Question

Evaluate the following limit:

$\underset{x\to \infty }{lim}\frac{\sin x}{x}.$

Answer 1

$\underset{x\to \infty }{lim}\frac{\sin x}{x}=\underset{x\to \infty }{lim}\left(\frac{1}{x}\right).\underset{x\to \infty }{lim}\sin x$
$=0\times$ (numbers lying between -1 and 1)$=0$