Tìm giới hạn \(C=\lim\limits _{x \rightarrow+\infty}\left(\sqrt{4 x^{2}+x+1}-2 x\right)\)

* Hướng dẫn giải

\(\text { Ta có: } C=\lim\limits _{x \rightarrow+\infty} \frac{x+1}{\sqrt{4 x^{2}+x+1}+2 x}=\lim\limits _{x \rightarrow+\infty} \frac{x\left(1+\frac{1}{x}\right)}{|x| \sqrt{4+\frac{1}{x}+\frac{1}{x^{2}}}+2 x}=\lim\limits _{x \rightarrow+\infty} \frac{1+\frac{1}{x}}{\sqrt{4+\frac{1}{x}+\frac{1}{x^{2}}}+2}=\frac{1}{2}\)