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Math Help - Taylor's Inequality

  1. #1
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    Taylor's Inequality

    ok i dont know how to find the error bound plz help?


    (a) Approximate f by a Taylor polynomial with degree n at the number a.
    T2(x) = Enter a mathematical expression.
    12+(1/4)*(x-4)-(1/64)*(x-4)^2

    (b) Use Taylor's Inequality to estimate the accuracy of the approximation f Tn(x) when x lies in the given interval. (Round the answer to six decimal places.)

    i think i find M to be .001953125 to use in the formula (M/(n+1)!)|x-a|^n+1 but i dont know what to do on this anyone help? THANKS!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ahawk1 View Post
    ok i dont know how to find the error bound plz help?


    (a) Approximate f by a Taylor polynomial with degree n at the number a.
    T2(x) = Enter a mathematical expression.
    12+(1/4)*(x-4)-(1/64)*(x-4)^2

    (b) Use Taylor's Inequality to estimate the accuracy of the approximation f Tn(x) when x lies in the given interval. (Round the answer to six decimal places.)

    i think i find M to be .001953125 to use in the formula (M/(n+1)!)|x-a|^n+1 but i dont know what to do on this anyone help? THANKS!
    I believe the approximation of the function using a Taylor polynomial of degree 2 should be:

    2 + \frac{x - 4}{4} - \frac{(x-4)^2}{64}
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  3. #3
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    Quote Originally Posted by icemanfan View Post
    I believe the approximation of the function using a Taylor polynomial of degree 2 should be:

    2 + \frac{x - 4}{4} - \frac{(x-4)^2}{64}
    i already had that in my answer up top but i need to know the error bound not that actual polynomial but thanks!
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