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What is the Taylor Series of f of x equals x squared minus x cubed centered at a equals 2?
Wiki User
∙ 12y ago
f(x)=x2-x3
f(2) = 4-8 = -4
f'(x) =2x-3x2
f'(2) = 4-12=-8
f''(x) = 2 -6x
f''(2)= -10
f'''(x)= -6
f(n)(x) = 0 for all n > 3.
f(x) = f(2) + (x-2) f'(2) / 1! + (x-2)2 f''(2) /2! + (x-2)3 f'''(2)/3! + . . .
f(x) = -4 -8(x-2) -10(x-2)22/2-6(x-2)3/6 + 0 + 0 + ...
f(x) = -4 -8(x-2) -5(x-2)2 - (x-2)3
Wiki User
∙ 12y ago
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