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Taylor Polynomial Error-Please help!

  1. Apr 13, 2008 #1
    Taylor Polynomial Error--Please help!

    Use Taylor's theorem to determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than .001.

    e^.3



    So is the procedure to take the derivatives and plug in 0 (since c=0) and find an expression for the n+1 derivative?

    f'(c) = 1 f''(c)=1 f'''(c) =1 ......

    so the n+1 derivative is 1

    So Rn= 1/(n+1)! * (.3) ^(n+1)

    Then I set up an equality to find n so that Rn < .001

    and n = 3 ???


    I want to be sure I am taking the right approach on these problems, so is this the way to do it?
     
  2. jcsd
  3. Apr 13, 2008 #2
    Personally I think the best way to do these is to first find the series for the function and then to plug in a few values. The summation for the exponential function is:
    [tex] e^{x} = \sum^{\infty}_{n=0}\frac{x^{n}}{n!}[/tex]

    if you compute a few setting x = .3, you will see how many terms you need

    [tex] e^{.3} = \sum^{\infty}_{n=0}\frac{.3^{n}}{n!} = 1+ \frac{.3}{1!}+\frac{.3^{2}}{2!}+...[/tex]
     
    Last edited: Apr 13, 2008
  4. Apr 14, 2008 #3

    benorin

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    Homework Helper

    Solving the inequality Rn < .001 will give the answer. It is easy to solve this by just plugging in values of n until it is satisfied.
     
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