Question

Solve:
$\underset{x\to 0}{lim}\frac{\tan 2x}{x-\frac{\pi }{2}}$

Answer 1

$\underset{x\to 0}{lim}\frac{\tan 2x}{(x-\frac{\pi }{2})}$

$\Rightarrow \underset{x\to 0}{lim}\left(\frac{\tan 2x}{2x}\right)\times \frac{\left(2x\right)}{(x-\frac{\pi }{2})}$

$\Rightarrow \underset{x\to 0}{lim}\frac{2x}{(x-\frac{\pi }{2})}$

$\Rightarrow \frac{2\left(0\right)}{(0-\frac{\pi }{2})}\Rightarrow 0$

$\therefore \underset{x\to 0}{lim}\frac{\tan 2x}{(x-\frac{\pi }{2})}=0$