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If f(x)=sin^(-1)x and lim(xto1//2+)f(3x-...

If `f(x)=sin^(-1)x and lim_(xto1//2+)f(3x-4x^3)=a-3lim_(xto1//2+)f(x)`, then [a] is equal to {where [] denotes G.I.F}

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Knowledge Check

  • lim_(xto1) (1-x^(2))/(sin2pix) is equal to

    A
    0
    B
    `oo`
    C
    -2
    D
    2

  • lim_(xto1)(1/(1-x)-3/(1-x^3)) is equal

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

  • f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim _(x to 0^(-)){(f (x))/(tna ^(2)x)} +|lim _(x to 2 ^(-))f (x)|+ lim _(x to 2 ^(+)) (5 f (x)) is equal to (where {.} denotes fraction part function)

    A
    7
    B
    8
    C
    12
    D
    Non-existent