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Find underset( x rarr 0 ) ( "Lim") ( e^(...

Find `underset( x rarr 0 ) ( "Lim") ( e^(sin x) -sin x -1)/( x^(2))`

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Knowledge Check

  • If underset( x rarr 0 ) ("Lim") ( sin 2x + a sinx )/( x^(3)) = p ( finite ) , then

    A
    `a = - 2`
    B
    `a = -1 `
    C
    `p = - 2 `
    D
    ` p = - 1`

  • If l = underset( x rarr 0) ("Lim")( x ( 1+ a cos x ) - bsin x ) /( x^(3))= underset( x rarr 0 ) ("Lim") ( 1+a cos x ) /( x^(2))- underset( x rarr 0 ) ("lim")( b sin x )/( x^(3)) , where l in R , then

    A
    ` ( a, b ) = ( -1,0)`
    B
    a & b are nay real numbers
    C
    l = 0
    D
    `l = ( 1)/( 2)`

  • underset( x rarr 0 ) ( "lim")((1+sin x )/( 1- sin x ))^("cosec x ") is equal to :

    A
    e
    B
    1
    C
    `e^(2)`
    D
    None

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