Giới hạn lim(căn bậc hai n^2-n+1 - căn bậc hai n^2+1) bằng? A.0 B.-1/2 C.-1/căn bậc hai 2 D.1/căn bậc hai 2

* Hướng dẫn giải

$\begin{array}{l}\lim (\sqrt{n^2-n+1}-\sqrt{n^2+1})\\ =\lim \frac{(\sqrt{n^2-n+1}-\sqrt{n^2+1})(\sqrt{n^2-n+1}+\sqrt{n^2+1})}{\sqrt{n^2-n+1}+\sqrt{n^2+1}}\\ =\lim \frac{n^2-n+1-n^2-1}{\sqrt{n^2-n+1}+\sqrt{n^2+1}}\\ =\lim \frac{-n}{\sqrt{n^2-n+1}+\sqrt{n^2+1}}\\ =\lim \frac{-1}{\sqrt{1-\frac{1}{n}+\frac{1}{n^2}}+\sqrt{1+\frac{1}{n^2}}}\\ =-\frac{1}{2}\end{array}$