Posted by KIKSY on Monday, March 7, 2011 at 9:18pm.
Hi~ Thank you for your help!
I was trying to work on a problem about Taylor series, but i don't think im approaching the problem the right way.
I have to find the fifth order Taylor polynomial and Taylor series for the function f(x) at x = 0.
f(x) = 1/(x+2)
I tried to just write out the first and second and third derivatives, and this was fine, but then i got to the fourth and fifth derivatives and the quotient rule made the derivative look really confusing....is there a better way to approach this problem?
I might be doing this totally wrong since we just started learning Taylor series today in class, so any advice is much appreciated.

Calculus  MathMate, Monday, March 7, 2011 at 9:36pm
It turns out that if you had done your derivatives correctly, you would have found the rule:
for f(x)=1/(x+2)
f^{(n)}(x) = (1)^{(n)}n!/(x+2)^{n+1}
I got f^{(5)}(x)=120/(x+2)^{6}.
Hope that helps.