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March 1, 2015

March 1, 2015

Posted by **KIKSY** on Monday, March 7, 2011 at 9:18pm.

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 9:36pmIt 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.

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