\documentstyle{letter}
\textwidth 6.2in
\textheight 8.7in  \parindent 0cm
\topmargin -1cm
\oddsidemargin 0.7cm

\begin{document}

\baselineskip 0.5cm
\everyproblem={\mathsurround=4pt}
\normalafterproblemskip=2.5cm
\pageannouncements={usual}
%%%%%%%%%%%%%%%%%%%%%%%% Change this %%%%%%%%%%%%%%%%%%%%%%%%%%%%

\input examIperms     
\lastversion=4

%%%%%%%%%%%%%%%%%%%%%%%% Change this %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\title{{\large\bf Math 105, Test 1}}
\comment{ \large 
\begin{minipage}[c]{6.2in}
1. Please cross \fbox{$\times $} the correct answers. \\
2.  This test will be exactly 60 minutes in length.  
When you are told to begin, but not before, glance 
through the entire test and put your name on each
page.  It is YOUR RESPONSIBILITY to make sure your 
test consists of a PARTIAL CREDIT SECTION of 3 problems , 2 of which are worth 15
points and one 10 points, and a MULTIPLE CHOICE SECTION of 12 problems ( 5 points
each). \\
\end{minipage}} 
\answersheetfootline{\large\bf 
\fbox{\rule[-2mm]{0mm}{8mm}Sign your name:\hspace{6cm}}
\hspace{6cm}}
\twocolumn{12} 
\date{{\large September 15, 1992}}
\vertmultchoice=2.5in
\multiplechoiceskip=0.8cm \let\ansborder=\boxborder \boxwidth=1cm
\boxdepth=0.4cm

\pagenumberstyle=1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\note
\begin{center}
{{\bf PARTIAL CREDIT SECTION}}
\end{center}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem
\afterproblemskip = 6cm
 Compute $$\lim_{x \rightarrow 2} \frac{x^3 + x^2 -6x}{x - 2}$$
( {{\bf 10 points}})

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem
 \afterproblemskip = 6cm
Write the equation of the line tangent to the graph of $f(x) = \frac{1}{x} + 1$
at $x = 2$. ( {{\bf 15 points}})

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem
\afterproblemskip = 6cm
Given $f(x) = x^2 + 2x$ and $g(x) = (x + 1)^{75}$ compute the derivative
of $f(g(x))$. ({{\bf 15 points}})

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\note 
\begin{center}
{{\bf MULTIPLE CHOICE SECTION}}
\end{center}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

 Compute $$\lim_{x \rightarrow \infty} \frac{2x^2 + 1}{x^2 - x}$$

\correct $ 2$
\wrong $1$
\wrong $0$
\wrong $\infty$
\wrong $1/2$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem
 
Find the domain of $f(x) = \frac{1}{\sqrt{x + 3}}$

\correct $x>-3$
\wrong $x\neq 3$
\wrong $x\geq -3$
\wrong all reals
\wrong $x\neq - 3$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem
\afterproblemskip = 1.cm
 Which of the following curves are graphs of functions?

\picture4.93in by 3.92in (grafici2)


\correct 2,4
\wrong None
\wrong All of them
\wrong 2,3,4
\wrong 1,2

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

Find the slope of the line through the points $A = (- 1,2)$ and $B = (1,-2)$.

\correct $-2$ 
\wrong $2$
\wrong $0$
\wrong $ - \frac{1}{2}$
\wrong$\frac{1}{2}$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

 Given $f(x) = \frac{2x}{x + 1}$ and $g(x) = \frac{x - 1}{x + 2}$ express $f(x) +
g(x)$ as a rational function.

\correct $\frac{3x^2 + 4x -1}{x^2 + 3x + 2}$
\wrong $\frac{3x^2 + 3x -1}{x^2 + 3x +2}$
\wrong $\frac{3x - 1}{2x + 3}$
\wrong $\frac{2x^2 - 1}{x^2 + 3}$
\wrong $\frac{x^2 + 5x + 2}{x^2 +2x}$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

Find the coordinates of the points of intersection of the graphs of $y_1 = x^2 + x + 1$ and $ y_2 = -x + 1.$

\correct $(0,1) , (-2,3)$
\wrong none
\wrong $(0,1)$
\wrong $ (\sqrt{2}, 3 + \sqrt{2}) , (- \sqrt{2},3 - \sqrt{2})$
\wrong $(0,1) , (2,7)$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

 Given $$f(x) = \left\{ \begin{array}{lr} 
x+1 & x\leq 1\\
-2x + 2 & x>1
\end{array} \right. $$

Compute $$\lim_{x \rightarrow 1}f(x)$$

\correct It does not exist
\wrong $2$
\wrong $0$
\wrong $-2$
\wrong $\infty$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

Differentiate $f(x) = \sqrt{x^2 + 2x}.$

\correct $\frac{x + 1}{\sqrt{x^2 + 2x}}$
\wrong $\frac{x^2 + 2x}{2}$
\wrong $\frac{1}{2} (x^2 + 2x) ( 2x + 2)$
\wrong $\frac{1}{2}(x^2 + 2x)^{-1/2}$
\wrong $(x^2 + 2x)^{3/2}(x+1)$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

Simplify the following expression:
$$\left(\frac{5^3 \sqrt{5}}{5^{3/2}}\right)^{1/2}$$

\correct $5$
\wrong $1$
\wrong $\sqrt{5}$
\wrong $25$
\wrong $5^{5/2}$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

Given $f(x) = |x^2 - 1|$ evaluate $f(0) , f(\sqrt{2}) , f(-\sqrt{2})$

\correct $1,1,1$
\wrong $1,1,3$
\wrong $-1,-1,-1$
\wrong $ -1,1,1$
\wrong $ -1,1,-3$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

Differentiate $$f(x) = 15 (\frac{x}{3} + 1)^{\frac{1}{5}}$$

\correct $(\frac{x}{3} + 1)^{-4/5}$
\wrong $x + 3$
\wrong $3(\frac{x}{3} + 1)^{-4/5}$
\wrong $x/3 + 1$
\wrong $\frac{1}{15} (\frac{x}{3} + 1)^{-4/5}$


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem

Find all the real solutions of the following equation:
$$2x^3 + 6x^2 + 5x = 0$$

\correct $0$
\wrong $0,-1,-2$
\wrong $0,1,2$
\wrong it has no solutions
\wrong $-1,-2$

\endtest