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Math Help - Taylor Polynomials Approx. Error

  1. #1
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    Taylor Polynomials Approx. Error

    Hello. I have the following problem:

    Let f(x) = -0.5 cos(2x)

    Determine the Taylor Polynomial at x = 0

    I have : f(x) = -0.5 + x^2 which should be correct

    Now i have to show that the approx. Error in the Intervall [-0.1;0.1] is smaller than 10^{-4} How do i do that ? I have a formula for Langrage´s Rest but not sure how to apply it here

    Edit: I should mention that we have to evaluate the polynomial to the 3rd term
    Last edited by coobe; October 23rd 2009 at 02:50 AM.
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  2. #2
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    The error will be less than the first non-calculated term. So calculate the next term and work out its largest possible value. If my mental arithmetic is correct it will be:
    |\frac 8 {4!} (0.1)^4|<10^{-4}
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