\(\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} - 4}}{{\left| {x - 2} \right|}}\) bằng

* Hướng dẫn giải

Ta có

\(\begin{array}{l}
\mathop {\lim }\limits_{x \to {2^ + }} \frac{{{x^2} - 4}}{{\left| {x - 2} \right|}} = \mathop {\lim }\limits_{x \to {2^ + }} \frac{{{x^2} - 4}}{{x - 2}} = \mathop {\lim }\limits_{x \to {2^ + }} \left( {x + 2} \right) = 4\\
\mathop {\lim }\limits_{x \to {2^ - }} \frac{{{x^2} - 4}}{{\left| {x - 2} \right|}} = \mathop {\lim }\limits_{x \to {2^ - }} \frac{{{x^2} - 4}}{{ - \left( {x - 2} \right)}} = \mathop {\lim }\limits_{x \to {2^ - }} \left[ { - \left( {x + 2} \right)} \right] =  - 4\\
 \Rightarrow \mathop {\lim }\limits_{x \to {2^ + }} \frac{{{x^2} - 4}}{{\left| {x - 2} \right|}} \ne \mathop {\lim }\limits_{x \to {2^ - }} \frac{{{x^2} - 4}}{{\left| {x - 2} \right|}}
\end{array}\)

Do đó \(\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} - 4}}{{\left| {x - 2} \right|}}\) không tồn tại