Mathematics - Limits Question with Solution | TestHub

$$\begin{array}{rl}& \underset{x\to 2}{\lim }\frac{\sqrt{2{\sin }^2(x-2)}}{x-2}\\ & \underset{x\to 2}{\lim }\frac{\sqrt{2}|\sin (x-2)|}{x-2}\\ & \text{ R.H.L. }=\sqrt{2},\text{ L.H.L. }=-\sqrt{2}\end{array}$$ Limit does not exist.