Tính giới hạn \(\mathop {\lim }\limits_{} \frac{{2n + 1}}{{n + 2}}.

* Hướng dẫn giải

a) \(\mathop {\lim }\limits_{} \frac{{2n + 1}}{{n + 2}} = \mathop {\lim }\limits_{} \frac{{2 + 1/n}}{{1 + 2/n}} = 2.\)

b) 

\(\begin{array}{l}
\mathop {\lim }\limits_{} \left( {\sqrt {4{n^2} + 8n + 5}  - 2n} \right) = \mathop {\lim }\limits_{} n\left( {\sqrt {4 + 8/n + 5/{n^2}}  - 2} \right)\\
 = \mathop {\lim }\limits_{} n\frac{{8/n + 5/{n^2}}}{{\sqrt {4 + 8/n + 5/{n^2}}  + 2}} = \mathop {\lim }\limits_{} \frac{{8 + 5/n}}{{\sqrt {4 + 8/n + 5/{n^2}}  + 2}} = 2.
\end{array}\)