Answer Happy

(a) Find divF and curlF for the vector field F(x,y,z)=xyzi+5zj+yz2k. (b) Use Green's Theorem to evaluate ∮C​(x2−y)dx+xdy where C is the circle x2+y2=9 oriented counterclockwise. (c) Use the Divergence Theorem to find the outward flux Φ of the vector field F(x,y,z)=(x−z)i+(y−x)j+(z−y)k across the cube with vertices (0,0,0),(2,0,0),(2,0,2),(0,0,2),(0,2,2),(2,2,2),(2,2,0), and (0,2,0)