Question: We define the vector field F :R 3 R 3 by F (x,y,z):=(6x+12xy+2x 2 , 6y 2 +3e z ,6z+6ycos(2x)+7z 2 ) (a) We calculate

We define the vector field F:R3R3 by

F(x,y,z):=(6x+12xy+2x2, 6y2+3ez,6z+6ycos(2x)+7z2)

(a) We calculate divF (x,y,z).

(b) Let: A:= {(x,y,z):x2+y2z1

Using the Gaussian divergence theorem, calculate

dAFdS

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