Suppose vec$(grad)*vec(F)=xy{z}^2.$

$($a$)$ Find vec$(grad)*vec(F)$ at the point $(5,4,4).[$Note: You are given vec$(grad)*vec(F),$ not vec$(F).]$

$(vec(grad)*vec(F))(5,4,4)=$

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$($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 $0\mathrm{.}15$ centered at the point $(5,4,4)$ and with edges parallel to the axes.

flux ~~

$($c$)$ Without computing the vector field vec$(F),$ calculate the exact flux out of the box.

flux $=$

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