Đáp án:
1) lim=0
2) lim=+∞
Giải thích các bước giải:
\(\begin{array}{l}
1)\lim \frac{{{3^n} + {5^{(n + 1)}}}}{{{{3.4}^n} + {5^{2n}}}}\\
= \lim \frac{{{3^n} + {{5.5}^n}}}{{{{3.4}^n} + {{25}^n}}}\\
= \lim \frac{{{{\left( {\frac{3}{{25}}} \right)}^n} + 5.{{\left( {\frac{5}{{25}}} \right)}^n}}}{{3.{{\left( {\frac{4}{{25}}} \right)}^n} + 1}} = \frac{0}{1} = 0\\
2)\lim \left( {{{11}^n} - {3^{2n}}} \right)\\
= \lim \left( {{{11}^n} - {9^n}} \right)\\
= \lim {11^n}\left( {1 - \frac{{{9^n}}}{{{{11}^n}}}} \right) = + \infty \\
Do:\mathop {\lim }\limits_{x \to + \infty } {11^n} = + \infty \\
\lim \left( {1 - \frac{{{9^n}}}{{{{11}^n}}}} \right) = 1
\end{array}\)
