Question

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

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

Answer 1

Answer: (D)

The value of $\displaystyle\lim _{x \rightarrow \infty}\left(\frac{x^{2}}{3 x-2}-\frac{x}{3}\right)$ is
$=\displaystyle\lim _{x \rightarrow \infty} \frac{3 x^{2}-3 x^{2}+2 x}{(3 x-2) 3}$
$=\displaystyle\lim _{x \rightarrow \infty} \frac{2 x}{3(3 x-2)}$
$=\displaystyle\lim _{x \rightarrow \infty} \frac{2}{3\left(3-\frac{2}{x}\right)}=\frac{2}{9}$