Prove that $f(x)=x\sin(x)$ is not a uniformly continuous function

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I have this problem, and im really lost here, i need to show that. $f(x)=x\sin x$ is not an uniformly continuous function.

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Consider the sequences $x_n = 2n \pi$ and $y_n = 2n \pi + 1/n$.

What happens to $\lim_{n \to \infty} (x_n-y_n)$?

What happens to $f(x_n) - f(y_n)$?