Functions Question 220
Question: $ \underset{n\to \infty }{\mathop{\lim }},{{( \frac{n}{n+y} )}^{n}} $ equals
[AMU 1999]
Options:
A) 0
B) 1
C) 1/v
D) $ {e^{-y}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{n\to \infty }{\mathop{\lim }}{{( \frac{n}{n+y} )}^{n}}=\underset{n\to \infty }{\mathop{\lim }}{{( \frac{1}{1+\frac{y}{n}} )}^{n}} $ $ =\underset{n\to \infty }{\mathop{\lim }}{{( 1+\frac{y}{n} )}^{-n}} $ $ =\underset{n\to \infty }{\mathop{\lim }}{{[ {{( 1+\frac{y}{n} )}^{n}} ]}^{-1}}={e^{-y}} $ .
BETA
