What is taylor 7/x ,-1 ?

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

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taylor 7/x ,-1

taylor

\frac{7}{x}, - 1

- 7 - 7 (x + 1) - 7 (x + 1)^{2} - 7 (x + 1)^{3} - 7 (x + 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

y^{^{'}} + 4 y = 1, y (0) = 1

f (x) = x^{2} + 16, at x = - 3

(x + 5) cos (x)

y^{^{''}} + 4 y^{^{'}} + 9 y = 0

\int \frac{x ^{2}}{196 - x ^{2}} d x

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