
%  This is a LaTex file.

%  Homework for the course "Calculus II", 
%  Spring semester, 2024, Wei-Cheng Wang.

% \documentclass[12pt]{article}
% \usepackage{amsmath}
% \usepackage{amsfonts}
% \usepackage{amssymb}
\documentclass[12pt]{article}
\usepackage{amsmath,amsfonts,amssymb,amstext}
\DeclareSymbolFontAlphabet{\Bbb}{AMSb}


%          The page format, somewhat wider and taller page than in art12.sty.

\topmargin  0.1in \headsep 0in \textheight 8.9in \footskip 0.6in
\oddsidemargin 0in  \evensidemargin 0in  \textwidth 6.5in

\def\V{\mathcal V}
\def\L{\mathcal L}
\def\S{\mathcal S}
\def\T{\mathcal T}
\def\U{\mathcal U}
\def\A{\boldmath A}
\def\M{\boldmath M}
\def\l{\mbox{\boldmath $l$}}
\def\r{\mbox{\boldmath $r$}}
\def\v{\mbox{\boldmath $v$}}
\def\ds{\displaystyle}
\def\limi{\displaystyle{\lim_{n\to \infty}}}
\def\sumi{\displaystyle{\sum_{n=1}^\infty}}
\def\sumzi{\displaystyle{\sum_{n=0}^\infty}}
\def\sumk{\displaystyle{\sum_{n=1}^k}}
\def\sumkzi{\displaystyle{\sum_{k=0}^\infty}}
\def\limk{\displaystyle{\lim_{k\to \infty}}}


%          The page format, somewhat wider and taller page than in art12.sty.

\topmargin -0.1in \headsep 0in \textheight 8.9in \footskip 0.6in
\oddsidemargin 0in  \evensidemargin 0in  \textwidth 6.5in

\begin{document}

%          The title and header.

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

\begin{center}
\large
Homework 07   
\normalsize
\end{center}

\vspace{.3in}

%           The questions!

\begin{enumerate}

\item % 14.2: Limit and Continuity in Higher Dimensions.
% Section 14.2: Problems 41, 43, 49, 51, 57, 61, 63.
Section 14.2: Problems 41, 43, 48, 49, 51, 57, 61, 63, 67.

Hint for problems 61, 63: Read `Changing Variables to Polar Coordinates'.
on page 823.
Note that in equation (1), page 823,
$``|r|<\delta"$ should be $``0<|r|<\delta"$ instead.

Hint for problem 49: Find two paths that pass through $(1,1)$.


\end{enumerate}

\end{document}
