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Math Help - Remainder of Taylor Polynomial?

  1. #1
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    Remainder of Taylor Polynomial?

    I'm lost on why/how we are supposed to find this remainder. Can someone help me out with an explanation of this, I understand that it would be really hard to explain this over a forum but any help would be appreciated. I'm doing a problem right now and I found the Maclaurin polynomial for it, but my professor wants us to find the remainder for every problem. Here is the problem:

    Find the Maclaurin polynomial of degree n for the the function.
    f(x) = xe^x where n = 4

    I got the polynomial to be x + x^2 + 1/2 x^3 + 1/6 x^4. Now how do I find the remainder?
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  2. #2
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    Quote Originally Posted by element View Post
    I'm lost on why/how we are supposed to find this remainder. Can someone help me out with an explanation of this, I understand that it would be really hard to explain this over a forum but any help would be appreciated. I'm doing a problem right now and I found the Maclaurin polynomial for it, but my professor wants us to find the remainder for every problem. Here is the problem:

    Find the Maclaurin polynomial of degree n for the the function.
    f(x) = xe^x where n = 4

    I got the polynomial to be x + x^2 + 1/2 x^3 + 1/6 x^4. Now how do I find the remainder?
    The problem is this polynomial approximates the function for small x. Say when |x|<1. When x gets larger, say x=7 then the difference is huge and the approximation dies off. Thus, maybe you want to specify that |x|<1 ?
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  3. #3
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    ok so by the taylor's theorem, there exists a number c between 0 and x such that the taylor polynomial P is as what you stated above, and the remainder term (depending on the number of taylor polynomials you had, which is 4 in your case) is (f^5(c))/5!*x^5 by the definition on Taylor's theorem - Wikipedia, the free encyclopedia (by f^5 i mean the 5th derivative of the function, xe^x+5e^x)
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