 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/2i/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Apply exactness to

ℓ_{j}^{2}

A_{j} = \sum_{k} A_{k} ℓ_{j} (t_{k})^{2} = \int ℓ_{j}^{2} > 0

. Applying it to 1 gives

\sum A_{j} = 2

. For continuous

f

and any admissible

p

j \sum A_{j} f (t_{j}) - \int f \leq j \sum A_{j} ∥ f - p ∥_{\infty} + 2∥ f - p ∥_{\infty} = 4∥ f - p ∥_{\infty} .

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