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

The answer to taylor-1/(x^2),2 is -1/4+1/4 (x-2)-3/16 (x-2)^2+1/8 (x-2)^3-5/64 (x-2)^4+\ldots

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taylor-1/(x^2),2

taylor

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

- \frac{1}{4} + \frac{1}{4} (x - 2) - \frac{3}{16} (x - 2)^{2} + \frac{1}{8} (x - 2)^{3} - \frac{5}{64} (x - 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - \frac{1}{4} + \frac{\frac{1}{4}}{1 !} (x - 2) + \frac{- \frac{3}{8}}{2 !} (x - 2)^{2} + \frac{\frac{3}{4}}{3 !} (x - 2)^{3} + \frac{- \frac{15}{8}}{4 !} (x - 2)^{4} + \dots

Refine

= - \frac{1}{4} + \frac{1}{4} (x - 2) - \frac{3}{16} (x - 2)^{2} + \frac{1}{8} (x - 2)^{3} - \frac{5}{64} (x - 2)^{4} + \dots

What is taylor-1/(x^2),2 ?
The answer to taylor-1/(x^2),2 is -1/4+1/4 (x-2)-3/16 (x-2)^2+1/8 (x-2)^3-5/64 (x-2)^4+\ldots