Câu hỏi 33

\(\begin{array}{l}I = \lim \left[ {n\left( {\sqrt {{n^2} + 2}  - \sqrt {{n^2} - 1} } \right)} \right]\\I = \lim \dfrac{{n\left( {{n^2} + 2 - {n^2} + 1} \right)}}{{\sqrt {{n^2} + 2}  + \sqrt {{n^2} - 1} }}\\I = 3\lim \dfrac{n}{{\sqrt {{n^2} + 2}  + \sqrt {{n^2} - 1} }}\\I = 3\lim \dfrac{1}{{\sqrt {1 + \dfrac{2}{{{n^2}}}}  + \sqrt {1 - \dfrac{1}{{{n^2}}}} }}\\I = 3\lim \dfrac{1}{{1 + 1}} = \dfrac{3}{2}\end{array}\)

Chọn C.