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Math Help - 3 ques regarding diffrentiation: Taylor Polynomial, Newton-Raphson

  1. #1
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    3 ques regarding diffrentiation: Taylor Polynomial, Newton-Raphson



    any help will be appreciated. thanks!!
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  2. #2
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    Quote Originally Posted by samtrix View Post


    any help will be appreciated. thanks!!
    Hello,

    to #3:

    You are supposed to know the Raphson-Newton formula:

    If you are looking for the solutions of T(x) = 0 where T(x) is a term in x and you have found an initial approximate value for a solution then the next approximate value is:

    x_{n+1}=x_n-\frac{T(x_n)}{T'(x_n)} With your problem:

    x_{n+1}=x_n-\frac{\cos(x_n) - 1.4 \cdot \sqrt{x_n^3}}{-\sin(x_n) - 2.1 \cdot \sqrt{x_n}}

    Start with x_0 = 1
    Code:
    x_0        1
    x_1        0.70773205
    x_2        0.677232264
    x_3        0.676832564
    x_4        0.676832494
    All following values equal x_4 (but that depends on the calculator you use)
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  3. #3
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    Hello,

    to #3:

    you'll find additional information on Raphson-Newton method here: http://www.mathhelpforum.com/math-he...ns-method.html
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