Question

Вычислить пределы функций

Answer 1

$=\displaystyle \lim_{x \to 0}\dfrac{\Big(\sqrt[3]{27+x}-\sqrt[3]{27-x}\Big)\Big(\sqrt[3]{(27+x)^2}+\sqrt[3]{(27+x)(27-x)}+\sqrt[3]{(27-x)^2}\Big)}{x(1+2\sqrt[3]{x})\Big(\sqrt[3]{(27+x)^2}+\sqrt[3]{(27+x)(27-x)}+\sqrt[3]{(27-x)^2}\Big)}=$

$\displaystyle \lim_{x \to 0} \dfrac{\Big(\sqrt[3]{27+x}\Big)^3-\Big(\sqrt[3]{27-x}\Big)^3}{x\cdot \Big(1+2\sqrt[3]{0}\Big)\Big(\sqrt[3]{(27)^2}+\sqrt[3]{27^2}+\sqrt[3]{(27)^2}\Big)}=\lim_{x \to 0} \dfrac{27+x-27+x}{x\cdot 27}=\dfrac{2}{27}$