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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.

- Thread starter SoaringQuail
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- #1

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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.

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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

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.

[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 "x

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