Tìm giới hạn cho sau \(\mathop {\lim }\limits_{x \to 2} \dfrac{{{x^4} - 5{x^2} + 4}}{{{x^3} - 8}}\)

* Hướng dẫn giải

\(\begin{array}{l}\mathop {\lim }\limits_{x \to 2} \dfrac{{{x^4} - 5{x^2} + 4}}{{{x^3} - 8}}\\ = \mathop {\lim }\limits_{x \to 2} \dfrac{{\left( {{x^2} - 4} \right)\left( {{x^2} - 1} \right)}}{{\left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right)}}\\ = \mathop {\lim }\limits_{x \to 2} \dfrac{{\left( {x + 2} \right)\left( {{x^2} - 1} \right)}}{{{x^2} + 2x + 4}}\\ = \dfrac{{(2 + 2)({2^2} - 1)}}{{{2^2} + 2.2 + 4}} = 1\end{array}\)