$\underset{x→0}{\lim}\frac{\sqrt{\frac{1}{2}(1-\cos 2x)}}{x}$ is equal to

none of these

$\lim=\underset{x→0}{\lim}\frac{|\sin x|}{x}$

$R.H.L=\underset{h→0}{\lim}\frac{|sin(0+h)|}{0+h}=\underset{h→0}{\lim}\frac{\sin h}{h}=1$

$R.H.L=\underset{h→0}{\lim}\frac{|sin(0-h)|}{0-h}=\underset{h→0}{\lim}\frac{|-\sin h|}{-h}=-\underset{h→0}{\lim}\frac{\sin h}{h}=-1$

Since R.H.L. ≠ L.H.L.

∴ limit does not exist.