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\centerline
{
\bf ``QUIZ'' for Nov. 30, 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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{\bf 1.} 
Determine whether or not the vector field is conservative.
If it is, find a function $f$ such that ${\bf F}=\g f$.
$$
{\bf F}(x,y,z)= 
(3x^2y^3z^3+yz)\, {\bf i}+ 
(3x^3y^2z^3+xz) \, {\bf j}+ (3x^3y^3z^2+xy) \, {\bf k}
$$

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{\bf 2.} 
Evalute
$$
\int_C \,\, 5y \, dx + 10x \, dy \quad ,
$$
where $C$ is the closed curve consisting of the boundary of the rectangle
$$
\{ \, (x,y) \, | \, 0 \leq x \leq 1 \quad , \quad 0 \leq y \leq 1 \, \} .
$$


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