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Truncation Error and its Bounds

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data
    a) Derive a Taylor series with n+1 terms and the associated truncation error for
    the function [tex]f(x)=(log(x)-x+1)/(x-1)^2[/tex]
    b) Construct an expression that bounds the truncation error, assuming n > 2, for a given value of x

    2. The attempt at a solution
    a) So I came up with the following series: (from k=2 to k=n+2) [tex]Ʃ((-1)^k*(x-1)^{k-1})/(k+1)[/tex]

    But I'm not really sure how to derive the truncation error. Is the error simply in the n+2 term, and all I have to do is just sub it into the Lagrange remainder equation?

    b) not sure on what interval I should be doing it. As well as taking taking n+2 derivatives to figure out the bound doesn't seem right...

    Thanks for your help,
     
  2. jcsd
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