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\textbf{Math 225: Calculus III}
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\textbf{Quiz 4}\quad \textsl{Feb. 21/23, 1995}
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\begin{enumerate}
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\item 
Find the slope of the line tangent to the intersection of the plane $y
= 3$ and the surface $z = \frac{y^2-x^2}{y^2+x^2}$ at the point
$(1,3,4/5)$.

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\problemspace
\item 
Let $w = x^2y^3$ where $x=x(u,v)$ and $y=y(u,v)$ are functions of $u$ and $v$.
Suppose $x(1,0)= -1$, $y(1,0) = 1$, and
\[
\begin{array}{cc}
\d{x}/d{u}(1,0) = 2 &\d{x}/d{v}(1,0) = 3\\
\d{y}/d{u}(1,0) = 0 &\d{y}/d{v}(1,0) =-2\\
\end{array}
\]
Compute $\d{w}/d{u}$ and $\d{w}/d{v}$ at the point $(u,v) = (1,0)$.
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