Tìm giới hạn \(C=\lim \limits_{x \rightarrow \pm \infty}\left(\sqrt{x^{2}-x+1}-\sqrt{x^{2}+x+1}\right)\)

* Hướng dẫn giải

Ta có 

\(\begin{array}{l} \lim\limits _{x \rightarrow+\infty}\left(\sqrt{x^{2}-x+1}-\sqrt{x^{2}+x+1}\right)=\lim\limits _{x \rightarrow+\infty} \frac{-2 x}{\sqrt{x^{2}-x+1}+\sqrt{x^{2}+x+1}}=-1 \\ \lim\limits _{x \rightarrow-\infty}\left(\sqrt{x^{2}-x+1}-\sqrt{x^{2}+x+1}\right)=\lim\limits _{x \rightarrow-\infty} \frac{-2 x}{\sqrt{x^{2}-x+1}+\sqrt{x^{2}+x+1}}=1 \end{array}\)