Limit finding

1. Jan 27, 2008

fermio

1. The problem statement, all variables and given/known data
$$\lim_{x\to 8}\frac{x-8}{x^{\frac{1}{3}}-2}$$

2. Relevant equations

3. The attempt at a solution
$$\lim_{x\to 8}\frac{x-8}{x^{\frac{1}{3}}-2}= \lim_{x\to 8}\frac{(x^{\frac{1}{3}}-2)(x^{\frac{2}{3}}+2x^{\frac{1}{3}}+2^2)}{x^{\frac{1}{3}}-2}=\lim_{x\to 8}(x^{\frac{2}{3}}+2x^{\frac{1}{3}}+4)=12$$

Last edited: Jan 27, 2008
2. Jan 27, 2008

Shooting Star

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