Question

Найдите предел функции

Answer 1

$\displaystyle\lim_{n\to\infty}\frac{(2n+4)^4-(2n-4)^4}{(2n+4)^4+(2n-4)^4}=\frac{\infty}{\infty}=\lim_{n\to\infty}\frac{1-\frac{(2n-4)^4}{(2n+4)^4}}{1+\frac{(2n-4)^4}{(2n+4)^4}}=\\=\lim_{n\to\infty}\frac{1-(\frac{2n-4}{2n+4})^4_{\to1}}{1+(\frac{2n-4}{2n+4})^4_{\to1}}=\frac{0}{2}=0$