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Let f(x) {(-2sinx,- pi le x le - pi/2),(...

Let `f(x) {(-2sinx,- pi le x le - pi/2),(a sin x+b ,-pi/2 le x le pi/2),(cosx,pi/2 le x le pi):}`

A

a=1,b=1

B

a=-1,b=-1

C

a=-1 ,b=1

D

a=1 , b=-1

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • The value of a and b such that the function f(x) {:{(-2 sin x", "-pile x le -pi/2 ),(a sin x+b " ," -pi/2 lt x lt pi/2 ),(cos x", " pi/2 le x le pi ):} is continuous in [ - pi , pi ] are

    A
    `-1,0`
    B
    `1,0`
    C
    `1,1`
    D
    `-1,1`

  • The value of a and b such that the function f(x)={(-2sinx"," , -pi le x le -(pi)/(2)),(a sinx+b",", -(pi)/(2) lt x lt (pi)/(2)),(cosx",", (pi)/(2) le x le pi ):} is continuous in [-pi,pi] are

    A
    `-1, 0`
    B
    1, 0
    C
    1, 1
    D
    `-1, 1`

  • The function f(x) = {{:(x + asqrt(2) sin x, 0 le x lt pi//4),(2x cotx +6, pi//4 le x le pi//2),(a cos 2x-b sin x, pi//2 lt x le pi):} is continuous for 0 le x le pi then a, b are

    A
    `pi/6, pi/12`
    B
    `pi/3, pi/6`
    C
    `pi/6, -pi/12`
    D
    none of these

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