lim x→−∞ x+m/√x^2+1 bằng

Question

\({\mathop{\lim }\limits_{x\to -\infty }} \frac{x+m}{\sqrt{x^{2} +1} }\)  bằng

A. -1.

B. 1.

C. -m.

D. m.

Answer 1

Chọn A

Ta có

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