Don't forget to divide by the factorial.
Good morning,
I am working on Taylor Polynomials this morning, and am not entirely sure I understand what I am supposed to be doing. Would someone mind telling me if the following makes sense?
Compute the Maclaurin Polynomials of degree one, two, and three for
As I understand this the fact that this is a Maclaurin Polynomial simply means that the term becomes simply .
I get the following:
Am I way off target here?
Looking good there, now. That is what the factorial means. By convention, 0!=1. The generalization of the factorial is the gamma function, which is the reason for that convention. It also makes the MacLaurin expansion easier to write:
rather than separating out the earlier terms.
Another convention is that the zeroth derivative of a function is simply the function itself.
You can always go to WolframAlpha and use the Series command.
Series[Exp[-2x],{x,0,3}]
will give you the 3rd order MacLaurin expansion of the function in this thread.