Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

Let $f : R\rightarrow R$ be a positive increasing function with $\lim\limits_{x\to 0}\large\frac{f(3x)}{f(x)}$$=1$. Then $\lim\limits_{x\to \infty}\large\frac{f(2x)}{f(x)}$ = ?


Can you answer this question?

1 Answer

0 votes
$f(x)$ is a positive increasing function $0 < f(x) < f(2x) < f(3x)$
$\Rightarrow 0 < 1< \large\frac{f(2x)}{f(x)}$$ < \large\frac{f(3x)}{f(x)}$
$\Rightarrow \lim\limits_{x\to \infty}1 \leq \lim\limits_{x\to \infty}\large\frac{f(2x)}{f(x)}$$\leq \lim\limits_{x\to \infty}\large\frac{f(3x)}{f(x)}$
By sandwich theorem
$\lim\limits_{x\to 0}\large\frac{f(2x)}{f(x)}$$=1$
Hence (d) is the correct answer.
answered Dec 23, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App