 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/9/a/solution

For

r > 0

g (r) = 1/ r

\nabla \frac{1}{r} = - \frac{r}{r ^{3}} .

Equivalently each component is

- x_{j} / r^{3}

by differentiating

r^{2} = x^{2} + y^{2} + z^{2}

. The origin is excluded from the function's domain.

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