Question

Evaluate the limit:
$\underset{x\to 0}{lim}\frac{\sin x^{\circ }}{x^{\circ }}$

Answer 1

We have,

$\underset{x\to 0}{lim}\frac{\sin x^{\circ }}{x^{\circ }}$

$\because x^{\circ }=\frac{\pi }{180}x$

$\underset{x\to 0}{lim}\frac{\sin \frac{\pi }{180}x}{\frac{\pi }{180}x}=1[\because \underset{\theta \to 0}{lim}(\frac{\sin \theta }{\theta })=1]$

Therefore,

$\underset{x\to 0}{lim}\frac{\sin x^{\circ }}{x^{\circ }}=1$