What is taylor ((x^2-x+1))/(x+1) ?

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

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taylor ((x^2-x+1))/(x+1)

taylor

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

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

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{x ^{2} - x + 1}{x + 1} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{x ^{2} - x + 1}{x + 1} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{x ^{2} - x + 1}{x + 1} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} x + \frac{6}{2 !} x^{2} + \frac{- 18}{3 !} x^{3} + \frac{72}{4 !} x^{4} + \dots

Refine

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

\int 2 a x d x

\frac{\partial}{\partial x} (e^{- x^{8} - x^{4}})

x \to - 2 lim (\frac{x + 2}{4 - x ^{2}})

\frac{\partial}{\partial x} (\frac{( 3 x - y )}{( x + 2 y )})

\int \frac{7 x ^{2} + 2 x - 7}{x ^{3} - x} d x

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