Find the maclaurin polynomials of orders n=0,1,2,3, and 4, and then find the nth Maclaurin polynomials for the function in sigma notation.
cos(pi*x)
http://img382.imageshack.us/img382/5889/48183237ut4.png
This is the answer from the solution mannual
Can anybody tell me how it finds f(k) first? I mean not just for this question because all the solution about maclaurin and taylor, the solution finds f(k) first.
Another question, I do not understand the NB means? Why is it n/2 ?
the are the kth derivatives so lets get started
Now we need to evaluate each of these at the center for this series at x=0
so we get...
Now we can use these in taylor theorem for a power series centered at a is
so we get
we get this because everyother term is zero.
I hope this helps