Tính giới hạn \(I=\underset{x\to {{2}^{-}}}{\mathop{\lim }}\,\frac{3{{x}^{2}}-2}{x-2}\)

* Hướng dẫn giải

\(\left\{ \begin{array}{l} \mathop {\lim }\limits_{x \to {2^ - }} \left( {3{x^2} - 2} \right) = 3.{\left( { - 2} \right)^2} - 2 = 10 > 0\\ \mathop {\lim }\limits_{x \to {2^ - }} \left( {x - 2} \right) = 2 - 2 = 0\\ x \to {2^ - } \Rightarrow x < 2 \Rightarrow x - 2 < 0 \end{array} \right. \Rightarrow I = \mathop {\lim }\limits_{x \to {2^ - }} \frac{{3{x^2} - 2}}{{x - 2}} = - \infty .\)