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\noindent {\bf Problem statement} Suppose we know that $x$, $y$, and
$z$ are always related by the equation

$$ z^2 + 3xy^3 z + 4x^2 y = 11$$ 

\noindent The point $P= (2, 1, -1)$ is on the surface defined by this
equation.

\medskip

\noindent a) Do either i) or ii):

\medskip

\item{i)}Compute $U = {{\partial z}\over{\partial x}}$ . What is the
value of $U$ at $P$? 

\smallskip

\item{ii)}Compute $V = {{\partial z}\over{\partial y}}$ . What is the
value of $V$ at $P$?

\medskip

\noindent b) If you did i) above, do i) below. If you did ii) above,
do ii) below.

\medskip

\item{i)}Compute $S ={{\partial U}\over{\partial y}}$ . What is the
value of $S$ at $P$?

\smallskip

\item{ii)}Compute $T ={{\partial V}\over{\partial x}}$ . What is the
value of $T$ at $P$?










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