Functions Question 247
Question: $ \underset{x\to \infty }{\mathop{\lim }}{{( \frac{x+a}{x+b} )}^{x+b}}= $
[EAMCET 2001]
Options:
A) 1
B) $ {e^{b-a}} $
C) $ {e^{a-b}} $
D) $ e^{b} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to \infty }{\mathop{lim}}{{( \frac{x+a}{x+b} )}^{x+b}}=\underset{x\to \infty }{\mathop{lim}}{{( 1+\frac{a-b}{x+b} )}^{x+b}} $ $ =\underset{x\to \infty }{\mathop{lim}}{{{ {{( 1+\frac{a-b}{x+b} )}^{\frac{x+b}{a-b}}} }}^{a-b}}={e^{a-b}} $ .
BETA
