 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/26j/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Write

h_{x} = \partial_{x} h

and

h_{y} = \partial_{y} h

. Since

ϕ_{x} = (1, 0, h_{x}), ϕ_{y} = (0, 1, h_{y}),

I^{S} = (1 + h_{x}^{2} h_{x} h_{y} h_{x} h_{y} 1 + h_{y}^{2}) .

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