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

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

Grade:12

2 Answers

Padma Bhushan Borah
14 Points
12 years ago

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).

SAGAR SINGH - IIT DELHI
879 Points
12 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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All the best.

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