# Limit ( x^3 / 3x^2-4 -x^2 /3x+2) as x-->infinite

Solution:

$\lim_{x\to \infty}[\frac{x^{3}}{3x^{2}-4}-\frac{x^{2}}{3x+2}]\\ \\ \Rightarrow \hspace{0.5cm}\lim_{x\to \infty}\frac{2x^{3}+4x^{2}}{9x^{3}+6x^{2}-12x-8}\\ \\ \Rightarrow \hspace{0.5cm}\lim_{x\to\infty}\frac{2+\frac{4}{x}}{9+\frac{6}{x}-\frac{12}{x^{2}}-\frac{8}{x^{3}}}=\frac{2}{9}$

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