Question

Evaluate:

$\underset{x\to 0}{lim}\frac{1-\cos 2x}{x}$.

Answer 1

Now,

$\underset{x\to 0}{lim}\frac{1-\cos 2x}{x}$ $\left(\frac{0}{0}\right)$ form

Now applying L'Hospital's rule we get,

$=\underset{x\to 0}{lim}\frac{2\sin 2x}{1}$

$=0$.