What is taylor 1/x ,-3 ?

The answer to taylor 1/x ,-3 is -1/3-1/9 (x+3)-1/27 (x+3)^2-1/81 (x+3)^3-1/243 (x+3)^4+\ldots

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taylor 1/x ,-3

taylor

\frac{1}{x}, - 3

- \frac{1}{3} - \frac{1}{9} (x + 3) - \frac{1}{27} (x + 3)^{2} - \frac{1}{81} (x + 3)^{3} - \frac{1}{243} (x + 3)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - \frac{1}{3} + \frac{- \frac{1}{9}}{1 !} (x + 3) + \frac{- \frac{2}{27}}{2 !} (x + 3)^{2} + \frac{- \frac{2}{27}}{3 !} (x + 3)^{3} + \frac{- \frac{8}{81}}{4 !} (x + 3)^{4} + \dots

Refine

= - \frac{1}{3} - \frac{1}{9} (x + 3) - \frac{1}{27} (x + 3)^{2} - \frac{1}{81} (x + 3)^{3} - \frac{1}{243} (x + 3)^{4} + \dots

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What is taylor 1/x ,-3 ?
The answer to taylor 1/x ,-3 is -1/3-1/9 (x+3)-1/27 (x+3)^2-1/81 (x+3)^3-1/243 (x+3)^4+\ldots