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The range of sin^(-1)[x^2+1/2]+cos^(-1)[...

The range of `sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2]` , where [.] denotes the greatest integer function, is `{pi/2,pi}` (b) `{pi}` (c) `{pi/2}` (d) none of these

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Knowledge Check

  • Range of f(x)=sin^(-1)[x-1]+2cos^(-1)[x-2] ([.] denotes greatest integer function)

    A
    `{-(pi)/(2), 0}`
    B
    `{(pi)/(2), 2pi}`
    C
    `{(pi)/(4), (pi)/(2)}`
    D
    `{(3pi)/(2), 2pi}`

  • The value of int_(0)^(2pi)[sin 2x(1+cos 3x)]dx , where [t] denotes the greatest integer function, is:

    A
    `-pi`
    B
    `2pi`
    C
    `pi`
    D
    `-2pi`

  • The value of int_(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes greatest integer function) is equal to

    A
    `pi+ cot 1`
    B
    `pi+ cot 2`
    C
    `pi+ cot1 + cot2`
    D
    `cot 1+cot 2`

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    f(x)=lim_(n rarr oo)sin^(2n)(pi x)+[x+(1)/(2)], where [.] denotes the greatest integer function,is

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