Tính giới hạn lim x → − ∞ ( 3 √ x^3 − x^2 + 1 − √ x^2 + 3 ) .

19/55

Tính giới hạn \(\mathop {\lim }\limits_{x \to - \infty } \left( {\sqrt[3]{{{x^3} - {x^2} + 1}} - \sqrt {{x^2} + 3} } \right)\).

\(0\).

\( - \infty \).

\( + \infty \).

\(2\).

Giải thích

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

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