This question concerns the vector field F = -xy²i-r²yj + z(x² + y²) k. (a) Calculate the divergence of F. Use the divergence theorem to show that the flux of F over any closed surface is equal to zero. (b) A cylinder of height h and radius R has its base in the xy-plane and its axis of symmetry along the z-axis, as shown in the diagram below. X O R h SE Calculate the flux of F over the curved portion S of the surface of the cylinder by using the result of part (a) to relate the flux of F over S to the flux of F over the flat top surface T and the flux of F over the flat bottom surface B. (Hint: Calculating the flux of F over T and B is easier in cylindrical coordinates.) yus od bless (s

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