1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

    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

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, you did. And a good job too.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted