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Math Help - Taylor Polynomials error bounds

  1. #1
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    Taylor Polynomials error bounds

    Hi, I got a question on the error bound.
    lets say f(x) = (1)/(1-x) b=0 bound error (-1,1) and find where the error is <.001.
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  2. #2
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    Quote Originally Posted by khuezy View Post
    Hi, I got a question on the error bound.
    lets say f(x) = (1)/(1-x) b=0 bound error (-1,1) and find where the error is <.001.
    1+x+x^2+...+x^n = \frac{1 - x^{n+1}}{1 - x} = \frac{1}{1-x} - \frac{x^{n+1}}{1 - x}

    Note that 1+x+x^2+...+x^n = T_n(x) - the nth Taylor polynomial.

    Therefore, \left| T_n(x) - \frac{1}{1-x} \right| = \frac{|x|^{n+1}}{|1-x|}

    The error term \frac{|x|^{n+1}}{|1-x|} cannot be bounded uniformly.
    Only for a particular value of x\in (-1,1) can you make the error sufficiently small.
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