 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-2/15/a/ii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

The curl is

\nabla \times F_{2} = (2 z, 3 z^{2}, 0)

, which is not identically zero. A gradient of a smooth scalar potential has zero curl, so

F_{2}

is not conservative on

R^{3}

 New to topics? Read the docs here!