Functions Question 158
Question: If $ a,\ b,\ c,\ d $ are positive, then $ \underset{x\to \infty }{\mathop{\lim }},{{( 1+\frac{1}{a+bx} )}^{c+dx}}= $
[EAMCET 1992]
Options:
A) $ {e^{d/b}} $
B) $ {e^{c/a}} $
C) $ {e^{(c+d)/(a+b)}} $
D) $ e $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to \infty }{\mathop{\lim }}{{( 1+\frac{1}{a+bx} )}^{c+dx}}=\underset{x\to \infty }{\mathop{\lim }}{{{ {{( 1+\frac{1}{a+bx} )}^{a+bx}} }}^{\frac{c+dx}{a+bx}}}={e^{d/b}} $ $ { \because \underset{x\to \infty }{\mathop{\lim }}{{( 1+\frac{1}{a+bx} )}^{a+bx}}=e . $ and $ . \underset{x\to \infty }{\mathop{\lim }},\frac{c+dx}{a+bx}=\frac{d}{b} } $ .
BETA
