$
find $d^2y/dx^2$ at the point $(1,1)$.
\vfill\eject}
%\exam{Dwyer}
%\exam{Shaw}
%\exam{Taylor}
%\exam{Nollet}
%\exam{Budhiraja}
%\exam{Gekhtman \quad{\sl Section \#:}}
\exam{Bullwinkle}
\marked{}
\end

