$(4)$ Let $F=($:$x^2+y,cos(y)+x,2z$:$)$ be a vector field.

$($a$)$ Find the Curl$(F)$ and Div$(F).$

$($b$)$ Find a parametrization for the top hemisphere of the sphere of radius $16$ centered about the origin.

$($c$)$ Compute the work done by the vector field $F$ in moving a particle around the boundary of the above surface in the counterclockwise direction. $($You may assume either orientation$)$

$(30$ pts$)$