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Math Help - Taylor remainder function

  1. #1
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    Taylor remainder function

    1. The problem statement.

    I have to estimate the absolute value of the remainder, R2,x0=4(x), of the function f(x)=1/x1/2 on the interval ] 3.8 , 4.2 [ when x0 = 4 and n = 2.





    2. Relevant equations



    I've used this equation :

    Taylor remainder function-billede-1.png





    3. The attempt at a solution

    Taylor remainder function-billede-2.png

    I hope that someone will be able to look at this and help me because I think the result might be wrong, the absolute value of the remainder seems too small !
    Last edited by Tala; February 8th 2013 at 10:02 AM.
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  2. #2
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    Re: Taylor remainder function

    I think your calculations are pretty much correct, but you used the 3rd derivative instead of the 4th. Also your bounds are not really right. Here's more discussion:

    Taylor remainder function-mhfcalctaylorremainder.png
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  3. #3
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    Re: Taylor remainder function

    No I don't want the 4th derivative because n = 2 and according to the equation I'm using I need the n+1 = 2 + 1 = 3th derivative.
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  4. #4
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    Re: Taylor remainder function

    Sorry, for some reason I read n = 3. You should read the previous note to see a correct determination of bounds for a remainder. Generally, you need to consider properties of the function f^{(n+1)}(x) and (x-a)^{n+1}
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