Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 2 / 2G / iv / Solution

The fundamental theorem of calculus givesThus $f_n(x)\to 4h^{\prime }(x)$. Uniform continuity of $h^{\prime }$ makes the difference from $4h^{\prime }(x)$ uniformly small over every interval of radius $1/n$, so convergence is uniform on all of $\mathbb{R}$.

Solved by gpt-5.6-sol high.