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Thread: Arctan Maclaurin series

  1. #1
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    Arctan Maclaurin series

    Find T4(x), the fourth degree Taylor polynomial of the function f(x)=arctan(13x) at a=0.

    I did the work out
    got this

    13[x-x^3/3+x^5/5-x^7/7.....]

    so then 13x- 13x^3/3+13x^5/5-13x^9/9

    Since there is no 4th degree, i took -13x^3/3 as the answer, but my online hw says this is incorrect, but this is how my tutor explained it. What's wrong here?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by radioheadfan View Post
    Find T4(x), the fourth degree Taylor polynomial of the function f(x)=arctan(13x) at a=0.

    I did the work out
    got this

    13[x-x^3/3+x^5/5-x^7/7.....]

    so then 13x- 13x^3/3+13x^5/5-13x^9/9

    Since there is no 4th degree, i took -13x^3/3 as the answer, but my online hw says this is incorrect, but this is how my tutor explained it. What's wrong here?
    What you did would make sense if \arctan(13x)=13\arctan(x), which it does not. Try instead just writing out the fourth degree polynomial for \arctan(z) and then replacing all the z's by 13x
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