\(x>2\Rightarrow\lim\limits_{x\rightarrow2^+}\dfrac{x\left(x-2\right)}{x-2}=x=2\)
\(x< 2\Rightarrow\lim\limits_{x\rightarrow2^-}\dfrac{x\left(x-2\right)}{-\left(x-2\right)}=-x=-2\)
\(\Rightarrow\lim\limits_{x\rightarrow2^+}\dfrac{x^2-2x}{\left|x-2\right|}=2\ne\)\(\lim\limits_{x\rightarrow2^-}\dfrac{x^2-2x}{\left|x-2\right|}=-2\)
\(\Rightarrow\lim\limits_{x\rightarrow2}\dfrac{x^2-2x}{\left|x-2\right|}\) không tồn tại