What is taylor x^{-1} ?

The answer to taylor x^{-1} is 1-(x-1)+(x-1)^2-(x-1)^3+(x-1)^4+\ldots

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taylor x^{-1}

taylor

x^{- 1}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 1}{1 !} (x - 1) + \frac{2}{2 !} (x - 1)^{2} + \frac{- 6}{3 !} (x - 1)^{3} + \frac{24}{4 !} (x - 1)^{4} + \dots

Refine

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

d er i v a t i v e 45 x^{2} - 0.02 x^{3}

\int \frac{2}{3 x + 3} d x

\int \frac{1}{e ^{2 x} + e ^{- 2 x}} d x

z \to - i lim (\frac{z ^{4} - 1}{z + i})

\frac{d}{d x} (\frac{1}{x ^{2} + y ^{2} - 4})

What is taylor x^{-1} ?
The answer to taylor x^{-1} is 1-(x-1)+(x-1)^2-(x-1)^3+(x-1)^4+\ldots