 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/ii/paper-2/2f/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-05

h (u) = g (1/ u)

for

0 < u \leq 1

and

h (0) = 0

h

[0, 1]

R_{n}

with

sup_{0 \leq u \leq 1} ∣ R_{n} (u) - h (u) ∣ \to 0

. Since

t \mapsto 1/ t

[1, \infty)

onto

(0, 1]

t \geq 1 sup ∣ R_{n} (1/ t) - g (t) ∣ ⟶ 0.

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