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\noindent
\vfil \noindent
\large
\hfil Math 126 C - Winter 2006 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil January 31, 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
7 & 10 & \\ \hline
Total & 70 & \\ \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 Find the 2nd-degree Taylor polynomial, $T_2(x)$ for the
function $f(x)=\ln(\ln x)$ based at $x=e$.

\vfil

\item Approximate the integral 
\[
\int_0^{2} \sin(x^2) \, dx
\]
by using the first four non-zero terms of a Taylor series.
Given a decimal approximation of your result.

\newp

\item Write out the first four terms of the Taylor series for the
function
\[
f(x) = \frac{1}{1+5x} + \frac{1}{3+x}
\]

\vfil \vfil


\item Find the angle between the vectors $\vec a = <-3,4,1>$ and
$\vec b = <3,1,1>$.  Give a decimal value for the angle.

\newp

\item Suppose the vector $<x,3,2>$ is orthogonal to the 
vector $<2,3,x>$.  Find $x$.

\vfil

\item Find the equation of the plane through the three points
$(-3,4,0)$, $(1,7,-3)$ and $(2,-5,3)$.

\newp

\item Find the equation of the plane containing the line of 
intersection of the two planes
\[
x+y-z=3 \mbox{\hskip0.1in and \hskip0.1in} 2x-3y+4z=5
\]
and the point $(-2,7,3)$.



\end{enumerate}




\end{document}


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