a) Tính giới hạn \(\lim \frac{{{n^3} - 2n - 3}}{{2{n^3} - n + 1}}\)b) Tính giới hạn \(\lim \frac{{1 - {3^n}}}{{{2^n} + {{4.

* Hướng dẫn giải

a) \(\lim \frac{{{n^3} - 2n + 1}}{{2{n^3} - n + 3}} = \lim \frac{{\frac{{{n^3} - 2n + 1}}{{{n^3}}}}}{{\frac{{2{n^3} - n + 3}}{{{n^3}}}}} = \lim \frac{{1 - \frac{2}{{{n^2}}} + \frac{1}{{{n^3}}}}}{{2 - \frac{1}{{{n^2}}} + \frac{3}{{{n^3}}}}} = \frac{1}{2}\)

b) \(\lim \frac{{1 - {3^n}}}{{{2^n} + {{4.3}^n}}} = \lim \frac{{\frac{{1 - {3^n}}}{{{3^n}}}}}{{\frac{{{2^n} - {{4.3}^n}}}{{{3^n}}}}} = \lim \frac{{\frac{1}{{{3^n}}} - 1}}{{{{\left( {\frac{2}{3}} \right)}^n} + 4}} =  - \frac{1}{4}\)