 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/8/b/solution

For the divergence in Cartesian coordinates, differentiate each component with respect to its own coordinate:

\nabla \cdot G = 2 x z + 3 y^{2} z + 0 = z (2 x + 3 y^{2}) .

The third component contributes zero because it is independent of

z

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