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If lim(x to 0) ("sin" 2X + a "sin" x)/(...

If `lim_(x to 0) ("sin" 2X + a "sin" x)/(x^(3)) =b` (finite), then `(ab)^(2)` equals…..

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Knowledge Check

  • lim_(x to 0) (2 sin x - sin 2x)/(x^(3)) ie equal to

    A
    2
    B
    1
    C
    2
    D
    `-1`

  • lim_(x to 0) (sin x + cos 3x)^(2//x) =

    A
    1
    B
    `e^2`
    C
    `e^(2//3)`
    D
    does not exist

  • lim_(x to 0) ((1- cos 2x)sin 5x)/(x^(2) sin 3x) =

    A
    `10//3`
    B
    `3//10`
    C
    `6//5`
    D
    `5//6`