(A)Compute the Flux of the Vector Field $\vec { F } = y \vec { i } - x \vec { j } + 5 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) z \vec { k }$

Essay

(a)Compute the flux of the vector field $\vec { F } = y \vec { i } - x \vec { j } + 5 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) z \vec { k }$ through S_a, the sphere of radius a, $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = a ^ { 2 }$ , oriented outward.
(b)Find $\lim _ { a \rightarrow 0 } \int _ { S _ { 0 } } \vec { F } \cdot d \vec { A }$ .