Originally Posted by

**topsquark** Check that again:

$\displaystyle \lim_{x \to \infty} \dfrac{5x^2}{\sqrt[3]{{\left( {x^3 + 5x^2 } \right)^2 }} + x\sqrt[3]{{x^3 + 5x^2 }} + x^2 }$

$\displaystyle = \lim_{x \to \infty} \dfrac{5}{\frac{1}{x^2}\sqrt[3]{{\left( {x^3 + 5x^2 } \right)^2 }} + \frac{1}{x}\sqrt[3]{{x^3 + 5x^2 }} + 1 }$

$\displaystyle = \lim_{x \to \infty} \dfrac{5}{\sqrt[3]{{\left( {1 + \frac{5}{x} } \right)^2 }} + \sqrt[3]{{1 + \frac{5}{x} }} + 1 }$

$\displaystyle = \frac{5}{1 + 1 + 1} = \frac{5}{3}$

-Dan