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
f ''' (x) = 6x

f (-1) = -1
f ' (-1) = 3
f '' (-1) = -6
f ''' (-1) = -6

using taylor series equation.. my final answer that was wrong:

((-1(x+1)^0)/(0!))+((3(x+1)^1)/(1!))+((-6(x+1)^2)/(2!))+((-6(x+1)^3)/(3!))

.. is this what the question was asking for? if not, what is it then? thank you very much for your assistance.

f ''' (x) = 6

f'''(-1) = 6

  1. 👍 0
  2. 👎 0
  3. 👁 157
asked by COFFEE
  1. Looks good, assuming your arithmetic is ok.

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    how do i use a taylor series centered at some x value to approximate the value of the function centered at a different x value? for example, if im given some taylor series centered at 5 of f(x) but i want to find f(3), how do i do

    asked by Marli on March 15, 2011
  2. Math

    Hi Trying to work with confusing Taylor series....any assistance would be much appreciated!! How can I use T(x)=5-9((x-2)^2)-3((x-2)^3) to approximate the f(0) ???? I realize that Taylor series

    asked by Kiksy on March 15, 2011
  3. calculus repost, please assist pleassssssse

    Hi Trying to work with confusing Taylor series....any assistance would be much appreciated!! How can I use T(x)=5-9((x-2)^2)-3((x-2)^3) to approximate the f(0) ???? I realize that Taylor series

    asked by kiksy on March 15, 2011
  4. 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

    asked by Alice on April 27, 2017
  5. 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

    asked by s17 on April 24, 2016
  6. 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

    asked by Jay on April 24, 2016
  7. Calculus

    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

    asked by KIKSY on March 7, 2011
  8. Calculus

    Find the first four non-zero terms and the general term for the Taylor Series centered at c = 1 for the integral of ln(x).

    asked by Joe Bob on May 7, 2012
  9. 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

    asked by Steven on March 17, 2007
  10. 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?

    asked by Em on July 31, 2011

More Similar Questions