Question: Find the limit. If it doesn’t exist, explain

\[\underset{x\to 2}{\mathop{\lim }}\,f\left( x \right)\]

where

\[f\left( x \right)=\left\{ \begin{aligned} & {{x}^{2}}-4x+6\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x<2 \\ & -{{x}^{2}}+4x-2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ge 2 \\ \end{aligned} \right.\]