Question

Solve it :-
$\underset{x\to 0}{lim}\frac{{\tan }^{2}3x}{x^2}$

Answer 1

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

we know that $\underset{x\to 0}{lim}\frac{\tan ax}{ax}=1$

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

$\underset{x\to 0}{lim}9{\left(\frac{\tan 3x}{3x}\right)}^2$

$=9\times 1$

$=9$