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Math Help - error bound taylor polynomial

  1. #1
    Junior Member
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    error bound taylor polynomial

    Use taylor's theorem to bound the error in approximating the function f(x) = e^x with the maclaurin series M_6(x) on the interval [-1,1]
    The formual for this type of thing is
    |f(x) - P_n(x)| \leq \frac {K_{n + 1}} {(n + 1)!}|x - x_0|^{n + 1}

    the max bound is K_{n + 1} = e^1 x_0 =0, n = 6

    \frac {e^1} {7!} |-1|^7 \approx 5.39 * 10^-4

    is this correct?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by diroga View Post
    The formual for this type of thing is
    |f(x) - P_n(x)| \leq \frac {K_{n + 1}} {(n + 1)!}|x - x_0|^{n + 1}

    the max bound is K_{n + 1} = e^1 x_0 =0, n = 6

    \frac {e^1} {7!} |-1|^7 \approx 5.39 * 10^{-4}

    is this correct?
    More or less, but you need to improve your notation and explain what things are.

    CB
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