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\noindent
\vfil \noindent
\large
\hfil Math 126 C - Autumn 2010 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil October 26, 2010 \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 
 

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{\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 the angle between the vectors $\langle 3,4,-1 \rangle$ and
$\langle 5,2,8 \rangle$.

\newp

\item Find the plane containing the line 
\[
x=3-t, y=2-\frac{1}{2}t, z=6+2t
\]
and the point $(4,-5,2)$.

\newp

\item Where does the plane
\[
3x-y+5z=12
\]
intersect the line
\[
x=5t+1, \, y=4t+2, \, z=5t-1 ?
\]

\newp

\item Find the arc length of the curve
\[
x=t^2, \, y=\frac{2}{3}t^3
\]
for $0 \le t \le 5$.

\newp

\item Let $C$ be the polar curve
\[
r=\theta^2.
\]

\begin{enumerate}
\item $C$ intersects the line $y=x$ infinitely many times.  
Give the Cartesian coordinates of one point of intersection which is not the origin.
\vfil

\item Find the slope of the tangent line to $C$ at the point you gave in (a).
\end{enumerate}

\vfil \vfil



\end{enumerate}


\end{document}


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