 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-4/7e/b/i/solution

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

For

M = max {∣ s ∣, ∣ t ∣, 1}

∣ s^{j} - t^{j} ∣ = ∣ s - t ∣ \sum_{l = 0}^{j - 1} s^{j - 1 - l} t^{l} \leq j M^{j - 1} ∣ s - t ∣.

Consequently the polynomial

f

∣ f (s) - f (t) ∣ \leq A M^{d - 1} ∣ s - t ∣, A = j = 1 \sum d j ∣ α_{j} ∣.

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