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\noindent
\vfil \noindent
\large
\hfil Math 126 C - Spring 2010 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 20, 2010 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hrulefill
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\vfil
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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}
}
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\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 Determine whether or not the line
\[
x = 4t-7, y= 5t-16, z=-2t+14
\]
and the line
\[
x =t+7, y=-3t-7, z=7t+22
\]
intersect.  If they do, give the point of intersection.

\newp

\item Let $P$ be the plane containing the points
$(1,5,2), (2,3,6)$ and $(7,4,1)$.  
Find the intersection of $P$ with the $y$-axis.

\newp

\item Consider the polar curve
\[
r = \sin \theta \tan \theta.
\]

\begin{enumerate}

\item Find an equivalent cartesian equation for this curve.

\vfil

\item The curve has a vertical asymptote.  What is the equation
of the asymptote?

\end{enumerate}

\newp

\item Let $S$ be the surface in 3D consisting of all points which are twice
as far from the $z$-axis as they are from the $x$-axis.

\begin{enumerate}
\item Give an example of a point on this surface, other than the origin.
\vfil
\item Give an equation for this surface.
\vfil
\item Describe this surface (if it is a quadric surface, categorizing it (i.e., 
ellipsoid, eliptic paraboloid, etc.) is sufficient).
\end{enumerate}


\newp

\item Let $P$ be the point in the first quadrant on the curve
\[
x = \cos t, y = \csc t
\]
such that the tangent line to the curve at $P$ passes
through the origin.  Find the coordinates of $P$.

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\end{enumerate}


\end{document}


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