Question

The value of ${lim}_{x\to o}\frac{\sqrt{\frac{1}{2}(1-cos2x)}}{x}$

• A. 1
• B. -1
• C. 0
• D. none of these

Answer 1

The correct option is A 1

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

$={lim}_{x\to 0}\frac{\sqrt{\frac{1}{2}(1-(1-2{\sin }^{2}x))}}{x}$

$={lim}_{x\to 0}\frac{\sqrt{\frac{1}{2}(1-1+2{\sin }^{2}x)}}{x}$

$={lim}_{x\to 0}\frac{\sqrt{\frac{1}{2}\left(2{\sin }^{2}x\right)}}{x}$

$={lim}_{x\to 0}\frac{\sqrt{{\sin }^{2}x}}{x}$

$={lim}_{x\to 0}\frac{\sin x}{x}$

$=1(\because {lim}_{x\to 0}\frac{\sin x}{x}=1)$