\hfill \thepage} %} \input{tcilatex} \begin{document} MA116\qquad \qquad \qquad \qquad \qquad \qquad \qquad TEST\ III\qquad \qquad \qquad \qquad \qquad 4/6/98 \vspace{1pt} -------------------------------- Name \vspace{1pt} SHOW\ \underline{ALL}\ WORK \vspace{1pt} 1. Let $\overrightarrow{v}=2\overrightarrow{i}-\overrightarrow{j}+2% \overrightarrow{k}$ ;$\overrightarrow{w}=3\overrightarrow{i}-4% \overrightarrow{k}$ \ \ \ a) Find the angle between $\overrightarrow{v}$ and \ $\overrightarrow{w% }$ \ \ b) Find the area of the parallelogram spanned by $\overrightarrow{v}$ and $\overrightarrow{w}$ \ \ c) Find $proj_{\overrightarrow{w}}\overrightarrow{v}$\newpage 2. a) Let $z=f(x,y).$ Find $\frac{\partial x}{\partial y}$ if $% 3xyz+2e^{yz}-3y^{2}\cos x=0.$ \ \ b) Find the equation of the plane tangent to $f(x,y)=x^{y}$ at $(2,3).$% \newpage 3. Find the equation of the plane through (3,2,-1) and (1,-1,2) which is parallel to the line $\frac{x-1}{3}=\frac{y+1}{2}=\frac{z}{-2}.$ \newpage 4. a) What is the largest possible domain of \ $f(x,y)=\ln (x^{2}+y^{2}-4)$ ? \vspace{1pt} \vspace{1pt}\qquad \qquad \qquad \qquad \qquad \qquad \qquad \ b) show that $f(x,y)=$ $\left\{ \begin{array}{l} \frac{x^{2}-y^{2}}{x^{2}+y^{2}\text{ \ }}\ \ (x,y)\neq (0,0) \\ \\ \text{ \ }0\ \ \ \ \ \ (x,y)=(0,.0) \end{array} \right. $\ \qquad \qquad \vspace{1pt} \vspace{1pt} is not continuous at $(0,0).$\newpage \end{document}