Tính các giới hạn sau:

\(\lim \frac{{{3^n} + {{4.9}^n}}}{{{{3.4}^n} + {9^n}}}\)\( = \lim \frac{{{9^n}\left[ {{{\left( {\frac{1}{3}} \right)}^n} + 4} \right]}}{{{9^n}\left[ {3.{{\left( {\frac{4}{9}} \right)}^n} + 1} \right]}}\)\( = \lim \frac{{{{\left( {\frac{1}{3}} \right)}^n} + 4}}{{3.{{\left( {\frac{4}{9}} \right)}^n} + 1}}\)

\( = \frac{{\lim \left[ {{{\left( {\frac{1}{3}} \right)}^n} + 4} \right]}}{{\lim \left[ {3.{{\left( {\frac{4}{9}} \right)}^n} + 1} \right]}} = \frac{4}{1} = 4\).