\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 - Winter 2006 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil February 16, 2006 \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
6 & 10 & \\ \hline
Total & 60 & \\ \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 Eliminate the parameter in the following parametric equation pair
to get a Cartesian equation for the curve that involves no trigonometric functions.

\[
x = \cos t, y = \sin t - \cos t
\]







\newp

\item Consider the curve defined parametrically by the parametric equations
\[
x = \ln \ln t, y = \ln t - (\ln t)^2.
\]

Find the equation of the tangent line to the curve at the
point $t=e$.






\newp

%\item Find all points of intersection between the curve defined by the
%polar equation 
%\[
%r = 4 \csc \theta
%\]
%and the line $y=x$.  


%\newp

%\item Find the unit tangent vector $\vec{T}(t)$ at the point given by
%$\dsps t=\frac{\pi}{2}$ on the curve defined by the vector function
%\[
%\vec{r}(t) = 3 \sin t \vec{i} + 5 \cos t \vec{j} + 7 \sin^2 t \vec{k}
%\]

%\vfil

\item Find the parametric equations for the tangent line to the
curve defined by
\[
x = t^3-t, y = t^6+t^2+1, z = \frac{1}{2}t^2+5t
\]
at the point $(0,1,0)$.

\newp

\item At what point does the curve $y=e^x$ have maximum curvature?

\newp

\item Find the length of the curve defined by
\[
\vec{r}(t) = \left\langle \frac{2\sqrt{2}}{3} t^{3/2},t, \frac{1}{2}t^2 \right\rangle,
0 \le t \le 4
\]

\newp

\item Find the curvature of the curve defined by
\[
\vec{r}(t) = \left\langle \frac{1}{2}t^2-2t,t^2-t,t^2+t \right\rangle
\]
at the point $t=0$.






\end{enumerate}




\end{document}


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