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\begin{document}
\begin{center}{\bf Math 1312} --- {\bf Worksheet \# 2}\\
{\bfseries\itshape Taylor Series}
\end{center}
\medskip\hrulefill\\
\noindent Find the Taylor series with center $x_0$ of the
functions $f(x)$ below, and compute their radii of convergence.
\begin{multicols}{2}
\begin{enumerate}
\item\ilf{f(x)=\frac{1}{x+1}\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\frac{1}{x+4}\quad x_0=2}\vspace{.1\baselineskip}
\item\ilf{f(x)=\frac{1}{x^2+4}\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\frac{1}{x^2-2x+4}\quad x_0=1}\vspace{.1\baselineskip}
\item\ilf{f(x)=\frac{x-5}{x^3-1}\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\cosh x\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\ln x\quad x_0=3}\vspace{.1\baselineskip}
\item\ilf{f(x)=\frac{1}{\sqrt{x+1}}\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\frac{1}{\sqrt{x+1}}\quad x_0=2}\vspace{.1\baselineskip}
\item\ilf{f(x)=\sqrt{x^2+4}\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\sin (x^2)\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\arcsin(x)\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\arctan(x^2)\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=x\arctan(x^2)\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\int e^{-x^2}\,dx\quad x_0=0}\vspace{.1\baselineskip}
\item\ilf{f(x)=\int\frac{\sin x}{x}\,dx\quad x_0=0}\vspace{.1\baselineskip}
\end{enumerate}
\end{multicols}
\vspace*{\fill} \vspace*{\fill} \flushright \tiny Update: January
13, 2001
\end{document}