Question

Evaluate the limit : $\underset{x\to 0}{lim}\frac{x^{2/3}-9}{x-27}$

Answer 1

Using direct substitution method,

$\underset{x\to 0}{lim}\frac{x^{2/3}-9}{x-27}=\frac{0^{2/3}-9}{0-27}$

$=\frac{-9}{-27}$

$=\frac{1}{3}$

Therefore

$\underset{x\to 0}{lim}\frac{x^{2/3}-9}{x-27}=\frac{1}{3}$