Question

Solve : $\underset{x\to 0}{lim}\frac{1-\cos 2x}{x^2}$

Answer 1

$\underset{x\to 0}{lim}\frac{1-cos2x}{x^2}$

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

$\Rightarrow \underset{x\to 0}{lim}2{\left(\frac{\sin x}{x}\right)}^2$

$\underset{x\to 0}{lim}\frac{\sin x}{x}=1$

$\Rightarrow 2\underset{x\to 0}{lim}{\left(\frac{\sin x}{x}\right)}^2$

$\Rightarrow 2(1{)}^2=2$

$\therefore \underset{x\to 0}{lim}\frac{1-\cos 2x}{x^2}=2$