Tính lim x->2 trị tuyệt đối (x^2 -3x +2)/(x-2

* Hướng dẫn giải

$$\begin{gathered} \underset{x\to 2^{+}}{\lim }\frac{\left|\left(x-2\right)\left(x-1\right)\right|}{x-2}=\underset{x\to 2^{+}}{\lim }\frac{\left(x-2\right)\left(x-1\right)}{x-2}=\underset{x\to 2^{+}}{\lim }\left(x-1\right)=1 \\ \underset{x\to 2^{-}}{\lim }\frac{\left|\left(x-2\right)\left(x-1\right)\right|}{x-2}=\underset{x\to 2^{+}}{\lim }\frac{-\left(x-2\right)\left(x-1\right)}{x-2}=\underset{x\to 2^{+}}{\lim }\left(1-x\right)=-1 \\ \Rightarrow \underset{x\to 2^{-}}{\lim }\frac{\left|\left(x-2\right)\left(x-1\right)\right|}{x-2}\ne \underset{x\to 2^{+}}{\lim }\frac{\left|\left(x-2\right)\left(x-1\right)\right|}{x-2} \\ \Rightarrow \cancel{\exists }\underset{x\to 2}{\lim }\frac{\left|x^2-3x+2\right|}{x-2} \end{gathered}$$

Chọn đáp án A