Đáp án:
$1.\lim \dfrac{2n^n+5^{n+1}}{1+5^n}=5\\= \lim \dfrac{\dfrac{2^n}{5^n}+\dfrac{5^{n+1}}{5^n}}{\dfrac{1}{5^n}+1}=\dfrac{5^1}{1}=5\\2.\lim \dfrac{1+2.3^n-7^n}{5^n-2.6^n}=\lim \dfrac{\dfrac{1}{7^n}+2.\dfrac{3^n}{7^n}-1}{\dfrac{5^n}{7^n}-2.\dfrac{6^n}{7^n}}=+\infty\\3.\lim \dfrac{2n^4+n^2-3}{3n^3-2n^2+1}\\ \text{ Do Bậc TỬ > Bậc mẫu , nên } \\=+\infty\\4.\lim\dfrac{2n+5}{\sqrt{n^2+1}-n}\\ =\lim\dfrac{n(2+\dfrac{5}{n})}{n(\sqrt{1+\dfrac{1}{n^2}}-1)}=+\infty\\5.\lim\dfrac{(3n-1)^4.(n-2)}{1-2n)^2}\\ \text{ Do Bậc TỬ > Bậc mẫu , nên } \\=+\infty$
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