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Math Help - Consider the function...

  1. #1
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    Consider the function...

    Need help revising on this question. Not sure what to search for :s.


    Consider the function f(x) = x + lnx - 2 = 0.


    1. Find two appropriate rearrangement for the equation x + lnx - 2 = 0 in the form of xn-1 = g(Xn):
    2. By considering the derivative of g(x) explaining which one of the rearrangement is likely to converge to a suspected root near x = 1.4.
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  2. #2
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    Re: Consider the function...

    Quote Originally Posted by passingtime View Post
    Not sure what to search for
    ... iterative methods.

    There are two ways to make one of the x's in the equation the subject.

    (One way is to add 2 to and subtract lnx from both sides, and the other is to add 2, subtract x and then take the exp of each side.)

    Label the subject term xn+1 and the other x term xn. Then iterate.

    In general the method fails if absolute value of g'(xn) is greater than 1 near the root.

    So if you proceed as suggested in step 2 you'll see which arrangement is going to work near 1.4.
    Last edited by tom@ballooncalculus; March 13th 2012 at 05:00 AM.
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  3. #3
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    Re: Consider the function...

    I'll get back to u on this. This seems a little complicated right now.

    Thanks a lot for the reply it has helped.
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