Ask Questions, Get Answers

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

Let $f:R\rightarrow R$ be such that $f(1)=3$ and $f'(1)=6$. Then $\lim\limits_{x\to 0}\big[\large\frac{f(1+x)}{f(1)}\big]^{\Large\frac{1}{x}}$ equals


Can you answer this question?

1 Answer

0 votes
Given that $f: R\rightarrow R$ such that
$f(1)=3$ and $f'(1)=6$
Then $\lim\limits_{x\to 0}\bigg[\large\frac{f(1+x)}{f(1)}\bigg]^{1/x}$
$\Rightarrow e^{\lim\limits_{x\to 0}\large\frac{1}{x}[\log f(1+x)-\log f(1)]}$
$\Rightarrow e^{\large\lim\limits_{x\to 0}\Large\frac{1/f(1+x)f'(1+x)}{1}}$
Using L Hospital rule
$\Rightarrow e^{\large\frac{f'(1)}{f(1)}}$
$\Rightarrow e^{\Large\frac{6}{3}}$
$\Rightarrow e^2$
Hence (c) is the correct answer.
answered Dec 31, 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