Tìm giới hạn \(A=\lim\limits _{x \rightarrow+\infty}\left(\sqrt{x^{2}+x+1}-\sqrt[3]{2 x^{3}+x-1}\right)\)

* Hướng dẫn giải

\(\begin{array}{l} \text { Ta có: } A=\lim\limits _{x \rightarrow+\infty}\left(|x| \sqrt{1+\frac{1}{x}+\frac{1}{x^{2}}}-x \sqrt[3]{2+\frac{1}{x^{2}}-\frac{1}{x^{3}}}\right) \\ \quad=\lim\limits _{x \rightarrow+\infty} x\left(\sqrt{1+\frac{1}{x}+\frac{1}{x^{2}}}-\sqrt[3]{2+\frac{1}{x^{2}}-\frac{1}{x^{3}}}\right)=-\infty \end{array}\)