What is taylor 1/x 2 ?

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

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taylor 1/x 2

taylor

\frac{1}{x} 2

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{- 2}{1 !} (x - 1) + \frac{4}{2 !} (x - 1)^{2} + \frac{- 12}{3 !} (x - 1)^{3} + \frac{48}{4 !} (x - 1)^{4} + \dots

Refine

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

\int (n x)^{\frac{n - 1}{n}} d x

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

\int \frac{sec ( x )}{2} d x

x \to + \frac{7}{8} lim (x^{4})

\frac{d}{d x} (sinh (cosh (x^{3})))

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