posted by .

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 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 -

    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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus-- need help desperately!

    The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=5 is given by f^(n) (5)= (-1)^n(n!)/((2^n)(n+2)), and f(5)=1/2. Write third degree Taylor …
  2. Calculus

    Please.... I need your help! I posted this question yesterday and no one has answered it yet. Can anyone help me please?
  3. Calculus - Taylor #2

    Find the Taylor series for f(x) centered at the given value of 'a'. (Assume that 'f' has a power series expansion. Do not show that Rn(x)-->0.) f(x) = x3, a = -1 and what i've done so far: f (x) = x^3 f ' (x) = 3x^2 f '' (x) = 6x^1 …
  4. Math

    Hello, I am learning about Taylor series in school, but they are quite confusing.. Can you please explain how I should do this problem?
  5. Calc 2 taylor series

    use the definition of a taylor series to find the Taylor series (centeredat c) for the function. f(x)= 7/x c=1 so what is f(x) as n goes from 0 to infinity?
  6. math (taylor polynomials)

    Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(7x+50)4/3 at a=2 Find the second-degree Taylor polynomial for f(x)=4x2−7x+6 about x=0 thank you! (:
  7. math

    ms.sue help asap 1. which exponent makes the statement true?
  8. Maths

    Use the binomial series to find the Taylor series about 0 for the function f(x) = (1 + x)−3/5, giving all terms up to the one in x4. I have the answer; f(x)=1-3/5(x) +12/25(x^2) -52/125(x^3) + 234/625(x^4) but i am not sure how …
  9. Urgent help Maths Ms sue

    Use binomial series to find the Taylor series about 0 for the function f(x)=(1+x)^-3/5 giving all terms up to the one in x^4. Then use this series and Taylor series for sin x to find the quartic Taylor polynomial about 0 for the function …
  10. Calculus Help Please

    Hello! I am struggling with this problem: Find the Taylor Series for sin(x-2) centered at c=3. My work so far: sin(1)+(x-3)cos(1)-(1/2)(x-3)^2sin(1)-(1/6)(x-3)^3cos(1)+(1/24)(x-3)^4sin(1)... I know that the Taylor series for sign is …

More Similar Questions