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Let f: RvecR be a differentiable functio...

Let `f: RvecR` be a differentiable function having `f(2)=6,f^(prime)(2)=1/(48)dot` Then evaluate `("lim")_(xvec2)int_6^(f(x))(4t^3)/(x-2)dt`

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Knowledge Check

  • Let f:R to R be a differentiable function having f(2)=6,f'(2) =(1)/(12) . Then, lim_(x to 2)overset(f(x))underset(6)int(4t^(3))/(x-2)dt , equals

    A
    18
    B
    12
    C
    36
    D
    24

  • Let f:R to R be a differentiable function such that f(2)=2 . Then, the value of lim_(xrarr2) int_(2)^(f(x))(4t^3)/(x-2) dt , is

    A
    `6f'(2)`
    B
    `12 f'(2)`
    C
    `32f'(2)`
    D
    none of these

  • Let f : R to R be a differentiable function and f(1) = 4 . Then, the value of lim_(x to 1)int_(4)^(f(x))(2t)/(x-1)dt is :

    A
    `8 f'(1)`
    B
    `4 f'(1)`
    C
    `2 f'(1)`
    D
    `f'(1)`

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    Let f : R to R be a continuously differentiable function such that f(2) = 6 and f'(2) = 1/48 * If int_(6)^(f(x)) 4t^(3) dt = (x-2) g(x)" than" lim_( x to 2) g(x) is equal to

    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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