Functions Question 204
Question: $ \underset{x\to \infty }{\mathop{\lim }},{{
[ 1+\frac{1}{mx} ]}^{x}} $ equal to [Kurukshetra CEE 1998]
Options:
A) $ {e^{1/m}} $
B) $ {e^{-1/m}} $
C) $ e^{m} $
D) $ m^{e} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y=\underset{x\to ,\infty }{\mathop{\lim }}{{( 1+\frac{1}{mx} )}^{x}}=\underset{x\to ,\infty }{\mathop{\lim }}{{( 1+\frac{1}{mx} )}^{mx\cdot \frac{1}{m}}} $
$ \Rightarrow y={e^{1/m}},,( \because \underset{x\to ,\infty }{\mathop{\lim }}{{( 1+\frac{1}{x} )}^{x}}=e ) $ .
BETA
