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\title{\vspace*{-1.5in}\textbf{Taylor Polynomials}\\\normalsize (Thanks to Faan Tone Liu)}
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\maketitle
%\underline{Math 1300-400: Quiz 1}
\lhead{Math 2300-007: Calculus II}
\rhead{March 16, 2018}
\chead{Taylor Polynomials}
\vspace{-.8in}
\noindent
\textbf{Key Points:}
\begin{itemize}
\item The formula for $T_n(x)$, the $n$th degree taylor polynomial for $f(x)$ centered at $x=a$ is:\begin{center}\framebox{\begin{minipage}[t]{.7\textwidth}\vspace*{1in}\hspace*{3cm} \end{minipage}}\end{center}

\item Other notes:\vskip1in
\end{itemize}
\noindent
\textbf{Examples:}\vskip12pt
\begin{enumerate}
\item \begin{enumerate}[(a)]
\item Find $T_6(x)$ the 6th degree Taylor Polynomial for $f(x) = \cos(x)$ centered at $a = 0$. \vfill\vfill
\item Use your $T_6(x)$ to estimate $\cos(5^\circ)$.\vfill
\end{enumerate}
\newpage
\item What is $T_n(x)$, the $n$th degree Taylor polynomial for $f(x) = \ln(x)$ centered at $a = 1$?\vfill\vfill\vfill
\item How could you estimate $\ln(1.6)$? What could you to do improve your estimate?\vfill\vfill
\end{enumerate}
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