Cho A = Lim căn {2x + 1} - 1 / x}
Giải thích
Chọn A
\(A = \mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {2x + 1} - 1}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{2}{{\sqrt {2x + 1} + 1}} = 1\).
\(C = \mathop {\lim }\limits_{x \to 1} \frac{{x - 1}}{{\sqrt x - 1}} = \mathop {\lim }\limits_{x \to 1} \left( {\sqrt x + 1} \right) = 2\).
\(N = \mathop {\lim }\limits_{x \to + \infty } \left( {\sqrt {{x^2} + 4x} - x} \right) = \mathop {\lim }\limits_{x \to + \infty } \frac{{4x}}{{\sqrt {{x^2} + 4x} + x}} = \mathop {\lim }\limits_{x \to + \infty } \frac{4}{{\sqrt {1 + \frac{4}{x}} + 1}} = 2\).
\(O = \mathop {\lim }\limits_{x \to - \infty } \frac{{12}}{{{x^{2023}}}} = 0\).