What is taylor 3/x ,-1 ?

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

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taylor 3/x ,-1

taylor

\frac{3}{x}, - 1

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - 3 + \frac{- 3}{1 !} (x + 1) + \frac{- 6}{2 !} (x + 1)^{2} + \frac{- 18}{3 !} (x + 1)^{3} + \frac{- 72}{4 !} (x + 1)^{4} + \dots

Refine

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

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