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Math Help - MacLaurin polynomial

  1. #1
    Junior Member superman69's Avatar
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    Lightbulb MacLaurin polynomial

    Let .
    Find the MacLaurin polynomial of degree 5 for .

    Use this polynomial to estimate the value of .

    I don't understand this. For the MacLaurin polynomial do I take derivative until the 5th derivative?
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by superman69 View Post
    Let .
    Find the MacLaurin polynomial of degree 5 for .

    Use this polynomial to estimate the value of .

    I don't understand this. For the MacLaurin polynomial do I take derivative until the 5th derivative?
    F'(x) = e^{-4x^4} \approx 1 - 4x^4

    F(x) \approx x - \frac{4x^5}{5}

    approximate F(0.16)
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  3. #3
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by superman69 View Post
    Let .
    Find the MacLaurin polynomial of degree 5 for .

    Use this polynomial to estimate the value of .

    I don't understand this. For the MacLaurin polynomial do I take derivative until the 5th derivative?
    Yup.

    F(0)=0

    F'(x)=e^{-4x^4}, F'(0)=1

    F''(x)=-16x^3e^{-4x^4}, F''(0)=0

    So the polynomial of degree 2 is f_2(x)=x.

    Just keep going til you hit 5; then plug in 0.16.
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  4. #4
    Junior Member superman69's Avatar
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    yeah okay i got that part how do i do the first part Find the MacLaurin polynomial of degree 5 for F(x) I spended about 45 mins on that and still couldn't find the correct answer
    Last edited by superman69; October 28th 2009 at 04:33 PM. Reason: error
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  5. #5
    Junior Member superman69's Avatar
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    But this is what I got so far.
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  6. #6
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by superman69 View Post


    But this is what I got so far.
    Should be 1+(-4x^4)+\frac{(-4x^4)^2}{2!}+\frac{(-4x^4)^3}{3!}...

    Then integrate to find the series for F(x), just like Skeeter said. Note that you only need the first two terms of this sequence, since all the rest have \text{deg}\geq5.

    \int 1-4x^4\,dx=x-\frac{4x^5}{4}
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