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\textbf{Math 225: Calculus III}
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\textbf{Quiz 4}\quad \textsl{October 4, 2001}
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1. Suppose $F(x,y)$ is a function of $x$ and $y$, and $x$ and $y$ are
functions of the variables $u$ and $v$. Given the following conditions
  \[ \begin{array}{llll}
  x(1,2)=3, &\frac{\partial F}{\partial x}(3,4)=11, &
  \frac{\partial x}{\partial u}(1,2)=-2, &
  \frac{\partial x}{\partial v}(1,2)=7, \\
  \\
  y(1,2)=4, & \frac{\partial F}{\partial y}(3,4)=15, &
  \frac{\partial y}{\partial u}(1,2)=6, &
  \frac{\partial y}{\partial v}(1,2)=-8,
  \end{array}
  \]
find $\frac{\partial F}{\partial u}$ and $\frac{\partial F}{\partial v}$
when $u = 1$ and $v = 2$.

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2. Find the equation of the plane tangent to the surface defined by
$z^5 - x^3 y^2 + x z - y = 0$ at the point $(1,1,1)$.

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