 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/3/a/ii/solution

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

The

z

component of the curl is

\partial_{x} F_{y} - \partial_{y} F_{x} = e^{x + y} - x e^{x y}

, which is not identically zero; at the origin it is one. Hence the field is not conservative on $R^{3}$ and has no global scalar potential.

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