Please how can I show that $$\displaystyle\lim\_{x \rightarrow 0} \frac{1}{x} \sin\frac{1}{x}$$ does not exist?

I tried the substitution $u = \frac{1}{x}$ so that I'm now calculating $\lim\_{u \rightarrow + \infty} u \sin(u)$
But from there I don't know what to do.

Thanks in advance