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Taylor series

  1. Jun 25, 2008 #1
    1. The problem statement, all variables and given/known data
    using the Taylor Formula, find the series for the function f(x)=e^{2x}


    2. Relevant equations
    [tex]\sum \frac{f^{n}(a)}{n!} (x-a)^{n}[/tex]

    any help as to where i start would be great. new to series...
     
  2. jcsd
  3. Jun 25, 2008 #2

    Hootenanny

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    You missed out one important section:
    Even if you are new to series, you must have some idea of how to start.
     
  4. Jun 25, 2008 #3
    e^2x= 1+2x+ [tex]\frac{2x^{2}}{2!} +\frac{2x^{3}}{3!} +\frac{2x^{4}}{4!}+...[/tex]

    there is more to it i think.
     
  5. Jun 25, 2008 #4

    Hootenanny

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    No, that isn't correct. The question states that you must use Taylor's formula, have you tried using it?
     
  6. Jun 25, 2008 #5
    e^x = 1 + x + x^2/2!+ x^3/3! + ...

    You substituted 2x for x

    so .. x^2 should be (2x)^2 not 2x^2
     
  7. Jun 25, 2008 #6

    Hootenanny

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    To the OP: Although, substituting 2x for x in the Taylor series for ex as rootX has done is a totally valid (and preferable) method, the question specifically states that Taylor's Formula should be used. Try using it.
     
  8. Jun 25, 2008 #7
    so is this right?

    2^(n-1) f(x)=1+2x+4x^2/2!+8x^3/3!+....+2^(n-1)/(n!)...
     
  9. Jun 25, 2008 #8
    no!

    Steps:
    1. Find f' , f'', f''', ... for f(x) = e^(2x)
    2. plug values in your taylor formula

    No straight jumping to the answer.
     
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