Question

Evaluate the limit:
$\underset{x\to 0}{lim}\frac{{\tan }^{2}3x}{x^2}$

Answer 1

We have,

$\underset{x\to 0}{lim}\frac{{\tan }^{2}3x}{x^2}$

$=\underset{x\to 0}{lim}\frac{\tan 3x}{3x}\times \frac{\tan 3x}{3x}\times 9$

$=1\times 1\times 9[\because \underset{x\to 0}{lim}\frac{\tan x}{x}=1]$

$=9$

Therefore,

$\underset{x\to 0}{lim}\frac{{\tan }^{2}3x}{x^2}=9$