What is taylor 1/(x^4) ?

The answer to taylor 1/(x^4) is 1-4(x-1)+10(x-1)^2-20(x-1)^3+35(x-1)^4+\ldots

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taylor 1/(x^4)

taylor

\frac{1}{x ^{4}}

1 - 4 (x - 1) + 10 (x - 1)^{2} - 20 (x - 1)^{3} + 35 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{1}{x ^{4}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x ^{4}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x ^{4}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 4}{1 !} (x - 1) + \frac{20}{2 !} (x - 1)^{2} + \frac{- 120}{3 !} (x - 1)^{3} + \frac{840}{4 !} (x - 1)^{4} + \dots

Refine

= 1 - 4 (x - 1) + 10 (x - 1)^{2} - 20 (x - 1)^{3} + 35 (x - 1)^{4} + \dots

\int_{0}^{4} (4 e^{- 0.25 x} - 6 x) d x

\frac{x}{lo g _{e} ( x )}

5 - 2 x

\int e^{x^{2}} \cdot x d x

(2 y - 2) \frac{d y}{d x} = 3 x^{2} + 4 x + 2

What is taylor 1/(x^4) ?
The answer to taylor 1/(x^4) is 1-4(x-1)+10(x-1)^2-20(x-1)^3+35(x-1)^4+\ldots