Question

The value of $\underset{x\to 0}{lim}\frac{2{\sin }^{2}3x}{x^2}$ is

Answer 1

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

$=\underset{x\to 0}{lim}18.\frac{{\sin }^{2}3x}{9x^2}=\underset{x\to 0}{lim}18{\left(\frac{\sin 3x}{3x}\right)}^2=18.$

$[\because \underset{x\to 0}{lim}\frac{\sin 3x}{3x}=1]$