Question

Tìm giới hạn :

A = lim \(\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x+x}\right)\)

A. +\(\infty\)

B. \(-\infty\)

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

D. 0

help me !!!!!!

Answer 1

Nếu

\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x+1}\right)=\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{1+\frac{1}{x}+\frac{1}{x^2}}-2\sqrt{1-\frac{1}{x}+\frac{1}{x^2}}\right)\)

\(=+\infty.\left(1-2\right)=-\infty\)

Nếu:

\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x+1}\right)=\lim\limits_{x\rightarrow-\infty}x\left(-\sqrt{1+\frac{1}{x}+\frac{1}{x^2}}+2\sqrt{1-\frac{1}{x}+\frac{1}{x^2}}\right)\)

\(=-\infty.\left(-1+2\right)=-\infty\)