% HMC Math dept HW template example
% v0.04 by Eric J. Malm, 10 Mar 2005
\documentclass[12pt,letterpaper,boxed]{hmcpset}

% set 1-inch margins in the document
\usepackage[margin=1in]{geometry}

% include this if you want to import graphics files with /includegraphics
\usepackage{graphicx}

% include this to have lists enumerated by letters
\renewcommand{\labelenumi}{(\alph{enumi})}

% info for header block in upper right hand corner
\name{}
\class{Math 315}
\assignment{Homework \#12}
\duedate{5/19/2017}

% macros
\newcommand{\NN}{\mathbb{N}}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\II}{\mathbb{I}}

\begin{document}

\problemlist{Abbott: 4.2.7, 4.2.8}

\begin{problem}[4.2.7]
Let $g \colon A \to \RR$ and assume that $f$ is a bounded function on $A$, in the sense that there exists $M > 0$ satisfying $|f(x)| \leq M$ for all $x \in A$.

Show that if $\lim_{x \to c} g(x) = 0$, then $\lim_{x \to c} g(x) f(x) = 0$ as well.
\end{problem}

%\begin{solution}
%
%\end{solution}

\newpage

\begin{problem}[4.2.8]
Compute each limit or state that it does not exist. Use the tools developed in this section to justify each conclusion.
\begin{enumerate}
\item $\lim_{x \to 2} \frac{|x-2|}{x-2}$
\item $\lim_{x \to 7/4} \frac{|x-2|}{x-2}$
\item $\lim_{x \to 0} (-1)^{[[1/x]]}$
\item $\lim_{x \to 0} \sqrt[3]{x}(-1)^{[[1/x]]}$
\end{enumerate}
\end{problem}

%\begin{solution}
%
%\end{solution}


\end{document}
