Question

Solve :
$\underset{x\to 0}{lim}\left[\frac{\tan x}{x}\right]$

Answer 1

$\underset{x\to 0}{lim}\left[\frac{\tan x}{x}\right]$

at $x\to 0$

$\Rightarrow \tan x\ge x$

$\therefore \frac{\tan x}{x}\in [1,2]$ as $x\to 0$

$\therefore \underset{x\to 0}{lim}\left[\frac{\tan x}{x}\right]=\underset{x\to 0}{lim}1=1$. Answer.