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Math Help - I have 2 " Numerical analysis problems that I need help with

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    Post I have 2 " Numerical analysis problems that I need help with

    I have 2 " Numerical analysis problems that I need help with-screen-shot-2012-12-12-10.15.10-am.png

    I am currently working on these 2 problem on the picture but I am not sure if I am doing it right. Any help will be very appreciated.... Thanks
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    MHF Contributor Drexel28's Avatar
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    Re: I have 2 " Numerical analysis problems that I need help with

    For the second one, merely check that the k+1st Newton iterate is x_{k+1}=\frac{1}{2}\left(x_k+\frac{5}{x_k}\right). Now, I'm sure that you can prove that whatever your initial guess x_0 is, that this sequence will be monotone and bounded and so convergent.
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