\documentclass[12pt]{article}
\usepackage{amsmath,verbatim,graphpap}
\def\ds {\displaystyle}
\def\ra {\rightarrow}
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\begin{document}
{\large
MATH 176 - Exam One   \quad\quad\quad\quad Name:\underbar{\hskip 2.0truein}\\
\indent November 7, 2001 \quad\quad\quad\quad \quad Instructor:\underbar{\hskip
1.5truein} section: \underbar{\hskip .5truein}\\
\indent * * * SHOW YOUR WORK * * *\\
\hspace*{4.8in}
\vspace*{-.75in}
\begin{tabular}{|l|l|l|}
\hline
prob&points&score\\
\hline
1&30&\\
\hline
2&10&\\
\hline
3&30&\\
\hline
4&10&\\
\hline
5&10&\\
\hline
6&10&\\
\hline
\hline
Total&100&\\
\hline
\end{tabular}}
\vspace*{-1.5in}
\begin{itemize}
\item[ 1.] Find the derivative of the following functions \\
({\bf DO NOT SIMPLIFY}):
\begin{itemize}
\item[a.] $\ds y = \rm{Arcsin}(x^3)$
\vspace{1.2in}
\item[b.] $\ds y = \rm{Arctan}(\frac{2}{x})$
\vspace{1.2in}
\item[c.] $\ds y = x^2 \ln( 2 x)$
\vspace{1.2in}
\item[d.] $\ds y = (\ln (2x))^2$
\vspace{1.2in}
\item[e.] $\ds y = xe^{-2x} $
\vspace{1.2in}
\item[f.] $\ds y = \sec(e^{x+2})$

\end{itemize}


\newpage



\item[2.] Find the following integrals:
\begin{itemize}
\item[a.] $\ds \int \sin^{3}(x) \cos(x) ds$
\vspace{1.2in}
\item[b.] $\ds \int (10+ e^{x})^{1/2} e^{x} dx $
\vspace{1.2in}
\item[c.] $\ds \int \frac{1+e^{x}}{x+e^{x}} dx$
\vspace{1.2in}
\item[d.] $\ds \int x^{4} e^{x^{5}} dx$
\vspace{1.2in}
\item[e.] $\ds \int x^{2} \cos(x^{3}) dx$
\vspace{1.2in}
\item[f.] $\ds \int \frac{ dx}{x^2 + 4 x + 8} $

\end{itemize}

\newpage


\item[3.] A force is given as a function of the distance from the
origin by $F = \frac{\sin (x)}{2 + \cos(x)}$. Compute the
work, $W$,  done by this force as a function of $x$ if $W=0$ when $x=0$. 

\vspace{3in}



\item[4.] Find the equation of the line normal to
the graph of $y = x^2 \ln(x)$ at $(1,0)$.


\vspace{3in}


\item[5.] The vapor pressure $P$ over a liquid may be related to
temperature by $\log P = (a/T) + b$. Solve for $P$. 


\vspace{3in}


\item[6.] Find the volume generated by rotating
the area bounded by $y=\sqrt{1-x^2}$, $x=0$, $y=0$ about the
$y$-axis. 


\end{itemize}
\end{document}