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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 126 C - Spring 2008 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 24, 2008 \hfil \pp
\hfil Answers \hfil \pp
\normalsize

\begin{enumerate}

\item (a) $\dsps T_2(x) = \frac{1}{3}+\frac{1}{36}x+\frac{1}{432}x^2$

(b) $\dsps|f(x)-T_2(x)| \le \frac{8}{279841} = 0.00002858766... .$

\item (a) $\dsps \frac{1}{2}x^2 - \frac{1}{16}x^8 \frac{1}{336} x^{14} - \frac{1}{14400}x^{20}$

(b) $\dsps h^{(20)}(0) = -\frac{19!}{6!}$

\item $\dsps \frac{1}{2}x-\frac{1}{4}x^3+\frac{1}{8}x^5-\frac{1}{16}x^7$

\item (a) slope = $\dsps \frac{48-4\pi}{\pi(\pi-24)} = -0.540735... .$

(b) $\theta=6-\pi$

\item There are infinitely many solutions.  One is 
$\dsps \left\langle \frac{2}{\sqrt{13}},\frac{3}{\sqrt{13}},0 \right\rangle$.

\end{enumerate}

\end{document}


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