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Math Help - Remainder in Tailor Polynomial

  1. #1
    Junior Member
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    Remainder in Tailor Polynomial

    Hey I have a test tommorow and am brushing up on some stuff...

    Can someone please explain (not using too many complicated symbols =P)how to get the remainder for a Tailor series, ie using e(x)=1+x+(x^2)/2... as an example.
    Thanks.
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  2. #2
    MHF Contributor
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    I think you mean e^x, not e(x).

    So I don't know exactly what you need but I'll try. Obviously a finite number of terms in a functions Taylor expansion is only an estimate and has an error, which is written in terms of of (n+1), with n terms in the expansion.

    Generally, R_{n+1}(x)=\frac{f^{n+1}(t)}{(n+1)!}(x-c)^{n+1}, where c is the center and t is some value between x and a.
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  3. #3
    MHF Contributor
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    So for example let's say you are estimating e^x centered at 0. Let's use 4 terms. As you said, the first four terms would be 1+x+\frac{x^2}{2}+\frac{x^3}{6} and now let's say that the original function is these terms plus a remainder or error term.

    e^x =1+x+\frac{x^2}{2}+\frac{x^3}{6} + \frac{e^t}{24} x^4 , where 0 < t < x.
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