 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-2/7c/e/solution

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

lo g (1 + a e^{- a}) = a - \frac{3}{2} a^{2} + O (a^{3}),

we obtain

t^{*} = 3 - \frac{3}{2} a + O (a^{2}), t^{*} ⟶ 3 as a \to 0 .

When cooling is negligible, the milk lowers the temperature by one unit at

t = 1

. The hot-water term begins at

t = 2

and raises it at one unit per unit time, so one further unit of time is needed to erase the deficit.

 New to topics? Read the docs here!