Solution
= Solution
The function $x\mapsto x^2$ is not uniformly continuous on $\mathbb R$. Take $x_n=n$ and $y_n=n+1/n$. Then $|x_n-y_n|\to0$, whereas
$$
|y_n^2-x_n^2|=2+\frac1{n^2}\longrightarrow2.
$$
This contradicts the <sequential criterion for uniform continuity>.