Limite da função

[Anna Menina]

\(\lim_{h\to 0}\frac{\sqrt[3]{8 + h} - 2}{h}\)

[Man Utd]

\(\lim_{h\to 0}\frac{\sqrt[3]{8 + h} - 2}{h}\)

olá, lembre-se de \(a^{3}-b^{3}=(a-b)*(a^{2}+ab+b^{2})\)

\(\\\\\\ \lim_{h\to 0}\frac{(\sqrt[3]{8 + h} - 2)*((\sqrt[3]{8 + h})^{2}+2*\sqrt[3]{8 + h}+4)}{h*((\sqrt[3]{8 + h})^{2}+2*\sqrt[3]{8 + h}+4)} \\\\\\ \lim_{h\to 0}\frac{8+h-8}{h*((\sqrt[3]{8 + h})^{2}+2*\sqrt[3]{8 + h}+4)} \\\\\\ \lim_{h\to 0}\frac{1}{(\sqrt[3]{8 + h})^{2}+2*\sqrt[3]{8 + h}+4} =\frac{1}{12}\)

confira com o gabarito por favor.