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

Using the Taylor expansionwe obtainWhen 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.