Tính I = lim [ n ( √ n^ 2 + 2 − √ n ^2 − 1 ) ] .

3/22

Tính \(I = \lim \,\left[ {n\left( {\sqrt {{n^2} + 2} - \sqrt {{n^2} - 1} } \right)} \right]\).

\(I = + \infty \)

\(I = \frac{3}{2}\)

\(I = 1,499\)

\(I = 0\)

Giải thích

Chọn B

Ta có: \(I = \lim \,\left[ {n\left( {\sqrt {{n^2} + 2} - \sqrt {{n^2} - 1} } \right)} \right]\)\( = \lim \,\frac{{3n}}{{\sqrt {{n^2} + 2} + \sqrt {{n^2} - 1} }}\)\( = \lim \,\frac{3}{{\sqrt {1 + \frac{2}{{{n^2}}}} + \sqrt {1 - \frac{1}{{{n^2}}}} }} = \frac{3}{2}\)