IF F(x) is increasing function and limit x→infinity f(3x)/f(x) =1 then limit x→infinity f(2x)/f(x) =?

since f(x) is increasing, so       f(3x)>f(2x)>f(x) => f(3x)/f(x)>f(2x)/f(x)>1 so  Lt of x->infinity=>f(2x)/f(x)=1 (by sandwich theorem).

Approved

Dear rohit,

since f(x) is increasing, so       f(3x)>f(2x)>f(x)

Hence we can say,

f(3x)/f(x)>f(2x)/f(x)>1 so  Lt of x->infinity=>f(2x)/f(x)=1

Here we have used sandwich theorem.

To know more abt the theorem, please refer: http://www.sosmath.com/calculus/limcon/limcon03/limcon03.html

We are all IITians and here to help you in your IIT JEE preparation.

All the best.

 If you like this answer please approve it....

win exciting gifts by answering the questions on Discussion Forum

Approved