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Math Help - NRM approximation

  1. #1
    Member
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    NRM approximation

    can someone show me how this is done.. the lnx function has me a bit confuse

    lnx = 4-x

    starting with 2.9 as s first approximation to this roots use newton-rapson method to evaluate successive approximations to this root to 2 decimal places.
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  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
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    We want to find the solution to...

    f(x) = 0 where f(x) = \ln(x) + x - 4.

    We also have,

    f'(x) = \frac{1}{x} + 1

    Newtons Method (aka Newton-Rapson Method) is

    x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}

    Which for our problem is...

    x_{n+1} = x_n - \frac{\ln(x_n) + x_n - 4}{1/x_n + 1}

    So we get...

    x_0 = 2.9

    x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 2.9 - \frac{f(2.9)}{f'(2.9)}

    x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}

    Etc...

    I'll leave it to you to compute each x_n
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