lim (căn bậc hai (4n^2 + 1) - căn bậc hai (n+2))/(2n - 3)

* Hướng dẫn giải

Chọn A

$$\begin{gathered} \lim \frac{\sqrt{4n^2+1}-\sqrt{n+2}}{2n-3} \\ =\lim \frac{n\sqrt{4+\frac{1}{n}}-n\sqrt{\frac{1}{n}+\frac{2}{n^2}}}{n\left(2-\frac{3}{n}\right)} \\ = \lim \frac{\sqrt{4+\frac{1}{n}}-\sqrt{\frac{1}{n}+\frac{2}{n^2}}}{\left(2-\frac{3}{n}\right)}= \frac{\sqrt{4+0}- \sqrt{0+0}}{2- 0}=1 \end{gathered}$$