Question

Помогите решить срочно )

Answer 1

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

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