Evaluate $lim_{x\to 0} \frac {x}{|x|^s}$ for $s<1$ and $x\in \mathbb R^n$. For $n = 1$, I think this limit is equal to $0$. However I am trying to evaluate it when $x$ is an vector in arbitrary dimension. Does this limit exist?
2026-04-13 18:00:57.1776103257
evaluate the limit of $\frac {x}{|x|^s}$ as $s<1$ and $x$ goes to $0$
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Hint: $\displaystyle\left\|\frac x{\sqrt{\|x\|}}\right\|=\sqrt{\|x\|}$.