4 Problem 4.4 1 Verify that the following vector field is conservative and then find the corresponding potential. F=2xyi-(x+2yz)j + (y² + 4)k. Problem 4.5 5 Compute the surface integral s F-ndo. F = xyi + Zj+yk. The surface is the curved exterior side of the cylinder y² + 2 = 9 in the first octant bounded by x=0, x= 1, y = 0 and z=0. Problem 4.8 4 Verify the divergence theorem using the following vector field and volume. F = xi + yj + zk and the volume V is the cylinder defined by the surfaces + y = 1, z = 0 and z= 1.
4 Problem 4.4 1 Verify that the following vector field is conservative and then find the corresponding potential. F=2xyi-(x+2yz)j + (y² + 4)k. Problem 4.5 5 Compute the surface integral s F-ndo. F = xyi + Zj+yk. The surface is the curved exterior side of the cylinder y² + 2 = 9 in the first octant bounded by x=0, x= 1, y = 0 and z=0. Problem 4.8 4 Verify the divergence theorem using the following vector field and volume. F = xi + yj + zk and the volume V is the cylinder defined by the surfaces + y = 1, z = 0 and z= 1.
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Problem 4.4 1
Verify that the following vector field is conservative and then find the corresponding
potential.
F = 2xyi-(x + 2yz)j + (y² + 4)k.
Problem 4.5 5
Compute the surface integral s F-ndo. F = xyi+ Zj+ yk. The surface is the curved
exterior side of the cylinder y + z = 9 in the first octant bounded by x= =0, x= 1, y = 0
and z= 0.
Problem 4.8 4
Verify the divergence theorem using the following vector field and volume.
F = xi+yj + zk and the volume V is the cylinder defined by the surfaces + y² = 1,
z = 0 and z= 1.
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