\(\mathop {\lim }\limits_{x \to + \infty } \frac{{\sqrt {4{x^2} + 2} - \sqrt {x + 3} }}{{2x - 3}}\) có giá trị là bao nhiêu?

* Hướng dẫn giải

\(\begin{array}{l}
\mathop {\lim }\limits_{x \to  + \infty } \frac{{\sqrt {4{x^2} + 2}  - \sqrt {x + 3} }}{{2x - 3}}\\
 = \mathop {\lim }\limits_{x \to  + \infty } \frac{{\sqrt {4 + \frac{2}{{{x^2}}}}  - \sqrt {\frac{1}{x} + \frac{3}{{{x^2}}}} }}{{2 - \frac{3}{x}}} = 1
\end{array}\)