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Determine the value of k, if f(x) = {((k...

Determine the value of k, if `f(x) = {((kcosx)/(pi-2x),if x!=(pi)/2),(3,if x = (pi)/2):}`

Text Solution

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The correct Answer is:
k = 6
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Knowledge Check

  • The value of lim_(n rarr pi/2) (cotx-cosx)/((pi-2x)^(3)) , is

    A
    (1/2)
    B
    (1/4)
    C
    (1/8)
    D
    (1/16)

  • The value of the intergal int_0^(pi//2) (phi(x))/(phi (x) + phi(pi/2 -x)) dx is

    A
    `pi//4`
    B
    `pi//2`
    C
    `pi//6`
    D
    `pi`

  • The maximum value of the function f(x) = sin (x+pi/6)+ cos (x+pi/6) in the interval (0, pi/2) occurs at

    A
    `pi/12`
    B
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    C
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    D
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    f(x) = {{:((k cos x)/(pi - 2x) "if" , x ne (pi)/(2)),( 3, "if" x=(pi)/(2)):} at x= pi/2 , f (x) is containuous , find the value of k .

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