Question

Evaluate:${lim}_{x\to 0}x\sin \frac{1}{x}$

Answer 1

$\sin \frac{1}{x}$ is a bounded function.

$\Rightarrow -1\le \sin \frac{1}{x}\le 1$

$\therefore x\sin \frac{1}{x}=0\times$any number between $-1$ and $1=0$