\input epsf
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\vtop{\hsize=3.5in \noindent {\bf Problem statement} a) If
$f(x,y,z)=x^2+y^2$, compute $\nabla f(x,y,z)$.  What are $f(2,1,2)$
and $\nabla f(2,1,2)$?

\medskip

\noindent b) If $g(x,y,z)=x^2+y^2+z^2-xy-yz$, compute $\nabla g(x,y,z)$. 
What are $g(2,1,2)$ and $\nabla g(2,1,2)$?

\medskip

\noindent c) The point $(2,1,2)$ is on both the surface $x^2+y^2=5$, a
circular cylinder whose axis of symmetry is the $z$-axis, and the
surface $x^2+y^2+z^2-xy-yz=5$, an ellipsoid tilted with respect to the
coordinate axes. The surfaces intersect in a curve. The surfaces and
the curve are shown in the picture to the right. Find a vector tangent
to that curve at $(2,1,2)$. The answers to a) and b) can be used here.

}


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