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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) =?
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).
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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