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Math Help - Lagrange error bound. What is it?

  1. #1
    JRH
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    Lagrange error bound. What is it?

    This is a sample from the AP calculus exam. "If the function e^(-3x)/27 is approximated using the Maclaurin polynomial 1/27-x/9+x^2/6, what is the Lagrange error bound for the maximum error on |x|<0.5?" The textbook I'm using has no definition for Lagrange error bound, so I don't know what is being asked or how to find it.
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  2. #2
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    Re: Lagrange error bound. What is it?

    It's also called the Lagrange remainder.

    Given a Taylor series with n terms, the Lagrange remainder is R_n=\frac{f^{(n+1)}(\xi)}{(n+1)!}(x-x_0)^{n+1} for some \xi.

    What you need to do is to find f^{(n+1)}(x) and pick |\xi|<0.5 and |x|<0.5 so that R_n is maximized. That tells you the maximum error when using the Taylor series with n terms as the approximation.
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