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Find Taylor Series

  1. Sep 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the taylor series representation for the following function
    f(x) = cos(x) in powers of x-pi

    2. Relevant equations



    3. The attempt at a solution

    I don't know what they mean by "in powers of x-pi", that's the part i'm confused with. Can somebody please explain that part for me, thanks
     
  2. jcsd
  3. Sep 23, 2014 #2

    ShayanJ

    User Avatar
    Gold Member

    That just means you should expand around [itex] x=\pi [/itex] rather than the usual [itex] x=0 [/itex].
     
  4. Sep 23, 2014 #3
    Does that mean the "a" value is pi ?
     
  5. Sep 23, 2014 #4

    ShayanJ

    User Avatar
    Gold Member

    If you write [itex] f(a+\delta)=\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} \delta^n [/itex], then yes!
     
  6. Sep 23, 2014 #5
    I use this formula

    f^(n)(a)*((x-a)^n)/n!

    And sub in pi for a, thanks
     
  7. Sep 23, 2014 #6

    Mark44

    Staff: Mentor

    Yes, this is what the general term in your Taylor series will look like. Note that a Maclaurin series is a special case of a Taylor series, where a = 0.
     
  8. Sep 26, 2014 #7
    Ok , thanks
     
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