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Let f:""RrarrR be a positive increas...

Let `f:""RrarrR` be a positive increasing function with `lim_(xrarroo)f(3x)/(f(x))=1` . Then `lim_(xrarroo)f(2x)/(f(x))=` (1) `2/3` (2) `3/2` (3) 3 (4) 1

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`x>0 => 0 < f(2x) < f(2x) < f(3x) `
`0<1< (f(2x))/(f(x)) < (f(3x))/(f(x))`
`1 <= lim_(x-> oo) (f(2x))/(f(x)) <= lim_(x->oo) (f(3x))/(f(x))`
`1 <= lim_(x-> oo) (f(2x))/(f(x)) <= 1`
`lim_(x-> oo) (f(2x))/(f(x)) = 1`
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Knowledge Check

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    A
    1
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    D
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    is 0
    B
    does not exist
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    D
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  • Let f: RrarrR be a differential function, such that f(3) = 3 and f'(3) =1/2 then lim_(x rarr3)((int_3^(fx)x.t^2dt)/(x^2-9)) is

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