Check the pointwise and uniform convergence of $$f_n:[0,\infty[\to\mathbb{R}, x\mapsto\sqrt[n]{x}$$
i assume that $f_n \to f$ is pointwise convergent with $f:[0,\infty[\to \mathbb{R},f(x):= \begin{cases} 1 &, x\gt 0 \\[2ex] 0 &, x=0 \end{cases}$
since for all $\lim_{n->\infty} \sqrt[n]{x}\to 1, \forall x\gt0 $ and $\lim_{n->\infty} \sqrt[n]{x}\to0 $ for $x=0$
My question is, is it sufficient enough that the $f$ it approaches is not continuous to say that $f_n$ is not uniform continuous?