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

3 years ago

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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).

3 years ago
                    

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



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Sagar Singh


B.Tech IIT Delhi


sagarsingh24.iitd@gmail.com


3 years ago

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