Calculus  Taylor #2
posted by COFFEE .
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

Looks good, assuming your arithmetic is ok.
Respond to this Question
Similar Questions

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 … 
Math
Hi Trying to work with confusing Taylor series....any assistance would be much appreciated!! How can I use T(x)=59((x2)^2)3((x2)^3) to approximate the f(0) ? 
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? 
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)=59((x2)^2)3((x2)^3) to approximate the f(0) ? 
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? 
Calculus
a) Find the Taylor series associated to f(x) = x^2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of … 
Calculus Derivative Taylor Series?
let f(x)= x/x1 find f'(x) f ''(x) and a formula for f ^ (n) * x. I found the first and second derivatives but do not know how to make a general equation for this. I have not learnt the Taylor or Maclaurin Series either. Thank you. 
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)=13/5(x) +12/25(x^2) 52/125(x^3) + 234/625(x^4) but i am not sure how … 
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 … 
Calculus Help Please
Hello! I am struggling with this problem: Find the Taylor Series for sin(x2) centered at c=3. My work so far: sin(1)+(x3)cos(1)(1/2)(x3)^2sin(1)(1/6)(x3)^3cos(1)+(1/24)(x3)^4sin(1)... I know that the Taylor series for sign is …