Differentiation Question 172
Question: $ \underset{x\to \infty }{\mathop{\lim }}( \frac{x^{2}}{3x-2}-\frac{x}{3} )= $
Options:
A) $ \frac{1}{3} $
B) $ \frac{2}{3} $
C) $ \frac{-2}{3} $
D) $ \frac{2}{9} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Consider $ \underset{x\to \infty }{\mathop{\lim }}[ \frac{x^{2}}{3x-2}-\frac{x}{3} ] $
$ =\underset{x\to \infty }{\mathop{\lim }}[ \frac{3x^{2}-x(3x-2)}{3(3x-2)} ]=\underset{x\to \infty }{\mathop{\lim }}\frac{2x}{3(3x-2)} $
$ =\underset{x\to \infty }{\mathop{\lim }}\frac{2}{3}\frac{1}{( 3-\frac{2}{x} )}=\frac{2}{9} $
BETA
