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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 03
\normalsize
\end{center}

\noindent

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

\begin{enumerate}

% 10.3: The Integral Test
\item
Section 10.3:
Study the statement and proof of the integral test (Theorem 9)
and Bounds for the Remainder in the Integral Test (page 611).
Practice with examples. In particular,
derive and memorize the convergence/divergence of a $p$-series.
%% 

% 10.3: The Integral Test
% \item
% Section 10.3:
% Study Bounds for the Remainder in the Integral Test (page 611).
% add Section 10.3: problem 51 next time.

% (see Example 6)
% 10.4: Comparison Tests
\item 
Section 10.4:
Study The Comparison Test and The Limit Comparison Test.
Focus on how to find a suitable target series to compare with.
In almost all cases, the target series can be found from
the geometric series, the $p$-series or series 
of the form $\displaystyle{ \sum_{n=1}^\infty f(n)}$ where
$\displaystyle{ \int_1^\infty f(x) \, dx}$ is easy to compute.

% 10.5: Absolute Convergence, The Ratio and Root Tests.
\item
Section 10.5:
Study the Absolute Convergence Test,
the Ratio Test and the Root Test.
Practice each of these tests with some examples
(such as section 10.4: problems 17-44).
% \item
% Study the proof of 
% the Ratio Test and the Root Test.
% \end{enumerate}

\end{enumerate}

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