\documentclass[12pt]{report} 

\usepackage{palatino}
\usepackage{epsfig}

\pagestyle{empty} %%% this results in no pagenumbers (footer is empty}

\addtolength{\oddsidemargin}{-1.0in}
\addtolength{\evensidemargin}{-1.0in}
\addtolength{\textwidth}{1.5in}
\addtolength{\topmargin}{-0.5in}
\addtolength{\textheight}{1.0in}

\baselineskip=20pt

\newcommand{\dsps}{\displaystyle}
\newcommand{\pp}{\par \noindent}
\newcommand{\newp}{\vfil \eject}
%\newcommand{\newp}{\bigskip}

\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 126 D - Spring 2011 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil May 17, 2011 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hspace{0.5in} Student ID no. : \hrulefill

\vfil

\hfil Signature: \hrulefill \hrulefill \hrulefill \hspace{0.5in} Section: \hrulefill 
 

%\hspace{0.5in}
% Section: \hrulefill
\vfil
\begin{center}
{\large
\begin{tabular}{||c|c|r||} \hline 
 1 & 10 &\hspace{10mm} \hfil\\ \hline 
 2 & 10 &       \\ \hline
 3 & 10 &      \\ \hline
4 &  10 &    \\ \hline
5 & 10 & \\ \hline
Total & 50 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all questions. 
\item You may use a scientific, non-graphing calculator during this
examination.  
Other electronic devices are not allowed, and should be
turned off for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method
when an algebraic method is available, you will not receive full credit.
\item You may use one hand-written 8.5 by 11 inch page of notes.
\item Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item Find and classify all critical points of the function $f(x,y)=x^2y+x^2+y^2$.

\newp

\item Find the equation of the tangent plane to the surface
\[
z=x e^{y^2} -\frac{y}{x+y}
\]
at the point $(0,1,-1)$.
\newp

\item You wish to build an open-top steel box with rectangular sides.  
The base will be made with thick steel which costs \$50 per square meter.
The sides will be made with thin steel which costs \$20 per square meter.
The box will have a volume of 2 cubic meters.

What dimensions will minimize the cost of the box?

\newp

\item Evaluate the following integrals.  It may be helpful to reverse the 
order of integration on either or both of these integrals.

\begin{enumerate}
\item $\dsps \int_{e}^{e^2} \int_{\frac{1}{x}}^{\frac{2}{x}} e^{xy} \, dy \, dx$

\vfil

\item $\dsps \int_{0}^{2} \int_{x^2}^4 xy \sin y^3 \, dy \, dx$


\end{enumerate}

\newp

\item Evaluate the integral 
\[
\int \int_D xy \, dA
\]
where $D$ is the region entirely contained in the first quadrant which is
bounded by the circles $x^2+y^2=1$ and $x^2+y^2=4$, the $y$-axis, and the line $y=x$.

\end{enumerate}


\end{document}


% \epsfig{file=enclosure01.eps, 
% width=11cm,
% angle=0 }