Question

Solve:
$\underset{x\to 27}{lim}\frac{x^{2/3}-9}{x-27}$

Answer 1

$\begin{array}{c}\Rightarrow {lim}_{x\to 27}\frac{x^{2/3}-{\left(27\right)}^{2/3}}{x-27}\\ \Rightarrow \frac{2}{3}\times {\left(27\right)}^{\frac{2}{3}-1}\\ \Rightarrow \frac{2}{3}\times {\left(27\right)}^{-1/3}\\ \Rightarrow \frac{2}{3}\times 3^{3\times \frac{-1}{3}}\\ \Rightarrow \frac{2}{3}\times 3^{-1}=\frac{2}{3}\times \frac{1}{3}=\frac{2}{9}\end{array}$