What is taylor x^{-2},1 ?

The answer to taylor x^{-2},1 is 1-2(x-1)+3(x-1)^2-4(x-1)^3+5(x-1)^4+\ldots

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taylor x^{-2},1

taylor

x^{- 2}, 1

1 - 2 (x - 1) + 3 (x - 1)^{2} - 4 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} (x - 1) + \frac{6}{2 !} (x - 1)^{2} + \frac{- 24}{3 !} (x - 1)^{3} + \frac{120}{4 !} (x - 1)^{4} + \dots

Refine

= 1 - 2 (x - 1) + 3 (x - 1)^{2} - 4 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

\frac{\partial}{\partial y} (\frac{x + 2}{y + 1})

\int (x + 2) (x - 3) d x

\int_{0}^{1} t 4 + 9 t^{2} d t

\int e^{-}

\frac{d}{d x} (\frac{1}{2 π} e^{\frac{- x ^{2}}{2}})

What is taylor x^{-2},1 ?
The answer to taylor x^{-2},1 is 1-2(x-1)+3(x-1)^2-4(x-1)^3+5(x-1)^4+\ldots