Question

Carilah deret taylor di x=1 dari f(x) = e^(x^2 - 1)

Answer 1

F(x) = e^(x^2 - 1)
f(1) = e^(1 - 1) = 1

f'(x) = (2x).e^(x^2 - 1)
f'(1) = 2

f''(x) = 2.e^(x^2 - 1) + 4x^2.e^(x^2 - 1)
f''(1) = 6

f'''(x) = 4x.e^(x^2 - 1) + 8x.e^(x^2 - 1) + 8x^3.e^(x^2 - 1)
f'''(x) = 20

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f(x) = 1.(x - 1)^0/0! + 2.(x - 1)^1/1! + 6.(x - 1)^2/2! + 20.(x - 1)^3/3! + ...
= 1 + 2(x - 1) + 3(x - 1)^2 + (10/3)(x - 1)^3 + ...