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Đáp án:

$\begin{array}{l}\lim \left(\sqrt{n^2-n+1}-\sqrt{n^2+1}\right)\\ =\lim \frac{\left(\sqrt{n^2-n+1}-\sqrt{n^2+1}\right)\left(\sqrt{n^2-n+1}+\sqrt{n^2+1}\right)}{\left(\sqrt{n^2-n+1}+\sqrt{n^2+1}\right)}\\ =\lim \frac{n^2-n+1-n^2-1}{\left(\sqrt{n^2-n+1}+\sqrt{n^2+1}\right)}\\ =\lim \frac{-n}{n.\sqrt{1-\frac{1}{n}+\frac{1}{n^2}}+n.\sqrt{1+\frac{1}{n^2}}}\\ =\lim \frac{-1}{\sqrt{1-\frac{1}{n}+\frac{1}{n^2}}+\sqrt{1+\frac{1}{n^2}}}=\frac{-1}{\sqrt{1-0+\text{}0}+\sqrt{1+\text{}0}}=-\frac{1}{2}\end{array}$

Đáp án cần chọn là: B