_ x 0 1 2 (1- 2 x) x = - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{\sqrt{\frac{1}{2}(1-\cos 2 x)}}{x}=$

A
1
B
$-1$
C
$0$
✓
None of these

✓

Answer

Correct option: D.

None of these

(D)
$\lim _{x \rightarrow 0} \frac{\sqrt{\frac{1}{2}(1-\cos 2 x)}}{x}=\lim _{x \rightarrow 0} \frac{|\sin x|}{x}$
So, $\lim _{x \rightarrow 0^{+}} \frac{|\sin x|}{x}=1$ and $\lim _{x \rightarrow 0^{-}} \frac{|\sin x|}{x}=-1$
Hence, limit does not exist.

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