lim x→0 √1−x−1/x bằng:

Question

\({\mathop{\lim }\limits_{x\to 0}} \frac{\sqrt{1-x} -1}{x}\) bằng: 

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

\(B.0. \)

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

\(D. +\infty .\)

Answer 1

Chọn A

Ta có \({\mathop{\lim }\limits_{x\to 0}} \frac{\sqrt{1-x} -1}{x} ={\mathop{\lim }\limits_{x\to 0}} \frac{-x}{x\left(\sqrt{1-x} +1\right)} ={\mathop{\lim }\limits_{x\to 0}} \frac{-1}{\left(\sqrt{1-x} +1\right)} =-\frac{1}{2} . \)