displaystyle lim x arrow ∞((x2/3 x-2)-(x/3))=

Question

displaystyle lim x arrow ∞((x2/3 x-2)-(x/3))= (A) (1/3) (B) (2/3) (C) (-2/3) (D) (2/9)

Tardigrade Admin · Accepted Answer

Consider displaystyle lim x arrow ∞[(x2/3 x-2)-(x/3)] = displaystyle lim x arrow ∞[(3 x2-x(3 x -2)/3(3 x-2))] = displaystyle lim x arrow ∞ (2 x/3(3 x-2)) = displaystyle lim x arrow ∞ (2/3) (1/(3-(2)x))=(2/9)

Q. $x \to \infty lim (\frac{x ^{2}}{3 x - 2} - \frac{x}{3}) =$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{- 2}{3}$

$\frac{2}{9}$

Consider $x \to \infty lim [\frac{x ^{2}}{3 x - 2} - \frac{x}{3}]$
$= x \to \infty lim [\frac{3 x ^{2} - x ( 3 x - 2 )}{3 ( 3 x - 2 )}]$
$= x \to \infty lim \frac{2 x}{3 ( 3 x - 2 )}$
$= x \to \infty lim \frac{2}{3} \frac{1}{( 3 - \frac{2}{x} )} = \frac{2}{9}$

Q. x→∞lim​(3x−2x2​−3x​)=

31​

32​

3−2​

92​