Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 3 / 2G / b / iii

For each fixed real $x$, $x/n\to 0$, so the pointwise limit is zero. But ${\sup }_{x\in \mathbb{R}}|x/n|=\infty$ for every $n$. Alternatively, $x=n$ gives error one whatever $n$ is. Thus the convergence is not uniform on $\mathbb{R}$. It is uniform on each bounded interval, where $|x/n|\le M/n$.