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\begin{document}

\textbf{Math 210}
\hfill
\textbf{Fall 2016}\\
\begin{center}
\textbf{\Large Worksheet - Week 5}
\end{center}
$ $ 
\begin{enumerate}
\item For the following surfaces, find $xy-, yz-$, and $xz-$traces, and sketch a surface.
\begin{enumerate}
\item $x^2-\frac{y^2}{4}=1$
\item $\frac{x^2}{4}+y^2-\frac{z^2}{9}=4$
\item $x^2+y^2=z^2$
\end{enumerate}

\item Sketch the surface defined by $z=-\sqrt{x^2+y^2}$. What is different from the surface defined by $z^2=x^2+y^2$?

\item Graph several level curves of the following functions using the given window. Label at least two level curves with their $z$-values.
\begin{enumerate}
\item $z=\sqrt{4-x^2-y^2}$; $[-3,3] \times [-3,3]$
\item $z=xy$; $[-2,2] \times [-2,2]$
\end{enumerate}


\item Calculate the limit of multivariable functions or show that the limit does not exist.
\begin{enumerate}
\item $\lim\limits_{(x,y)\to (0,2)} \frac{4x^2-4xy+y^2}{2x-y}$
\item $\lim\limits_{(x,y)\to (0,0)} \frac{x^2+3y^4}{x-y^4}$
\item $\lim\limits_{(x,y,z)\to (-1,1,1)} \frac{xz+2x+y^2z+2y^2}{x+y^2}$
\end{enumerate}




\end{enumerate}
\end{document}

