Mathematics - Limits Question with Solution | TestHub

$${\mathrm{Lim}}_{x\to 0}\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}\Rightarrow {\mathrm{Lim}}_{x\to 0}\frac{\sqrt{1-\left(1-2{\sin }^{2}x\right)}}{\sqrt{2}x};{\mathrm{Lim}}_{x\to 0}\frac{\sqrt{2{\sin }^{2}x}}{\sqrt{2}x}\Rightarrow {\mathrm{Lim}}_{x\to 0}\frac{|\sin x|}{x}$$ the function does not exist or $\mathrm{LHS}\ne \mathrm{RHS}$