What is taylor 9/x ,1 ?

The answer to taylor 9/x ,1 is 9-9(x-1)+9(x-1)^2-9(x-1)^3+9(x-1)^4+\ldots

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taylor 9/x ,1

taylor

\frac{9}{x}, 1

9 - 9 (x - 1) + 9 (x - 1)^{2} - 9 (x - 1)^{3} + 9 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 9 + \frac{\frac{d}{d x} ( \frac{9}{x} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{9}{x} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{9}{x} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 9 + \frac{- 9}{1 !} (x - 1) + \frac{18}{2 !} (x - 1)^{2} + \frac{- 54}{3 !} (x - 1)^{3} + \frac{216}{4 !} (x - 1)^{4} + \dots

Refine

= 9 - 9 (x - 1) + 9 (x - 1)^{2} - 9 (x - 1)^{3} + 9 (x - 1)^{4} + \dots

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What is taylor 9/x ,1 ?
The answer to taylor 9/x ,1 is 9-9(x-1)+9(x-1)^2-9(x-1)^3+9(x-1)^4+\ldots