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

The answer to taylor-1/(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-1/(x^2)

taylor

- \frac{1}{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} ( - \frac{1}{x ^{2}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( - \frac{1}{x ^{2}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( - \frac{1}{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{4 x ^{2} - 3}{x - 1})

\frac{d}{d t} ((sin (t) + cos (t))^{2})

y = 5 x^{2} + \frac{6}{x}

y = \frac{8 t}{8 + t}

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

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