Tính các giới hạn sau:a.

* Hướng dẫn giải

a) \(\mathop {\lim }\limits_{x \to  - \infty } \left( {{x^3} - 2{x^2} + x + 1} \right) = \mathop {\lim }\limits_{x \to  - \infty } {x^3}\left( {1 - \frac{2}{x} + \frac{1}{{{x^2}}} + \frac{1}{{{x^3}}}} \right) =  - \infty \)

b) \(\mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {x + 1}  - 2}}{{x - 3}} = \mathop {\lim }\limits_{x \to 3} \frac{{(\sqrt {x + 1}  - 2)(\sqrt {x + 1}  + 2)}}{{(x - 3)(\sqrt {x + 1}  + 2)}} = \mathop {\lim }\limits_{x \to 3} \frac{1}{{\sqrt {x + 1}  + 2}} = \frac{1}{4}\)