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Taylor coefficient

  1. Apr 14, 2014 #1
    1. The problem statement, all variables and given/known data
    Determine its 13^{th} Taylor coefficient of the Taylor Series generated by f at x = 3.
    f(x)=e^(7x)


    2. Relevant equations
    I used the fact that the series for e^x was ∑x^n/n!



    3. The attempt at a solution
    Using that above, and replacing x with 7x, shouldnt my answer be 3x*7^13/13!
    But that is incorrect? Please advise where I am going wrong? Thank you
     
  2. jcsd
  3. Apr 14, 2014 #2

    LCKurtz

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    Here's a few questions for you. If$$
    f(x) = \sum_{n=0}^\infty \frac{ f^{(n)}(3)}{n!}(x-3)^n$$what value of ##n## gives the 13th term? Once you have that, what is that many derivatives of ##e^{7x}## and what do you get when you evaluate that at ##x=3##?
     
  4. Apr 14, 2014 #3
    Isn't it the 13th value of n that gives the 13th term?
     
  5. Apr 14, 2014 #4

    LCKurtz

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    No. Give it some thought. Write out some terms.
     
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