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Taylor series expansion

  1. May 18, 2012 #1
    how do you do the taylor series expansion of e(a+x)2
  2. jcsd
  3. May 18, 2012 #2


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    Hey Lizwi and welcome to the forums.

    This function is differentiable, continuous and can be expanded at any point where x is a real number.

    To start off though, do you know how to differentiate your function for the nth derivative?
  4. May 18, 2012 #3
    Yes, I think you use the chain rule
  5. May 18, 2012 #4


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    Yes you will do, but the key will be to expand your series about the point x=0 (in other words you need to find f'(0), f''(0) and so on).

    If you end up getting a specific form (which you will) and then the zero's cancel out terms, then you will get a simplification for the nth derivative.

    So expand out the first two or three derivatives (using the chain rule) and substitute in x = 0. What terms dissappear as a result of this?
  6. May 18, 2012 #5

    Do you know the MacClaurin series for [itex]\,e^x\,[/itex] : [tex]e^x=\sum_{n=0}^\infty\frac{x^n}{n!}\,?[/tex] Well, you can now input [itex]\,(a+x)^2\,[/itex] above as this series converges for any real number...

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