I have a function, $f$ that is differentiable on $(0,5)$, and I know it is continuous on $(0,5).$ Is it also uniformly continuous on $(0,5)?$ I believe it is.
I now know that it is not. Can someone give me a proof of this please
2026-03-28 06:48:19.1774680499
If $f$ is continuous on $(0,5)$, is it uniformly continuous on same interval
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Not necessarily. For example, define $f:(0,5)\rightarrow \mathbb{R}$ by $f(x) = 1/x$. $f$ is certainly differentiable and continuous on $(0,5)$, but it is not uniformly continuous.