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

y = \frac{x}{x ^{2} + 1}

3 x^{2} - \frac{1}{x}

f (x) = x^{2} + 2 x, at x = 34

x \to \infty lim (2^{x})

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

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