lim n → + ∞ ( − n^3 + n − 3 ) bằng

Đáp án đúng là: B

Ta có: \[\mathop {\lim }\limits_{n \to + \infty } {n^3} = + \infty ;\,\,\mathop {\lim }\limits_{n \to + \infty } \left( { - 1 + \frac{1}{{{n^2}}} - \frac{3}{{{n^3}}}} \right) = \mathop {\lim }\limits_{n \to + \infty } \left( { - 1} \right) + \mathop {\lim }\limits_{n \to + \infty } \frac{1}{{{n^2}}} - \mathop {\lim }\limits_{n \to + \infty } \frac{3}{{{n^3}}} = - 1.\]

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