\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 C - Spring 2007 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 19, 2007 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \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,
or read a numerical solution from a graph on your calculator,
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 Let $f(x) = e^x \sin x$.

\begin{enumerate}
\item Find the second-order Taylor polynomial $T_2(x)$ for $f(x)$ based at $b=0$.
\vfil
\item Give a bound on the error $|f(x)-T_2(x)|$ for $x$ in the interval $-0.1 \le x \le 0.1$.
\end{enumerate}

\newp

\item Find the first four non-zero terms of the Taylor series for
\[
f(x) = xe^{x^2} - \frac{1}{4+x^2}
\]
based at $b=0$.

\newp


\item Find the equation of the plane containing the line of intersection of the two planes
\[
x+y+z+5=0 
\mbox{ and }
3x+2y-z+2=0
\]
and the point $(1,2,1)$.

\newp

\item Find the point of intersection of the two lines
\[
x=4-t, y=6+2t, z=-1+3t 
\mbox{ and }
x=1+2t, y=14-8t, z=7-4t.
\]


\newp



\item Let $S$ be the surface defined as the set of points $p$ 
(in three-dimensional space) such that the
distance from $p$ to the plane $y=5$ equals the distance from $p$
to the line 
\[
y=1, z=2.\]

\begin{enumerate}
\item Find an equation for $S$.
\vfil
\item Find the equation of the trace of $S$ in the plane $z=6$.  Describe the trace (i.e. 
what kind of curve is it?).

\end{enumerate}


\end{enumerate}

\end{document}


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