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Newton's method (intersection points)

  1. Mar 22, 2007 #1
    1. The problem statement, all variables and given/known data

    Given two functions; y= ln(x) and y=(x^2)/8 - 2

    Use Newton's Method to approximate all intersection points of the given functions, each with 3 decimal places.

    2. Relevant equations

    Xn+1 = Xn - f(x) / f`(x)

    3. The attempt at a solution

    Step 1: I equated the two equations, and I got

    f(x) = ln(x) - (x^2)/8 +2

    Step 2: I found the derivative as f`(x) = 1/x - x/4

    Step 3: then I drew the graphs, and I found that they only intersect at a point near 5.4 (because ln(x) doesn't have any graph in the -x direction)

    so I started off x1 = 5.4 and then using the equation given above I found the following values:

    X2 = 5.435
    X3 = 5.436
    X4 = 5.435
    X5 = 5.436

    Can you guys please tell me if I did the solution right and at which point do I stop ... they keep going ... I'm not going same 3 decimal places for any of them ???
    I hope someone would answer soon because I have it due tomorrow early morning. Thanks and can you also tell that whatever I did was right and nothing else was to be done!

  2. jcsd
  3. Mar 23, 2007 #2


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    Staff Emeritus
    Science Advisor

    Yes, you are doing fine with one proviso- if you want the answer correct to 3 decimal places, use more than 3 decimal places, 4 should do, during your calculation. Continue until the 4 decimal places are the same or at least give the same answer rounded to 3 decimal places.
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