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Calculate an error bound of this interpolation value

  1. Sep 25, 2006 #1
    I attached the file. I am up to 1(c).

    Would the error bound of the interpolation value just be taylor series error term?

    Thanks
     

    Attached Files:

  2. jcsd
  3. Sep 25, 2006 #2

    HallsofIvy

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    Yes, that's just the Taylor Series error form:
    [tex]error< \frac{M_n}{n!}|x^n|[/tex]
    Where Mn is an upperbound on the nth derivative between 0 and x.
     
  4. Sep 25, 2006 #3
    so the 3rd derivative of ln(1+x)= 2/((1+x)^3)

    And the upper bound on that between 0 and x=1, since I was solving ln(1+1), is 2?



    so Mn=

    so error<(2/(3!))*1^3=0.333333333333333333?

    I was wondering is the error bound meant to be 0.333333333 each side or 0.3333333 overall so is it 0.1666666666666666666666 each side(ie. positive and negative) or 0.3333333333 a side so 0.66666666666666666666666 overall both sides?
     
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