Functions Question 288
Question: $ \underset{x\to \infty }{\mathop{\lim }},{{( 1-\frac{4}{x-1} )}^{3x-1}}= $
[Karnataka CET 2004]
Options:
A) $ e^{12} $
B) $ {e^{-12}} $
C) $ e^{4} $
D) $ e^{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to \infty }{\mathop{\lim }},{{( 1-\frac{4}{x-1} )}^{3x-1}}=\underset{x\to \infty }{\mathop{\lim }},{{[ {{( 1+\frac{(-4)}{x-1} )}^{( \frac{x-1}{-4} )}} ]}^{( \frac{-4}{x-1} )(3x-1)}} $ $ ={e^{\underset{x\to \infty }{\mathop{\lim }},[ \frac{-4( 3-\frac{1}{x} )}{( 1-\frac{1}{x} )} ]}}={e^{-12}} $ .
BETA
