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Taylor Series of cos(3x^2)

  1. Nov 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Determine the Taylor series for the function below at x = 0 by computing P5(x)
    f(x) = cos(3x2)

    2. Relevant equations
    Maclaurin Series for degree 5

    f(0) + f1(0)x + f2(0)x2/2! + f3(0)x3/3! + f4(0)x4/4! + f5(0)x5/5!

    3. The attempt at a solution
    I know how to do this but attempting to solve the 3rd derivative of cos(3x2) and onward is simply infeasible due to it requiring multiplication rule and stuff
    I remember my professor mentioning some sort of short cut to certain series
    Is there a short cut or heuristic to solve this or do I simply have to solve the higher order derivatives?

    Update
    I tried solving the series as cos(u) where u = 3x2 and got
    1 - 9x4/2 + 27x8/8
    which matches the result from a Taylor Series calculator online
    I feel like I am making a basic mistake right now please enlighten me

    Update
    Genius me did not realize that I needed to stop at the 4th degree even after doing to replacement
    1 - 9x4/2
    was accepted as the correct answer
    I guess I ended up answering my own question
     
    Last edited: Nov 10, 2016
  2. jcsd
  3. Nov 10, 2016 #2

    LCKurtz

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    Yes, you did. And a good job too.
     
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