What is taylor 7/(x^2),1 ?

The answer to taylor 7/(x^2),1 is 7-14(x-1)+21(x-1)^2-28(x-1)^3+35(x-1)^4+\ldots

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taylor 7/(x^2),1

taylor

\frac{7}{x ^{2}}, 1

7 - 14 (x - 1) + 21 (x - 1)^{2} - 28 (x - 1)^{3} + 35 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 7 + \frac{\frac{d}{d x} ( \frac{7}{x ^{2}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{7}{x ^{2}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{7}{x ^{2}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 7 + \frac{- 14}{1 !} (x - 1) + \frac{42}{2 !} (x - 1)^{2} + \frac{- 168}{3 !} (x - 1)^{3} + \frac{840}{4 !} (x - 1)^{4} + \dots

Refine

= 7 - 14 (x - 1) + 21 (x - 1)^{2} - 28 (x - 1)^{3} + 35 (x - 1)^{4} + \dots

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What is taylor 7/(x^2),1 ?
The answer to taylor 7/(x^2),1 is 7-14(x-1)+21(x-1)^2-28(x-1)^3+35(x-1)^4+\ldots