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.
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