Functions Question 239
Question: For $ x\in R,,\underset{x\to \infty }{\mathop{\lim }}{{( \frac{x-3}{x+2} )}^{x}} $ is equal to
[IIT Screening 2000]
Options:
A) e
B) $ {e^{-1}} $
C) $ {e^{-5}} $
D) $ e^{5} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to \infty }{\mathop{\lim }},{{( \frac{x+2-5}{x+2} )}^{x}}=\underset{x\to \infty }{\mathop{\lim }},{{[ {{( 1-\frac{5}{x+2} )}^{\frac{x+2}{-5}}} ]}^{-,\frac{5x}{x+2}}}={e^{-5}} $ $ ( \because ,\underset{x\to \infty }{\mathop{\lim }},\frac{-5x}{x+2}=,\underset{x\to \infty }{\mathop{\lim }},\frac{-5}{1+\frac{2}{x}}=-5 ) $ .
BETA
