Functions Question 161
Question: $ \underset{n\to \infty }{\mathop{\lim }},{{(4^{n}+5^{n})}^{1/n}} $ is equal to
Options:
A) $ 4 $
B) 5
C) $ e $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Given limit $ =\underset{n\to \infty }{\mathop{\lim }}{{(4^{n}+5^{n})}^{1/n}} $ $ =\underset{n\to \infty }{\mathop{\lim }}5,{{[ {{{ 1+{{( \frac{4}{5} )}^{n}} }}^{{{(5/4)}^{n}}}} ]}^{(1/n),.,{{(4/5)}^{n}}}}=5,.,e^{0}=5 $ . $ ( \because {{( \frac{4}{5} )}^{n}}\to 0,\text{as },n\to \infty ) $
BETA
