$\lim\limits_{x \rightarrow 0} \frac{\sqrt{\frac{1}{2}(1-\cos 2 x)}}{x}=$
Answer & explanation
Correct answer: option 4
Given limit is $\lim\limits_{X \rightarrow 0} \frac{|\sin x|}{x}$
$\lim\limits_{X \rightarrow 0^{+}} \frac{|\sin x|}{x}=1$ and $\lim\limits_{X \rightarrow 0^{-}} \frac{-\sin x}{x}=-1$
Hence (4) is the correct answer.