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%  Spring semester, 2024, Wei-Cheng Wang.


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\begin{document}


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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 02
\normalsize
\end{center}

\noindent

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

\begin{enumerate}

%  8.8: Improper integrals.
\item
Section 8.8:
Study the comparison Theorems (Theorem 2, Theorem 3) used to decide convergence/divergence
of improper integrals. Sample problems: section 8.8, problems 35-64.

%  8.8: Improper integrals.
\item
Section 8.8:
Study how to determine convergence/divergence of an improper integral
with multiple `improper' parts,
such as the domain contains both $x \to \pm \infty$,
and/or points of discontinuity within the domain.

% 10.1: Sequences.
% \item 
% Section 10.1: 
% Study and memorize the definition of convergence of a sequence, including the
% cases of the limit being $\pm \infty$.
% Sample problems: Lecture 02, page 2-3. Section 10.1, problem 125.

% 10.1: Sequences.
\item 
Section 10.1: 
Review the techniques of finding the limit of a sequence
including Sandwich Theorem for sequences,
L'H\^{o}pital's Rule, Theorem 2-4 and related examples.

Sample problems: 
The examples in Theorem 5.
Also memorize the results for future applications. 

\item 
Section 10.1: (Parts to skip) 

Skip the "Recursive Definition" part.

Skip the "Bounded Monotone Sequences" part.
We will come back to it later.

% 10.2: Infinite series
\item 
Section 10.2:

Study the definition of sum of a series (as a limit).

Study the $n$-th term test on its application
(Section 10.2, problem 31, 33, 41) and its proof.

Review conditions on convergence/divergence of a geometric series
(Section 10.2, problem 71, 78).

Review the technique of telescoping sum
% (Lecture 02, page 14; Section 10.2, problem 43, 65).
(Section 10.2, problem 43, 65).
\end{enumerate}

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