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Question

Let f:RR be a positive increasing function with limxf(3x)f(x)=1. Then limxf(2x)f(x)

A
32
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B
3
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C
1
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D
23
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Solution

The correct option is C 1
Given: f is a +ve increasing sunction
limxf(3x)f(x)=1
To find:limxf(2x)f(x)
Sol: f(x) is a positive increasing function
f(x)>0forallx

f(x)f(2x)f(3x)[increasingfunction]

f(x)f(x)f(2x)f(x)f(3x)f(x)[f(x)>0]

limx1limxf(2x)f(x)limxf(3x)f(x)[sandwichtheorem]

limxf(2x)f(x)=1
Hence, correct answer is 1


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