Problem 9. (a) For the vector field u = %, find div u. Answer: For 22+ +22 >0, divu=0. (b) For the same field, find [[ u-nds where S is the sphere 22 4+ y? + 22 = 1, and n is the unit outer a normal vector to S. Answer: [[u-nds = 4r. s () Explain why the results of (a) and (b) don't contradict the Divergence Theorem. Answer: The field u is not bounded near the origin x = y = z = 0, and therefore, the Divergence Theorem is not applicable