Question

Find the following limit:
$\underset{x\to 0}{lim}\frac{\sin 5x}{x}$

Answer 1

$\underset{x\to 0}{lim}\frac{\sin 5x}{x}$

$=\underset{x\to 0}{lim}\frac{\sin 5x}{5x}\times 5\left[\underset{x\to 0}{lim}\frac{\sin x}{x}=1\right]$

$=5$.