`lim_{x -> 1}` $\dfrac{\sqrt[3]{x + 7} - 2}{x - 1}$
`= lim_{x -> 1}` $\dfrac{x + 7 - 8}{(x - 1)[(\sqrt[3]{x + 7})^{2} + 2.\sqrt[3]{x + 7} + 8]}$
`= lim_{x -> 1}` $\dfrac{1}{(\sqrt[3]{x + 7})^{2} + 2.\sqrt[3]{x + 7} + 8}$
`= 1/((\sqrt[3]{1 + 7})^{2} + 2.\sqrt[3]{1 + 7} + 8)`
`= 1/16`