Question

Evaluate $\underset{x\to 0}{lim}\frac{\sin x}{x}$.

Answer 1

Let $L=\underset{x\to 0}{lim}\frac{\sin x}{x}$

The expression takes the form $\frac{0}{0}$.

Using L-Hospital Rule,

$L=\underset{x\to 0}{lim}\cos x$

$L=\cos 0=1$