\input{ThisWeek.tex}
\newcommand{\duedate}{Monday, September 22}
\input{../TemplateWeek/AtHomeWork.tex}
\input{Exercises.tex}

%\booltrue{teacher}

\begin{enumerate}
\item Suppose you know that $\lim_{x\rightarrow 2}g(x)=3$.  What is $\lim_{x\rightarrow 4}\frac{2+x}{g(x-2)}-3$?
\item Find $\lim_{x\rightarrow 3}4\frac{\sqrt{7-x}-2}{x-3}$.
\item Suppose that
 \[h(x)=\left\{\begin{array}{ll}
\cos x-a&\text{if }x< 0\\
x^2+2&\text{if }x\geq 0\\
 \end{array}\right.\]
is continuous everywhere.  What must $a$ be?
\item Find $\lim_{x\rightarrow 0^+}x^3\cos\frac{2}{x}$ using the Sandwich Theorem.
\item Show that there is some $x$ so that $x^2-\sin x=1$.
\end{enumerate}

\end{document}