Question: Consider the vector function F = (4xy, -4xy, 2z) (a) Show that V-F = 2. (b) Make use of the Divergence theorem and cylindrical-like

Consider the vector function F = (4xy, -4xy, 2z) (a) Show that V-F = 2. (b) Make use of the Divergence theorem and cylindrical-like coordinates x = 4r cos 0 y = 3r sin z = z [1 mark] [3 marks] dzdxdy = 12rdzdrde to evaluates F. n dS where S is the positively-oriented surface of the ellipsoid x y + +22 16 9 = 1 Note that -r rdr = =-1 (1-2) Ix It is not sufficient to simply quote the volume formula for an ellipsoid Y 3

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