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Find Taylor series generated by e^x centered at 0.

  1. Apr 15, 2013 #1
    1.
    a. Find Taylor series generated by ex2 centered at 0.

    b. Express ∫ex2dx as a Taylor series.

    2. For part a, I just put the value of "x2" in place of x in the general form for the e^x Taylor series:

    ex: 1 + x + x2/2! + x3/3! + ...

    ex2: 1 + x2 + x4/2! + x6/3! + ...


    For part b, I just took the integral of the Taylor series for ex2:

    = 0 + 2x + 1/2*4x3 + 1/6*6x5 + ...

    = 2x + 2x3 + x5 + ...

    Is this the right way to go about this?
    Thanks! :)
     
  2. jcsd
  3. Apr 15, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    HI Lo.Lee.Ta.! :smile:

    a. looks fine
    Looks like the derivative to me :redface:
     
  4. Apr 15, 2013 #3
    #O_O AGH! I did take the derivative! Thanks! ha

    So, it should be: x + 1/3(x3) + 1/10(x5) + 1/42(x7) + ...

    Is this right?

    Thanks! :)
     
  5. Apr 15, 2013 #4

    Mark44

    Staff: Mentor

    Don't forget the constant of integration ... Otherwise, it looks fine.
     
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