Tính lim x->2- (1/(x-2) - 1/(x^2-4

* Hướng dẫn giải

$$\begin{gathered} L=\underset{x\to 2^{-}}{\lim }\left(\frac{1}{x-2}-\frac{1}{x^2-4}\right) \\ =\underset{x\to 2^{-}}{\lim }\left(\frac{1}{x-2}-\frac{1}{\left(x-2\right)\left(x+2\right)}\right) \\ =\underset{x\to 2^{-}}{\lim }\frac{x+2-1}{\left(x-2\right)\left(x+2\right)}=\underset{x\to 2^{-}}{\lim }\frac{x+1}{\left(x-2\right)\left(x+2\right)} \end{gathered}$$

Ta có 

$$\begin{gathered} x\to 2^{-}\Rightarrow x<2\Rightarrow x-2<0 \\ \Rightarrow \underset{x\to 2^{-}}{\lim }\left(x-2\right)=0,\underset{x\to 2^{-}}{\lim }\left(x+1\right)=3,\underset{x\to 2^{-}}{\lim }\left(x+2\right)=4 \end{gathered}$$

 Kết luận $L=-\infty$

Chọn đáp án B