 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-1/10g/c/solution

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

For every

(x, y) \in [1, 2]^{2}

f_{n} (x, y) ⟶ \frac{x}{y} .

Moreover,

\frac{1 + n x}{1 + n y} - \frac{x}{y} = \frac{∣ y - x ∣}{y ( 1 + n y )} \leq \frac{1}{n + 1} .

The bound is independent of

(x, y)

and tends to zero, so

f_{n} \to [(x, y) \mapsto x / y] uniformly .

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