Ill take it from the top please excuse me for any misspellings.(adsbygoogle = window.adsbygoogle || []).push({});

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

Its not important how I solve it, i just need a solution, and guidelines to finding it...

Anyone up for the task?

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# Homework Help: Solving an difficult inequality

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