Consider the vector function F = (xy, -xy, z) (a) Show that F has unit divergence....

Transcribed Image Text:

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