For which $r$ element of $(0,\infty$) $|x|^r \to 0$ if $x \to 0$ For which $r$ element of $(0,\infty$) $|x|^r \to 0$ if $x \to 0$?
Somehow I have no idea how to solve the problem. I know that it's true for $r\geq 1$.

For all $r>0$, one has
$$
\lim_{x\to 0}|x|^r=0,
$$ not only for $r\geq1$.
