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If alpha is an integer satisfying |a|le4...

If `alpha` is an integer satisfying `|a|le4-|[x]|`, where x is a real number for which `2xtan^(-1)x` is greater than or equal to In `(1+x^(2))` , then the number of maximum possible values of a (where[.] represents the greatest integer function) is

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Knowledge Check

  • Lt_(x to oo) ([x])/(x) (where[.] denotes greatest integer function )=

    A
    0
    B
    1
    C
    2
    D
    3

  • The period of 3x - [3x] is (where [.] denote greatest integer function le x )

    A
    `(1)/(2)`
    B
    `1`
    C
    `2`
    D
    `(1)/(3)`

  • The range of the function f(x) =[sinx + cosx] , (where [x] denotes the greatest integer function) is:

    A
    [-2,1]
    B
    [-2,-1,0,1]
    C
    [-1,1]
    D
    [-2,-1,1]

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