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$\lim_{x \rightarrow \infty}\left(\frac{x^{2}}{3x-2}-\frac{x}{3}\right)$ = 

Answer:

Explanation:

Consider $\lim_{x \rightarrow \infty}\left(\frac{x^{2}}{3x-2}-\frac{x}{3}\right)$ 

=$\lim_{x \rightarrow \infty}\left[\frac{3x^{2}- x(3x-2)}{3(3x-2)}\right]$

= $\lim_{x \rightarrow \infty}\frac{2x}{3(3x-2)}$

= $\lim_{x \rightarrow \infty}\frac{2x}{3x(3-\frac{2}{x})}$

= $\lim_{x \rightarrow \infty}\frac{2}{3}\frac{1}{(3-\frac{2}{x})}$

= $\frac{2}{3}\times\frac{1}{(3-0)}$ = 2/9