Prove that function is not uniformly continuous

Question

I have to prove that the function $$f(x)=\left\{ \begin{array} \\ x^2 \cos\frac{1}{x},& x\neq 0\\ 0,& x=0 \end{array} \right.$$ is not uniformly continuous on $\mathbb{R}$ and I just can't find the two sequences to do that.

Any ideas which ones I should use?

Answer 1

Hint: Because $\cos (1/\sqrt {n+1}) > \cos (1/\sqrt {n}),$ we have

$$(n+1)\cos (1/\sqrt {n+1}) - n\cos (1/\sqrt {n})$$ $$ > (n+1)\cos (1/\sqrt {n+1}) - n\cos (1/\sqrt {n+1}).$$