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I am trying to understand the difference between a continuous function and a uniformly continuous function.

Is there example of a function that is continuous but not uniformly continuous and a function that is both continuous and uniform continuous?

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  • $\begingroup$ $f(x) = x^2$ is not uniformly continuous, $g(x) = x$ is. (Both with domain $\mathbb{R}$ I should add.) $\endgroup$ – James Jan 16 '16 at 14:54
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Consider , $f:\mathbb R\to \mathbb R$ by $f(x)=x^n$ , for $n>1$.

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    $\begingroup$ Most easy examples, like this one, will have a derivative that grows without bound. $\endgroup$ – Ross Millikan Jan 16 '16 at 15:05

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