Question

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

Answer 1

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

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

Using L-Hospital Rule,

$L=\underset{x\to 0}{lim}{\sec }^{2}x=1$