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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`
answer
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Knowledge Check

  • Let f: R to R be a positive increasing function with lim_(x to infty) (f(3x))/(f(x))=1 . Then lim_(x to infty) (f(2x))/(f(x)) =

    A
    1
    B
    `2/3`
    C
    `3/2`
    D
    3

  • Let f(x)=(sqrt(x+3))/(x+1) , then lim_(xrarr-3)f(x)

    A
    is 0
    B
    does not exist
    C
    is `1//2`
    D
    is `-1//2`

  • 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

    A
    `3/4`
    B
    `9/4`
    C
    `(-9)/4`
    D
    `9/2`