Đáp án:a)2
b)$\frac{2}{9}$
c)5
d)-1
Giải thích các bước giải:
a)$lim\frac{(2n+1)(n-5)}{n^{2}+1}$
=$lim\frac{2n^{2}-9n-5}{n^{2}+1}$
=$lim\frac{n^{2}(2-\frac{9}{n}-\frac{5}{n^{2}})}{n^{2}(1+\frac{1}{n^{2}})}$
=$2$
b)$lim\frac{2n^{4}-n^{3}+4}{(3n-5)^{2}(n^{2}+1)}$
=$lim\frac{2n^{4}-n^{3}+4}{(9n^{2}-30n+25)(n^{2}+1)}$
=$lim\frac{2n^{4}-n^{3}+4}{9n^{4}-30n^{3}+34n^{2}-30n+25}$
=$lim\frac{n^{4}(2-\frac{1}{n}+\frac{4}{n^{4}})}{n^{4}(9-\frac{30}{n}+\frac{34}{n^{2}}-\frac{30}{n^{3}}+\frac{25}{n^{4}})}$
=$\frac{2}{9}$
c)$lim\frac{3^{n}+5·4^{n}}{4^{n}+2^{n}}$
=$lim\frac{4^{n}[(\frac{3}{4})^{n}+5]}{4^{n}[1+(\frac{2}{4})^{n}]}$
=$5$
d)$lim\frac{2^{n}+7^{n}+2}{3·5^{n}-7^{n}}$
=$lim\frac{7^{n}[(\frac{2}{7})^{n}+1+\frac{2}{7^{n}}]}{7^{n}[3(\frac{5}{7})^{n}-1]}$
=$-1$
