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{:("Column-I","Column-II"),(A.lim(x to 0...

`{:("Column-I","Column-II"),(A.lim_(x to 0) (cos x - cos3x)/(x("Sin"x - "sin"3x)),p. 3),(B.lim_(x to 0) ("sin" 4x)/(tan 2x),q. -2),(C. lim_(x to oo) (x^(4) + 2x^(3) + 3)/(2x^(4) - x + 2),r.(1)/(2)),(D.lim_(x to 2) (sqrt(3x^(2) + 3x - 9) - sqrt(3x + 3))/(x - 2),s. 2):}`

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A(q),B(s),C(r ),D(s)
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Knowledge Check

  • 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) (x tan 3 x)/("sin"^(2) x) is

    A
    0
    B
    1
    C
    2
    D
    3

  • 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`

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    Explore conceptually related problems

    Evaluate lim_(x to 0) [(3x^(2) + 4x + 5)/(x^(2) - 2x + 3)]

    {:("Column-I","Column-II"),(A.lim_(x to 0) [("sin"[x])/([x])],p.0),(B.lim_(x to 0)) [(tan [x])/([x])],q.10),(C. lim_(x to 0) [x],r.9),(lim_(x + (pi)/(2)) [cos x],s.-1),( , t. lim_(x to (pi)/(2)) (e^(cosx) - 1)/(cos X)):}

    lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

    lim_(x to pi)(sin 3x)/(sin 2x) is equal to

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

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