Question

Помогите решить срочно )

Answer 1

$1)\; \; \lim\limits _{x \to 1} \frac{2x-2}{\sqrt[3]{26+x}-3} = \lim\limits _{x \to 1} \frac{2(x-1)(\sqrt[3]{(26+x)^2}+3\sqrt[3]{26+x}+9)}{(\sqrt[3]{26+x}-3)(\sqrt[3]{(26+x)^2}+3\sqrt[3]{26+x}+9)} =\\\\=\lim\limits _{x\to 1}\frac{2(x-1)(\sqrt[3]{(26+x)^2}+3\sqrt[3]{26+x}+9)}{26+x-27}=2\cdot (\sqrt[3]{27^2}+3\sqrt[3]{27}+9)=\\\\=2\cdot (3^2+3\cdot 3+9)=2\cdot 27=54$

$2)\; \; \lim\limits _{x \to \infty} \frac{\sqrt[3]{x^3+x}}{x+1}= [ \frac{:x}{:x} ]=\lim\limits _{x \to \infty} \frac{\sqrt[3]{1+\frac{1}{x^2}}}{1+\frac{1}{x}} = \frac{\sqrt[3]{1+0}}{1+0} =1$