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If x is real, prove that (x)/(x^(2)-5x+9...

If x is real, prove that `(x)/(x^(2)-5x+9)` lies between 1 and `(-1)/(11)`.

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Knowledge Check

  • If x is real then y= (2x^2+6x +5)/( x^2 +3x +2) ____ between -2 and +2

    A
    lies
    B
    does not lie
    C
    none
    D
    cannot be determined

  • Given that for all real x, the expression (x^(2)-2x+4)/(x^(2)+2x+4) lies between (1)/(3) and 3 the values between which the expression (9tan^(2)x+6tanx+4)/(9tan^(2)x-6tanx+4) lies are

    A
    0 and 2
    B
    -1 and 1
    C
    -2 and 0
    D
    `1//3` and 3

  • If x is real then the range of (x^(2)-2x+9)/(x^(2)+2x+9) is

    A
    `(-oo, 0] uu (1, oo)`
    B
    `[(1)/(2), 2]`
    C
    `(-oo, -(2)/(9)]uu(1, oo)`
    D
    `(-oo, -6]uu[-2, oo)`

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