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Math Help - Taylor series and error approximations

  1. #1
    Member Jones's Avatar
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    Taylor series and error approximations

    Hello,

    Im having some trouble with the error approximations in relation to Taylor series.

    For example [Math]f(x) = x^{1/3}[/tex] about x=8; approximate 9^{1/3}

    [Math]f(x)= (x+8)^{1/3}[/tex]
    f'(x) = 1/3(x+8)^{-2/3}
    f''(x) = -2/9(x+8)^{-5/3}

    f(1) = 2 + 1/12 - 1/288

    However i just can't get my head around how to do the error approximation.

    /Jones
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  2. #2
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    skeeter's Avatar
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    note that the series is alternating ... error < |first omitted term|
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  3. #3
    Member Jones's Avatar
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    Hmm, how do you mean?
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