Tính: lim n- cưn n^2+2n+3

* Hướng dẫn giải

a)

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