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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 Midterm 01
\normalsize
\end{center}

\noindent

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

\begin{enumerate}

\item
Review study guide for quiz 01-05 (section 8.8, 10.1-10.8).
In particular, pay attention to the items listed in the study guides 
but did not appear in the quizzes (due to time constraint).

% 10.9: Convergence of Taylor Series.
\item
Section 10.9:
Study the statement of Taylor's Theorem (Taylor's formula). % and its proof.
Study the Remainder Estimation Theorem and application on
elementary functions.

% 10.10: The Binomial Series and Applications of Taylor Series.
\item
Section 10.10:
Memorize the binomial series and the
Taylor series of basic functions in Table 10.1 (page 658).
Study how to identify a function
from its power series representation.
Practice on variants of the functions in Table 10.1:
Perform differentiation/integration on them and see
if you can recognize the resulting new series. 
Then practice on examples such as section 10.10, problems 41-52
and Chap 10, Practice Exercises, problems 51-56.
% sec(Power series) on page 624 (Chap 10).
% page 621 (10.10)  and problems 41-56 (Power series) on page 624 (Chap 10).
% Also study the multiplication and division of two Taylor series.

% 10.10: The Binomial Series and Applications of Taylor Series.
\item
Section 10.10:
Review the application of Taylor series in 
\begin{enumerate}
\item
Indeterminate forms (section 10.10, problems 29-40
and Chap 10, Practice Exercises, problems 73-79).
\item
Approximating functions and integrals and the error estimate
(such as section 10.10, problems 15-28).

\end{enumerate}

\end{enumerate}
\end{document}
