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\centerline
{
\bf ``QUIZ'' for Dec. 7, 2009
}
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{\bf NAME:} (print!) $\underline
{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
{\quad \bf Section:}
$\underline{\quad\quad\quad}$

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{\bf E-MAIL ADDRESS:} (print!) 
$\underline
{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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Let
$$
F(x,y,z) =
$$
$$
\langle \, \cos(\sqrt{1+x^7} +zy^9) \quad , \quad \tan(x^7+y^2+1/z) 
\quad , \quad
\tan^{-1} (e^{xyz}+\cos^6(x^8-y+3z) \, \rangle \quad ,
$$
and let $\langle P,Q,R \rangle = curl \,\, {\bf F}$. Compute
$$
{{\partial P} \over {\partial x}}+
{{\partial Q} \over {\partial y}}+
{{\partial R} \over {\partial y}} \quad .
$$
Be sure to explain everything.

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{\bf 2.} Calculate the surface integral \hfill\break
$\int\int_{S} {\bf F} \cdot d \, {\bf S}$, where
$$
{\bf F}(x,y,z)= \langle \, 2x+y+z \, , \, x+2y+z \, , \, x+y+2z \, \rangle
$$
where $S$ is the surface of the box bounded by
the planes 
$x=0$, $x=1$, $y=0$, $y=4$, $z=0$, $z=5$.

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