Giới hạn Lim căn {{x^2} - 3x + 4} - 2 / 2) bằng

11/39

Giới hạn \(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {{x^2} - 3x + 4} - 2}}{{2x}}\) bằng

\( - \frac{3}{8}\).

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

\(\frac{1}{2}\).

\( - \frac{2}{3}\).

Giải thích

Chọn A

\(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {{x^2} - 3x + 4} - 2}}{{2x}} = \mathop {\lim }\limits_{x \to 0} \frac{{{x^2} - 3x + 4 - 4}}{{2x.(\sqrt {{x^2} - 3x + 4} + 2)}} = \mathop {\lim }\limits_{x \to 0} \frac{{x.\left( {x - 3} \right)}}{{2x.(\sqrt {{x^2} - 3x + 4} + 2)}}\)\(\)\( = \mathop {\lim }\limits_{x \to 0} \frac{{x - 3}}{{2.(\sqrt {{x^2} - 3x + 4} + 2)}} = \frac{{ - 3}}{{2.(\sqrt 4 + 2)}} = \frac{{ - 3}}{8}\)