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%  Spring semester, 2024, Wei-Cheng Wang.


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\noindent
{\scriptsize Calculus II, Spring 2024 
(http://www.math.nthu.edu.tw/\~\,wangwc/)} \hfill 

\noindent
{\scriptsize Thomas' Calculus Early Transcendentals 13ed} \hfill 

\begin{center}
\large
Study guide for quiz 05
\normalsize
\end{center}

\noindent

\vspace{-.3cm}
Quiz problems include both the lecture contents and homework problems.

\begin{enumerate}


% 10.7: Power series.
\item
Section 10.7:

Study multiplication and division of two power series.

Study the statements of 
Term by Term Differentiation Theorem
and
Term by Term Integration Theorem.
Use them to derive the power series representation of 
$\ln (1\pm x) $ and $\tan^{-1}(x)$.

% 10.8: Taylor and MacLaurin Series.
\item
Section 10.8:

Memorize the definitions of Taylor polynomial of order $n$ generated by $f$
at $x=a$ 
and Taylor series generated by $f$ at $x=a$ (i.e. $T_{f,a}(x)$).
Study how to generate $T_{f,a}(x)$ and
why it is possible that $T_{f,a}(x) \neq f(x)$ on $x\neq a$.
Study how to generate $T_{f,a}(x)$ alternatively using Theorem A in Lecture 09.

\end{enumerate}

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