(mathop {lim }limits_{x o  + infty } left( { - {x^3} + {x^2} + 2} ight)) bằng

* Hướng dẫn giải

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

Ta có: \(\mathop {\lim }\limits_{x \to  + \infty } \left( { - {x^3}} \right) =  - \infty \) và \(\mathop {\lim }\limits_{x \to  + \infty } \left( { - 1 + \frac{1}{x} + \frac{2}{{{x^3}}}} \right) =  - 1\). Vậy \(\mathop {\lim }\limits_{x \to  + \infty } \left( { - {x^3} + {x^2} + 2} \right) =  - \infty .\left( { - 1} \right) =  + \infty \)