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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 126 C - Spring 2009 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 21, 2009 \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
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 

\begin{enumerate}

\item Find the equation of the plane $P$ containing the point (1,2,3) which is parallel
to the plane containing the points (0,3,4), (3,2,1), and (5,4,2).

\vfil \vfil

\item Give an example of a line contained in plane $P$.

\end{enumerate}

\newp

\item Thoroughly describe the surface defined as the set of points which are twice as far from the $z$-axis
as they are from the $xy$-plane.  

\newp

\item The curve defined by the polar equation $r=\sin^2 \theta$ is shown in the figure below.

\epsfig{file=126mt1-1.ps, 
 width=7cm,
 angle=270 }

\begin{enumerate}
\item Find the slope of the tangent line to the curve at the point where $\dsps \theta=\frac{\pi}{4}$.
\vfil
\item What is the maximum $x$-coordinate for a point on this curve?
\end{enumerate}

\newp

\item Where does the line which passes through the points $(0,5,-3)$ and $(1,2,8)$
intersect the plane $x-3y+4z=11$?

\newp

\item Consider the curve with the vector equation
\[
\vec{r}(t)= \langle t^2, 2t^2-t, 3t-t^2 \rangle
\]
Is there a point on this curve where the tangent line is parallel to the
vector $\langle 20, 38, -14 \rangle$? If so, find the point.  If not, explain why.

\end{enumerate}

\end{document}


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