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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
23
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B
32
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C
3
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D
1
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Solution

The correct option is C 1
x2x3x

f(x)f(2x)f(3x)

1f(2x)f(x)f(3x)f(x)

limx1limxf(2x)f(x)limxf(3x)f(x)

1limxf(2x)f(x)1

So, by Sandwich/ Squeeze Play Theorem of limit, we can conclude that,

limxf(2x)f(x)=1

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