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Solving an difficult inequality

  1. Sep 10, 2005 #1
    Ill take it from the top :smile: please excuse me for any misspellings.

    In Numerical analysis, I have to show that a function only converges towards a solution in a certain interval.
    The function is

    f(x)=x/8+arctg(x)

    Im using Newtons method, i.e.

    xk+1 = xk - f(x)/f'(x)

    And i know it will converge if I am in an interval that satisfies

    |xk-xk+1| < 2xk

    I then use that

    f(x)/f'(x) < 2xk

    giving me

    1+8*arctg(x)/x
    --------------- < 2
    1+8/1+x^2

    My problem is now how to solve this inequality, i'm trying with mathematica, but i cant make it work :cry:
    Its not important how I solve it, i just need a solution, and guidelines to finding it...
    Anyone up for the task?
     
  2. jcsd
  3. Sep 10, 2005 #2

    Fermat

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    Homework Helper

    I rearranged your inequality to get,

    x < tan{x(x²+17)/8(x²+1)}

    I plotted y = tan{x(x²+17)/8(x²+1)} and y = x using graphmatica and I got y = x < y = tan{x(x²+17)/8(x²+1)} for x < 1.829 (approx.)
     

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    Last edited: Sep 10, 2005
  4. Sep 10, 2005 #3
    Thanks!
    Sometimes I hate myself :-(
    The problem for mathematica is obviously the arctg expression, so y the h*** didnt i think of reaaranging it...
    i will go do that now... thanks man!
     
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