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Math Help - Taylor Polynomials redux

  1. #1
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    Taylor Polynomials redux

    I need to know this for a quiz tomorrow!


    1. Let f(x)=log(x) and determine Subscript[p, 2](x) where a=1, b=2. As above, determine the bound for the maximum error and make a graph.

    2.Do the same for f(x)=(1-x)/(1+x) on [.5 , 1] (i.e., a=.5, b=1).

    Thanks
    Last edited by ThePerfectHacker; November 8th 2007 at 07:04 PM.
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  2. #2
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    Quote Originally Posted by swimmerxc View Post
    1. Let f(x)=log(x) and determine Subscript[p, 2](x) where a=1
    I do the first one. So you are finding a Taylor polynomial centered at 1 for \log x which is equivalent for a Taylor polynomial centered at 0 for f(x) = \log (x+1).
    The Taylor polynomial of degree 2 is: x - \frac{x^2}{2}. If a>-1 then f' is bounded on (a,\infty) by 1/(a+1). Thus, \left| R_3(x) \right| \leq \frac{1}{3!(a+1)}
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  3. #3
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    Thanks but I don't get what you did with b=2?
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  4. #4
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    Quote Originally Posted by swimmerxc View Post
    Thanks but I don't get what you did with b=2?
    I understood that a=1 means a Taylor polynomial centered at 1. And b=2 to be a Taylr polynomial centered at 2. Thus, it was two seperate problems, and I did the first part with a=2. Is that what you meant? If
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  5. #5
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    no, I dont get the way how you solve the problem, can you please show me the steps? we were taught to use the Mean Value Theorem

    Thanks
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