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Thread: Higher Level Integration Marathon & Questions

  1. #251
    Cadet
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    Re: Higher Level Integration Marathon & Questions

    Show that



    where G is Catalan's constant.

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    Ancient Orator leehuan's Avatar
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    Re: Higher Level Integration Marathon & Questions

    @Paradoxica I think I finally figured what it should've been.



    Well, hopefully.
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    Ancient Orator leehuan's Avatar
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    Re: Higher Level Integration Marathon & Questions






    Shouldn't be hard assuming I didn't mess up typing the question.

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    -insert title here- Paradoxica's Avatar
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    Re: Higher Level Integration Marathon & Questions

    Quote Originally Posted by leehuan View Post





    Shouldn't be hard assuming I didn't mess up typing the question.
    For all positive real numbers, the iteration derived from Newton's Method applied to the equation q(x)=x²-2 results in the f(x) described above, and converges to the positive real root of the equation.

    Hence, fn(x) converges to √ ̅2 for x>0

    The point x=0 can be discarded, as it is a set of zero measure.

    Hence, the integral is equivalent to



    My only problem with this question is that students don't know how to handle problematic points on the domain of an integral.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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