Giá trị lim x → − ∞ (2x + 3)/( √ 5x^2 − 4x + 2 + x) bằng

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Giá trị \(\mathop {\lim }\limits_{x \to - \infty } \frac{{2x + 3}}{{\sqrt {5{x^2} - 4x + 2} + x}}\) bằng

\(0\).

\(\frac{{ - 2}}{{\sqrt 5 - 1}}\).

\(\frac{2}{{\sqrt 5 }}\).

\(\frac{2}{{\sqrt 5 + 1}}\).

Giải thích

\(\mathop {\lim }\limits_{x \to - \infty } \frac{{2x + 3}}{{\sqrt {5{x^2} - 4x + 2} + x}}\)\( = \mathop {\lim }\limits_{x \to - \infty } \frac{{2x + 3}}{{\left| x \right|\sqrt {5 - \frac{4}{x} + \frac{2}{{{x^2}}}} + x}}\)\( = \mathop {\lim }\limits_{x \to - \infty } \frac{{2 + \frac{3}{x}}}{{ - \sqrt {5 - \frac{4}{x} + \frac{2}{{{x^2}}}} + 1}}\)\( = \frac{2}{{1 - \sqrt 5 }}\). Chọn B.