Question

Write the value of ${lim}_{x\to 0}\frac{\sqrt{1-\cos 2x}}{x}$

Answer 1

${lim}_{x\to 0}\frac{\sqrt{1-\cos 2x}}{x}$
$={lim}_{x\to 0}\frac{\sqrt{2si{n}^{2}x}}{x}$
$={lim}_{x\to 0}\frac{\sqrt{2}sinx}{x}or{lim}_{x\to 0}\frac{-\sqrt{2}sinx}{x}$
$=\sqrt{2}or-\sqrt{2}$
Limit does not exists.