\documentclass[11pt]{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{definition}{Definition}

\title{Brief Article}
\author{The Author}
\begin{document}
\maketitle




\begin{minipage}[c]{6in}
This exam is worth a total of 100 points.  There are 11 problems -- 8 multiple choice 
and 3 partial credit.  Each multiple choice problem is worth 7 points.  Point values are
assigned next to the partial credit problems. Please show all work on the partial
credit section of the test inside the test booklet. Use the front sheet to answer 
the multiple choice section by putting a \fbox{$\times $} in the appropriate box.  
You will have until 9:20am to complete the exam. Good luck! 
\end{minipage}}

\answersheetfootline{\large\bf\fbox{\rule[-2mm]{0mm}{8mm}Sign
your name\hspace{6cm}}
\hspace{6cm}}\twocolumn{6}\noprofessor \nosection \vertmultchoice=2.5in
\multiplechoiceskip=0.8cm \let\ansborder=\boxborder \boxwidth=1cm
\boxdepth=0.4cm\pagenumberstyle=1
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\problem  
Evaluate $\int x^2+3\sin(2x)\,dx$.

\wrong  $\frac{1}{3}x^3-3\cos(2x)+C$
\correct $\frac{1}{3}x^3-\frac{3}{2}\cos(2x)+C$
\wrong  $\frac{1}{3}x^3+\frac{3}{2}\cos(2x)+C$
\wrong   $3x^3-3\cos(2x)+C$
\wrong   $3x^3+6\cos(2x)+C$

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\problem  

Evaluate $\int \ln x\,dx$



\correct $x\ln x-x+C$
\wrong  $\frac{1}{x}+C$
\wrong  $\frac{1}{2}(\ln x)^2+C$
\wrong  $\frac{\ln x}{x}+C$
\wrong  $\frac{e^x}{x}+C$

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\problem  
The marginal cost function for a company is given by $MC(x)=3x^2-17x+2000$.  If
the fixed costs for the company are \$12,000, what is the total cost function C(x)?

\wrong $ x^3-\frac{17}{2}x^2+2000x-12,000 $
\wrong $ 3x^3-17x^2+2000x-12,000$
\correct $x^3-\frac{17}{2}x^2+2000x+12,000 $
\wrong $ x^3-\frac{17}{2}x^2+2000x$
\wrong  It cannot be determined from the information provided.


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\problem  
Consider the following graph of the supply curve, S(q), and the demand curve, D(q) 
for a certain item.  Which region/regions denoted on the graph correspond to the
consumer's surplus?

\vspace{5.5cm}

\wrong A+B
\wrong  B
\correct A
\wrong A+B+C
\wrong  B+C

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\problem  

Determine the average value of the function $y=\cos x$ between $x=0$ and 
$x=\frac{\pi}{2}$.


\wrong 2
\wrong 0
\wrong $ 2\pi$
\wrong $ \frac{\pi}{2}$
\correct $ \frac{2}{\pi} $

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\problem  

Find the area underneath the curve $y=e^{-x/3}$ for $x\geq6$.


\wrong $ \frac{1}{3}e^{-2} $
\wrong $ e^{-2}$
\wrong $ \infty $
\wrong  1
\correct $ 3e^{-2} $

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\problem  

How long will it take an amount of money to triple if interest is 10\% compounded
continuously?  You may assume $\ln 3\approx1.1$.


\wrong 5
\wrong 12
\wrong  7
\wrong The answer cannot be determined without knowing the initial amount invested.
\correct 11

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\problem  

Approximate the value of the definite integral of the function f(x) from $x=1$
to $x=3$ using the table below and the left endpoint method.

\begin{tabular}{|c|c|c|c|c|c|}
\hline x & 1 & 1.5 & 2 & 2.5 & 3 \\
\hline f(x) & 1 & 2 & 2 & 3 & 5 \\
\hline
\end{tabular}


\wrong 8
\wrong 5
\wrong 6
\wrong 9
\correct 4

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\problem  


Suppose that a museum sells tickets for an exhibit and that the number of tickets
sold ($q$) depends upon the price of the ticket ($p$) so that $q=-100p+1000$.  (Note that
this means that for each \$1 decrease in price, 100 more people will buy a ticket.)
The museum wants to know at what price they should sell their tickets so as to maximize
their revenue.  What price would this be, and how much revenue would the museum make
at this price?  (16 points)

\vspace*{17cm}


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\problem  

(16 points)
Suppose that the demand curve for producing a quantity $q$ of some item is given by:
$$D(q)=\frac{50}{q+1}$$ and the supply curve is given by: $$S(q)=q+6.$$
\vspace{1cm}
a.  What is the equilibrium quantity $q_e$?

\vspace{4cm}

b.  What is the equilibrium price $p_e$?

\vspace{2cm}

c.  Compute the consumer surplus.

\vspace{5cm}

d.  Compute the producer surplus.

\vspace*{5cm}

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\problem

Find the area between the curves $y=x^2e^{2x}$ and $y=0$ from $x=0$ to $x=1$.  (Note that
the first function always has a positive value, so it is always greater than or equal to 0.)
(12 points)
\vspace*{17cm}

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 \end{document}


 