Thread: 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?

Originally Posted by radioheadfan

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 , which it does not. Try instead just writing out the fourth degree polynomial for and then replacing all the z's by