What is taylor f(x)=x^{-2} ?

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

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taylor f(x)=x^{-2}

taylor

f (x) = x^{- 2}

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{d}{d x} (\frac{sin ( x )}{x y})

\int 2 x^{2} + 3 x - 1 d x

f (x) = \frac{x}{x ^{2} + 5}

\int_{0}^{3} x^{2} e^{- x} d x

x^{\frac{5}{2}}

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