- #1
mcdowellmg
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Homework Statement
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) = x^3, a = -1
Homework Equations
f(x) = f(a)+f'(a)(x-a)+(f''(a)/2!)(x-a)^2+(f'''(a)/3!)(x-a)^3+...+(f(nth derivative)(a)/n!)(x-a)^n
The Attempt at a Solution
I found the following derivatives of x^3:
first: 3x^2
second: 6x
third: 6
fourth: 0
Then, I substituted: x^3 = (-1)^3+3^3(x+1)+(-6^3/2!)(x+1)^2+(6/3!)(x+1)^3+0
I reduced to -1-3(x+1)-6(x+1)^2+(x+1)^3, but WebAssign says that is wrong...
am I missing something here?