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\title{\vspace*{-1.5in}\textbf{\S8.7: Taylor Series}\\\normalsize (Created by Faan Tone Liu)}
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\maketitle
%\underline{Math 1300-400: Quiz 1}
\lhead{Math 2300-013: Calculus II}
\rhead{March 21, 2018}
\chead{\S8.7: Taylor Series}
\vspace{-.8in}
\noindent
\textbf{Key Points:}
\begin{itemize}
\item The Taylor Series for $f(x)$ centered at $x=a$ is given by\vskip1.5cm
\item If $f(x)$ has a power series representation, then it is the Taylor Series.
\item A Taylor Series centered at $x=0$ is also called a MacLauren Series.
\end{itemize}
\noindent
\textbf{Examples:}\vskip12pt
\begin{enumerate}
\item Find the Taylor Series for $f(x) = e^x$ about $x=0$\vfill
\item Find the Taylor Series for $f(x) = \sin(x)$ about $x=0$\vfill
\item Find the Taylor Series for $f(x) = \cos(x)$ about $x=0$\vfill\newpage
\item Find the Taylor Series for for $f(x) = \ln(1+x)$ about $x=0$\vfill
\item Evaluate $\displaystyle\int \frac{e^x-1}{x}\,dx$ using infinite Series. \vfill
\end{enumerate}
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