 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-2/11f/b/i/solution

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

True. For each

n

P_{n}

such that

sup_{∣ x ∣ \leq n} ∣ P_{n} (x) - f (x) ∣ < \frac{1}{n} .

For each fixed

x \in R

, this estimate applies once

n \geq ∣ x ∣

, so

P_{n} (x) \to f (x)

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