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Math Help - Convergents and Fixed Points

  1. #1
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    Convergents and Fixed Points

    Hey all. Could someone check my work here and get back to me before 9 central time. THanks, GREEN!

    *****Part A:

    Let f(x) = 1 / (x^2 + 3x -2)

    Find the fixed points for f.

    I got x = 0.85106383, x = -0.3191489, and x = -3.510638.

    Are these correct?


    *****Part B:

    Try different seeds to find out which, if any are convergent.

    To me it seems that it converges at -0.343379569, so according to this none are convergent.

    I am not sure about this though.

    Could someone please check my answers.

    GREEN
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  2. #2
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    Quote Originally Posted by Mr_Green View Post
    [B]Hey all. Could someone check my work here and get back to me before 9 central time. THanks, GREEN!

    *****Part A:

    Let f(x) = 1 / (x^2 + 3x -2)

    Find the fixed points for f.

    I got x = 0.85106383, x = -0.3191489, and x = -3.510638
    Are these correct?
    A fixed point has to exist by the Brouwer Fixed Point theorem (somebody correct me if I am wrong).
    If we solve,
    x=\frac{1}{x^2+3x-2}
    We get,
    x^3+3x^2-2x-1=0
    The solutions to this equation are roots.
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  3. #3
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    ok i checked my work, and i believe these are my new and improved answers ...


    part a:


    x = 0.834
    x = -0.343
    x = -3.491



    part b:

    remains the same, except now one of the fixed points are convergent.


    How's this look guys?



    Here is part c now:


    Zoom in on a convergent point until the graph of f looks like a straight line (this phenomenon is known as "local linerity.") Find the coordinates of two points on f - one to the left and one to the right of the convergent point. Then find the slope (rise over run) of the segment connecting these two points.

    I would also like to check my slope with someone, so if you find it, please let me know.



    Thanks again,
    GREEN
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