Finding the limit as x approaches 8 of (x-8)/(x^(1/3)-2)

[fermio]

Homework Statement

$$\lim_{x\to 8}\frac{x-8}{x^{\frac{1}{3}}-2}$$

Homework Equations

Answer is 12

The Attempt at a Solution

$$\lim_{x\to 8}\frac{x-8}{x^{\frac{1}{3}}-2}= \lim_{x\to 8}\frac{(x^{\frac{1}{3}}-2)(x^{\frac{2}{3}}+2x^{\frac{1}{3}}+2^2)}{x^{\frac{1}{3}}-2}=\lim_{x\to 8}(x^{\frac{2}{3}}+2x^{\frac{1}{3}}+4)=12$$

 

[Shooting Star]

Correct. The latex graphics is not showing everything correctly, though.