If f is continuos on an interval, is it then uniformly continuous

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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 now know that it is not. Can someone give me a proof of this please

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Consider $f(x)=\dfrac{1}{x}$ which is continuous on $(0,5)$.