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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 06
\normalsize
\end{center}

\noindent

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

\begin{enumerate}

\item % 14.2: Limit and Continuity in Higher Dimensions.
Section 14.2:
Review and memorize definitions of limit 
(page 816 and page 823, in polar coordinates)
and continuity (using $\varepsilon$ and $\delta$) for functions
of two or more variables. 
Note that in equation (1), page 823,
$``|r|<\delta"$ should be $``0<|r|<\delta"$ instead
(or you can write $``0<r<\delta"$ without the absolute value). 

Review the examples where the "Two-Path Test for Nonexistence of a Limit"
is applicable.

Keep in mind that, one dimensional test (limit along a path) 
either shows that the two dimensional limit does not exist
(two different limits on two different paths),
or is inconclusive (all limits are the same on all the paths
you tested does not mean the two dimensional limit exist).


\end{enumerate}

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