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Math Help - Newton's Method of Approximation

  1. #1
    Member purplec16's Avatar
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    Newton's Method of Approximation

    Use Newton's Method of Approximation to approximate the zero of the function in the indicated interval to six decimal places

    f(x)={x}^{3 }+3{x}^{ 2}-3 in the interval [-2,0]

    I know how to use Newton's method of Approximation but what I am confused with is 2 things:

    1. What number do I use in my approximation (i.e my {x}_{0 } )

    2. When it says to six decimal places does that mean I have to do the approximation six times?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by purplec16 View Post
    Use Newton's Method of Approximation to approximate the zero of the function in the indicated interval to six decimal places

    f(x)={x}^{3 }+3{x}^{ 2}-3 in the interval [-2,0]

    I know how to use Newton's method of Approximation but what I am confused with is 2 things:

    1. What number do I use in my approximation (i.e my {x}_{0 } )

    2. When it says to six decimal places does that mean I have to do the approximation six times?
    For question 1 you need to guess. Since

    f(-2)=1 and f(-1)=-1 I would guess the midpoint x=-\frac{3}{2}

    For number two you need to keep using newtons method until the 6th digit after the decimal place no longer changes it could be more of less than six times.

    P.S it will not take 6 iterations.
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  3. #3
    Member purplec16's Avatar
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    Ok thank you would -.5 be a good guess?
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    You can use the following to "know when to stop":

     |x_0-x_n|< \frac{M}{2m}|x_{n+1}-x_n}|


    Where  M=sup\{f''(x) | x\in I\} and  m=inf\{f'(x)| x\in I\}
    Last edited by Also sprach Zarathustra; June 13th 2011 at 09:54 AM.
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    You can use the following to "know when to stop":

     |x_0-x_n|< \frac{M}{2m}|x_{n+1}-x_n}|


    Where  M=sup\{f''(x) x\in I\} and  m=inf\{f'(x) x\in I\}
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