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\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{enumerate}

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\begin{document}

\begin{center}
{\Large Warm-Up Problems and Lecture Problems

April 25, 2003}
\end{center}

\[
\begin{array}{|rcl|}
\hline 
&& \\
%\begin{eqnarray*}
e^x & = & 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!}+ \frac{x^4}{4!} + \cdots \\
\sin x & = & x + \frac{x^3}{3!} + \frac{x^5}{5!}+ \frac{x^7}{7!} + \cdots \\
\cos x & = & 1 + \frac{x^2}{2!} + \frac{x^4}{4!}+ \frac{x^6}{6!} + \cdots \\
\frac{1}{1-x} & = & 1 + x + x^2 + x^3 + x^4 + \cdots \\
\tan^{-1} x & = & x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots \\
\ln(1-x) & = & -x - \frac{x^2}{2} - \frac{x^3}{3} - \frac{x^4}{4} - \cdots \\
\ln x & = & (x-1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + \cdots \\ 
&& \\
%\end{eqnarray*}
\hline
\end{array}
\]

\begin{enumerate}

\item  Which Taylor polynomial should you use to approximate $\sin(\Pi/5)$ to within $0.001$?
\inch

\lecture

\item  How accurate does the Taylor polynomial of degree $5$, $T_5(x)$, approximate $\sin(\pi/5)$?
\inch

\item For what values of $x$ does the Taylor polynomial of degree $5$ approximate $\sin(x)$ to within
	$0.001$?
\end{enumerate}


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