Tìm giới hạn sau: lim ( √ n^2 + 2n − 2 − n ) .

Trả lời:1

\(\lim \left( {\sqrt {{n^2} + 2n - 2} - n} \right) = \lim \frac{{{n^2} + 2n - 2 - {n^2}}}{{\sqrt {{n^2} + 2n - 2} + n}} = \lim \frac{{2n - 2}}{{n\sqrt {1 + \frac{2}{n} - \frac{2}{{{n^2}}}} + n}}\)

\( = \lim \frac{{n\left( {2 - \frac{2}{n}} \right)}}{{n\left( {\sqrt {1 + \frac{2}{n} - \frac{2}{{{n^2}}}} + 1} \right)}} = \lim \frac{{2 - \frac{2}{n}}}{{\sqrt {1 + \frac{2}{n} - \frac{2}{{{n^2}}}} + 1}} = \frac{2}{{\sqrt 1 + 1}} = 1.{\rm{ }}\)