Tìm giới hạn \(C = \mathop {\lim \to + \infty } \left( {\sqrt {4{x^2} + x + 1} - 2x}

* Hướng dẫn giải

\(\begin{array}{l}
C = \mathop {\lim }\limits_{x \to  + \infty } \left( {\sqrt {4{x^2} + x + 1}  - 2x} \right) = \mathop {\lim }\limits_{x \to  + \infty } \frac{{x + 1}}{{\sqrt {4{x^2} + x + 1}  + 2x}}\\
 = \mathop {\lim }\limits_{x \to  + \infty } \frac{{x\left( {1 + \frac{1}{x}} \right)}}{{x\sqrt {4 + \frac{1}{x} + \frac{1}{{{x^2}}}}  + 2x}} = \mathop {\lim }\limits_{x \to  + \infty } \frac{{1 + \frac{1}{x}}}{{\sqrt {4 + \frac{1}{x} + \frac{1}{{{x^2}}}} }} = \frac{1}{4}
\end{array}\)