tìm lim $\frac{5^{n}+pi^{2n}+7^n}{4^n +pi ^{2x+1}+6^n}$ jup vs nêu có bao nhiêu dạng tìm liim thì dc ctlhn

Đáp án:

$\lim\dfrac{5^n + \pi^{2n}+7^n}{4^n + \pi^{2n+1} + 6^n}=\dfrac{1}{\pi}$

Giải thích các bước giải:

$\begin{array}{l}\quad \lim\dfrac{5^n + \pi^{2n}+7^n}{4^n + \pi^{2n+1} + 6^n}\\ = \lim\dfrac{5^n + (\pi^{2})^n+7^n}{4^n + \pi .(\pi^{2})^n + 6^n}\\ = \lim\dfrac{\left(\dfrac{5}{\pi^2}\right)^n + 1 + \left(\dfrac{7}{\pi^2}\right)^n}{\left(\dfrac{4}{\pi^2}\right)^n + \pi + \left(\dfrac{6}{\pi^2}\right)^n}\\ = \dfrac{0 + 1 + 0}{0+\pi + 0}\\ = \dfrac{1}{\pi} \end{array}$