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LaGrange Error and power series

  1. Mar 15, 2007 #1
    There's a homework problem that I've been struggling over:

    Find a formula for the truncation error if we use 1 + x^2 + x^4 +x^6 to approximate 1/(1-x^2) over the interval (-1, 1).

    Now, I assume that you need to use LaGrange error but I'm not sure how to proceed. Any help would be greatly appreciated.
     
  2. jcsd
  3. Mar 15, 2007 #2

    HallsofIvy

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    Since you mention LaGrange error, presumably you know the formula for it! Off the top of my head, I believe it is
    [tex]E\le \frac{M}{(n+1)!}|x-a|^{n+1}[/tex]
    where M is an upper bound on the n+ 1 derivative. Here, by the way, you can take either n+1= 7 or replace "x2" by "y" and use n+1= 4 with the formula in y.
     
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