Question

$\underset{x\to \infty }{lim}(\frac{x^2}{3x-2}-\frac{x}{3})$ is equal to

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{-2}{3}$
• D. $\frac{-2}{9}$
• E. $\frac{2}{9}$

Answer 1

The correct option is E $\frac{2}{9}$

The value of $\underset{x\to \infty }{lim}(\frac{x^2}{3x-2}-\frac{x}{3})$ is
$=\underset{x\to \infty }{lim}\frac{3x^2-3x^2+2x}{(3x-2)3}$

$=\underset{x\to \infty }{lim}\frac{2x}{3(3x-2)}$
$=\underset{x\to \infty }{lim}\frac{2}{3(3-\frac{2}{x})}=\frac{2}{9}$