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Use Newton’s method with the specified initial approximation x1 to find x3.

  1. Jul 14, 2010 #1
    Please verify my answer.

    1. The problem statement, all variables and given/known data

    Use Newton’s method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)
    x^5+2=0, x_1=-1

    2. Relevant equations



    3. The attempt at a solution

    x5+2=0, x1=-1
    y'=5x4
    x(n+1)=xn-(x5+2)/(5x4 )

    For n=1
    x2=-1-((-1)5+2)/(5(-1)4 )=-6/5=-1.2
    For n=2

    x3=-1.2-((-1.2)5+2)/(5(-1.2)4 )= -1.2-0.4883/10.368=-1.2+0.047=-1.1530
     
  2. jcsd
  3. Jul 15, 2010 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This should be
    x(n+1)=xn-(xn5+2)/(5xn4 )

    Looks good, but you aren't at "4 decimal places" yet. Continue until you get two consecutive results that are the same to 4 decimal places (and I would recommend doing the calculations to at least 5 decimal places until then).
     
  4. Jul 15, 2010 #3
    Hi! What do you mean by
    ?

    The task says to do the third approximation, which I found already....
    Do you mean I should do the fourth...and the fifth?...
     
  5. Jul 15, 2010 #4

    Mark44

    Staff: Mentor

    I think that HallsOfIvy missed the part about the third approximation, so you're done.
     
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