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Taylor Series

  1. Nov 22, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the first 4 nonzero terms of:

    [itex]e^{t}cos(t)[/itex]

    2. Relevant equations



    3. The attempt at a solution

    I am trying to multiply the terms of two known series for my answer, but I'm not sure how to do it efficiently.

    Should I list 4 terms of each series, then multiply them as if they were just normal polynomials?

    EDIT, I tried doing that and it is completely unfeasible. What's the correct way?
     
    Last edited: Nov 22, 2011
  2. jcsd
  3. Nov 22, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What is "unfeasible" about it? It is unpleasant, maybe, but perfectly feasible. It is not how I would do it, however: I would use derivatives to get the coefficients in the expansion.

    RGV
     
  4. Nov 22, 2011 #3
    I see, so you would take the derivatives evaluated for 0? As the coefficients?

    Should I always try that method first?

    EDIT: Wait, why would you do it that way? Differentiating that 4 function 4 times would be terrible!
     
  5. Nov 22, 2011 #4

    Mark44

    Staff: Mentor

    It wouldn't be that bad. Give it a try.
     
  6. Nov 22, 2011 #5
    OK. Will report back.
     
  7. Nov 22, 2011 #6
    OK, it was definitely a lot easier than I anticipated. Thanks again.

    1st:
    e^t(cost - sint)

    2nd:

    -2e^t(sin t)

    3rd
    -2e^t(cos t + sin t)

    4th

    -4e^t(cos t)
     
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