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Homework Help: 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.


    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


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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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