Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 7C / e

Table of contents
- Solution e

Solution

Using the Taylor expansion

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.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version