# What is an example of a function that is continuous but not uniformly continuous? [duplicate]

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?

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

Consider , $f:\mathbb R\to \mathbb R$ by $f(x)=x^n$ , for $n>1$.