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calculus - limits

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limit as x approaches infinity; tan^(-1) (x^2 - x^4)

any help is appreciated =D

  • calculus - limits -

    I am going to use an intuitive approach

    let theta = tan^-1 (x^2 - x^4)

    or tan(theta) = x^2 - x^4
    now as x---> ∞ the right side of the above equation ---> - ∞

    I know that tan 90º or tan(pi/2) is undefined, but as I approach 90º or pi/2
    the tangent value becomes infinitely large positively,
    and the tangent of -90º or -pi/2 becomes -infinitely large.

    so
    limit tan^(-1) (x^2 - x^4) as x ---> ∞
    = -pi/2

    check:
    set your calculator to radians
    enter a huge number, multiply it by -1, then enter
    2nd Tan
    I got -1.570796 or - pi/2

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