Find $\lim\limits_{x \to \infty} x\sin\frac{11}{x}$ Find $$\lim_{x \to \infty} x\sin\left(\frac{11}{x}\right)$$
We know $-1\le \sin \frac{11}{x} \le 1 $ 
Therefore, $x\rightarrow \infty $
And so limit of this function does not exist. 
Am I on the right track? Any help is much appreciated.

Hint
$$\lim\limits_{x \to \infty} x\sin\left(\frac{11}{x}\right)=11\lim\limits_{x \to 0^+} \frac{\sin(11x)}{11x}$$
