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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 $|x/n|\le M/n$.

For each fixed $0<x<1$, $x^n\to 0$, so the pointwise limit is $f(x)=1/(1-x)$. Howeverfor every fixed $n$. Hence the error has infinite supremum on $(0,1)$ and the convergence is not uniform. This does not contradict uniform convergence on any smaller closed interval $[0,r]$, $r<1$, where the error is at most $r^n/(1-r)$.

The pointwise limit is zero, including at $x=0$. Differentiation givesso the maximum on $[0,\infty )$ is attained at $x=1/n$ and equals $1/(en)$. Thereforeand the convergence is uniform, even though the domain is unbounded.