Suppose $\mbox{div }\vec F = xyz^{2}$.

(a) Find $\mbox{div }\vec F$ at the point $(3,1,4)$. [Note: You are given $\mbox{div }\vec F$, not $\vec F$.]
$\mbox{div }\vec F\bigg|_{(3,1,4)} =$

(b) Using your answer to part (a), but no other information about the vector field $\vec F$, estimate the flux out of a small box of side $0.2$ centered at the point $(3,1,4)$ and with edges parallel to the axes.
$\mbox{flux} \approx$

(c) Without computing the vector field $\vec F$, calculate the exact flux out of the box.
$\mbox{flux} =$