LaGrange Error and power series

  • #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.
 

Answers and Replies

  • #2
HallsofIvy
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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.
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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