I'm lost on why/how we are supposed to find this remainder. Can someone help me out with an explanation of this, I understand that it would be really hard to explain this over a forum but any help would be appreciated. I'm doing a problem right now and I found the Maclaurin polynomial for it, but my professor wants us to find the remainder for every problem. Here is the problem:
Find the Maclaurin polynomial of degree n for the the function.
f(x) = xe^x where n = 4
I got the polynomial to be x + x^2 + 1/2 x^3 + 1/6 x^4. Now how do I find the remainder?
ok so by the taylor's theorem, there exists a number c between 0 and x such that the taylor polynomial P is as what you stated above, and the remainder term (depending on the number of taylor polynomials you had, which is 4 in your case) is (f^5(c))/5!*x^5 by the definition on Taylor's theorem - Wikipedia, the free encyclopedia (by f^5 i mean the 5th derivative of the function, xe^x+5e^x)