Tìm giới hạn B= lim(x->âm vô cùng)(x- căn (x^2+x+1))

* Hướng dẫn giải

Chọn B

$\begin{array}{l}B=\underset{x\to -\infty }{\lim }\left(x-\sqrt{x^2+x+1}\right)\\ =\underset{x\to -\infty }{\lim }\left(x-\left|x\right|\sqrt{1+\frac{1}{x}+\frac{1}{x^2}}\right)\\ =\underset{x\to -\infty }{\lim }x\left(1+\sqrt{1+\frac{1}{x}+\frac{1}{x^2}}\right)=-\infty \end{array}$

$\begin{array}{l}\underset{x\to -\infty }{\lim }x=-\infty ;\\ \underset{x\to -\infty }{\lim }\left(1+\sqrt{1+\frac{1}{x}+\frac{1}{x^2}}\right)=2>\text{}0\end{array}$