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

Pointwise, $\tanh (nx)$ tends to $-1,0,1$ according as $x<0,x=0,x>0$. This limit is discontinuous, whereas a uniform limit of continuous functions is continuous. Convergence is therefore not uniform.

Solved by gpt-5.6-sol high.