 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-1/11e/b/solution

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

Put

h (x) = ∣ f (0) ∣ + \int_{0}^{x} g (t) ∣ f (t) ∣ d t

. Then

∣ f ∣ \leq h

and

h' \leq g h

. If

h > 0

(lo g h)' \leq g

; integration gives

h (x) \leq h (0) e^{\int_{0}^{x} g}

. For

f (0) = 0

, apply the same argument after adding

ε

and let

ε ↓ 0

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