Functions Question 284
Question: $ \underset{n\to \infty }{\mathop{\lim }},{{(3^{n}+4^{n})}^{\frac{1}{n}}}= $
[Karnataka CET 2003]
Options:
A) 3
B) 4
C) $ \infty $
D) e
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{n\to \infty }{\mathop{lim}}{{(3^{n}+4^{n})}^{\frac{1}{n}}} $ $ =\underset{n\to \infty }{\mathop{lim}}{{(4^{n})}^{\frac{1}{n}}}{{[ \frac{3^{n}}{4^{n}}+1 ]}^{\frac{1}{n}}} $ $ =\underset{n\to \infty }{\mathop{lim}},4,{{[ 1+\frac{1}{{{( \frac{4}{3} )}^{n}}} ]}^{1/n}} $ $ =4\underset{n\to \infty }{\mathop{lim}}{{[ 1+\frac{1}{{{( \frac{4}{3} )}^{n}}} ]}^{1/n}} $ $ =4{{[ 1+\frac{1}{\infty } ]}^{0}}=4\times {{(1)}^{0}} $ $ =4\times 1=4 $ .
BETA
