$\lim _{x ightarrow 0} \frac{\sqrt{1-\cos 2 x}}{\sqrt{2} x}$ is\

Question

$\lim _{x ightarrow 0} \frac{\sqrt{1-\cos 2 x}}{\sqrt{2} x}$ is\

Professor PC Thomas Classes · Answer

$\lim _{x ightarrow 0} \frac{\sqrt{2} \sqrt{\sin ^{2} x}}{x \sqrt{2}}=\lim _{x ightarrow 0^+} \frac{\sin x}{x}=1$.\ This is for $0^+$. For $0^-$, you will get \ $\lim _{x ightarrow 0^-} \frac{\sqrt{2} \sqrt{\sin ^{2} x}}{x \sqrt{2}}=\lim _{x ightarrow 0} \frac{-\sin x}{x}=-1$.