Question

How to evaluate: lim (x->27) (∛x-3)/(x-27).

Answer 1

hint:
we can use this identity:
\[x - 27 = \left( {\sqrt[3]{x} - 3} \right)\left( {\sqrt[3]{{{x^2}}} + 9 + 3\sqrt[3]{x}} \right)\]

Answer 2

so we can write:
\[\Large \frac{{\sqrt[3]{x} - 3}}{{x - 27}} = \frac{{\sqrt[3]{x} - 3}}{{\left( {\sqrt[3]{x} - 3} \right)\left( {\sqrt[3]{{{x^2}}} + 9 + 3\sqrt[3]{x}} \right)}}\]
please simplify