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Let f : R to R ,f (a) =1, f '(a) = 2 th...

Let `f : R to R ,f (a) =1, f '(a) = 2 ` then prove that ` Lt _(x to 0) ((f ^(2) (a + x ) )/( f (a)))^(1/x) = e ^(4)`

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Knowledge Check

  • Let f:R to R be such that f(x)=3 and f'(1)=6 then Lt_(x to 0)((f(1+x))/(f(1)))^(1//x)=

    A
    e
    B
    `e^(2)`
    C
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    D
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  • Let f : R to R be a differentiable function such that f(2) = -40 ,f^1(2) =- 5 then lim_(x to 0)((f(2 - x^2))/(f(2)))^(4/(x^2)) is equal to

    A
    `e^(32)`
    B
    `sqrt(e)`
    C
    `1/(sqrt(e))`
    D
    `e`
  • If f : R to R is defined by f(x) = x^(2)- 6x + 4 then , f(3x + 4) =

    A
    `3x^(2) + 2x +2`
    B
    `9x^(2)+ 6x - 4`
    C
    `2x+2`
    D
    `x^(2) + 6x + 9`
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