\displaystyle \lim_{n \to \infty} \frac{1 + \sqrt[4]{n}}{5 + \sqrt[3]{n}} : \frac{\sqrt[3]{n}}{\sqrt[3]{n}} = \lim_{n \to \infty} \frac{\frac{1}{\sqrt[3]{n}} + \frac{1}{\sqrt[12]{n}}}{\frac{5}{\sqrt[3]{n}} + 1} = \frac{0 + 0}{0 + 1} = 0