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- Verify the divergence theorem for F= 3i+xyj+xk taken over the region bounded by z = 4-y^2 , x=0 and the xy-plane.Verify the divergence theorem for A = 2xyi -yz 2 j + xzk taken over the regionbounded by x = 0, y =0, z = 0 , x = 2, y = 1 and z = 3.Verify divergence theorem for f=x2i+zi+yzk taken over the cube bounded by x=0,x=1,y=0,y=1,z=0 and z=1
- Calculate the divergence of D at the point specified: D = (1/y2) [ 4xyz2 ax + xy2 ay – 10xy3 az] at P(-1,3,1)Verify the divergence theorem for F=3i + xy j + x k taken over the region bounded by z = 4 - y^2 , x = 0 , x = 3 , and the xy-plane.Use the divergence theorem to solve following a) F=xi-yj bounded by the planes z=0 and z=1 and the cylinder x^2+y^2=a^2 b) F=xi+yj+(z^2 +1) with the same bounds as part a.
- Verify the divergence theorem for F = 3 i+ xy j + x k taken over the region bounded by z = 4 − y2, x = 0, x = 3, and the xy-plane.use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the region cut from the first octant by the plane y+z=4 and the elliptical cylinder 4x^2+y^2=16Use the divergence theorem to calculate the flux of F across S