Question

найти предел:
(в знаменателе корень кубический)​

Answer 1

$\lim\limits _{n \to \infty}\frac{\sqrt{n^3+n^2-4}\; -\sqrt[5]{n^6}}{\sqrt[3]{n^5+2n}\; +\sqrt[4]{n^6+3n^4+2}}=\Big [\, \frac{:n^{5/3}}{:n^{5/3}}\, \Big ]=\\\\\\=\lim\limits _{n \to \infty}\frac{\sqrt{\frac{1}{n^3}+\frac{1}{\sqrt[3]{n^4}}-\frac{4}{\sqrt[3]{n^{10}}}}\, -\, \sqrt[5]{\frac{1}{\sqrt[3]{n^7}}}}{\sqrt[3]{1+\frac{2}{n^4}}\, +\, \sqrt[4]{\frac{1}{\sqrt[3]{n^2}}+\frac{3}{\sqrt[3]{n^8}}+\frac{2}{\sqrt[3]{n^{20}}}}}=\Big [\frac{0-0}{1+0}=\frac{0}{1}\; \Big ]=0$