 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-3/2e/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

x \mapsto x^{2}

is not uniformly continuous on

R

. Take

x_{n} = n

and

y_{n} = n + 1/ n

. Then

∣ x_{n} - y_{n} ∣ \to 0

, whereas

∣ y_{n}^{2} - x_{n}^{2} ∣ = 2 + \frac{1}{n ^{2}} ⟶ 2.

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