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E^(x^2) taylor series

  1. Dec 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the Taylor series of e^(x^2) about x=0

    2. Relevant equations

    Taylor Series = f(a) +f'(a)(x-a) + (f''(a)(x-a)^2)/2 ........

    3. The attempt at a solution

    So, the first term is pretty obvious. It's e^0^2, which is zero.

    The second term is what got me. (e^x^2)'=2x*(e^x^2), so at zero that is zero. Multiply by x, still zero. But the answer key says the second term is x^2. I really cannot understand this.

  2. jcsd
  3. Dec 5, 2011 #2
    My bad. e^0^2 is one. Typo.
  4. Dec 5, 2011 #3


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    Keep going. It's the f'' term that is the second term.
  5. Dec 5, 2011 #4
    Thank you so much!
  6. Dec 6, 2011 #5


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    Staff Emeritus
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    2016 Award

    You can also take the Taylor series of ex and then just fill in x2.
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