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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$f(x) = x^2$ is not uniformly continuous, $g(x) = x$ is. (Both with domain $\mathbb{R}$ I should add.) – 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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4Most easy examples, like this one, will have a derivative that grows without bound. – Ross Millikan Jan 16 '16 at 15:05