How do we find the maclaurin polynomial for

Its not the maclaurin polynomial part that i dont understand its how i differentiate the pairwise function and find

Thanks for any help

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- Dec 8th 2010, 07:23 AMhmmmmMaclaurin Polynomial
How do we find the maclaurin polynomial for

Its not the maclaurin polynomial part that i dont understand its how i differentiate the pairwise function and find

Thanks for any help - Dec 8th 2010, 07:50 AMTheEmptySet
- Dec 8th 2010, 08:03 AMhmmmm
sorry im still a bit confused with the pairwise part when x=0, I understand what you have do to get the maclaurin expansion when x is not 0 but what happens to the x=0 bit?

- Dec 8th 2010, 08:18 AMTheEmptySet
What I was trying to point out is that

So the function f is actually continuous moreover it actually infinity differentiable there. They key idea is that the function can be extended to be defined at 0.

The 2nd point is the series should sum to 0 at 0 right. So when we evaluate the series at zero we get 0. So the series does not care that the function was defined piecewise because of the continuous(analytic) extension. Maybe a plot of the function would help.Attachment 20024 - Dec 8th 2010, 08:28 AMhmmmm
ok Im pretty sure i understand what your getting at thanks very much sorry about that