How would you find the maclaurin series for this

sin(x^5)

thanks.

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- Jul 23rd 2007, 04:49 PMdavecs77maclaurin series
How would you find the maclaurin series for this

sin(x^5)

thanks. - Jul 23rd 2007, 04:55 PMJhevon
- Jul 23rd 2007, 05:02 PMtopsquark
- Jul 23rd 2007, 05:03 PMdavecs77
- Jul 23rd 2007, 05:05 PMJhevon
I don't like telling people to just memorize stuff, but yes, you should have the Maclaurin series for functions like sine, cosine, e^x, 1/(1 - x) ... memorized.

the Maclaurin series is just the Taylor series centered at zero. topsquark showed you how to derive it, but in this case, i think the memorization route is easiest. unless your professor requires you to derive it - Jul 23rd 2007, 05:09 PMtopsquark
- Jul 23rd 2007, 05:11 PMdavecs77
how would you find the Maclaurin series for this then:

1/(1+x^5) - Jul 23rd 2007, 05:13 PMJhevon
- Jul 23rd 2007, 05:16 PMtopsquark
- Jul 23rd 2007, 05:20 PMdavecs77
- Jul 23rd 2007, 05:22 PMThePerfectHacker
- Jul 23rd 2007, 05:29 PMJhevon
- Jul 23rd 2007, 05:35 PMtopsquark
Now me, I tend to forget that . (I try not to memorize too much! :) )

-Dan - Jul 23rd 2007, 05:35 PMdavecs77
The answer in the book is summation from n = 1 to infinity of (-1)^n times x^(5n)

I see the (-1)^n since the values are changing from positive to negative every time, but where does the x^(5n) come from? Also how did you find your results... 1 - x + x^2 - x^3 ... I don't quite understand. Thank you. - Jul 23rd 2007, 05:46 PMJhevon