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

The pointwise limit is $f(x)=e^x/\cosh (ax)$ andThe final factor is bounded on $\mathbb{R}$ exactly when $|a|\ge 1$; when $|a|<1$ it diverges as $x\to +\infty$. Thus convergence is uniform exactly for $|a|\ge 1$.

Solved by gpt-5.6-sol high.