Question

The value of $\underset{x\to 0}{lim}\frac{\sqrt{1/2(1-\cos 2x)}}{x}$ is equal to.

• A. $0$
• B. $-1$
• C. $1$
• D. None of these

Answer 1

Answer: (D)

None of these

$\underset{x\to 0}{lim}\frac{\sqrt{\frac{1}{2}(1=\cos 2x)}}{x}$

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

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

L.H.L

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

R.H.L

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

$L.H.L\ne R.H.L$

So Limit does not exist

$\left(D\right)$ option