What is taylor 2/(x^2-x) ?

The answer to taylor 2/(x^2-x) is 1+3/2 (x+1)+7/4 (x+1)^2+15/8 (x+1)^3+31/16 (x+1)^4+\ldots

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taylor 2/(x^2-x)

taylor

\frac{2}{x ^{2} - x}

1 + \frac{3}{2} (x + 1) + \frac{7}{4} (x + 1)^{2} + \frac{15}{8} (x + 1)^{3} + \frac{31}{16} (x + 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{3}{2}}{1 !} (x + 1) + \frac{\frac{7}{2}}{2 !} (x + 1)^{2} + \frac{\frac{45}{4}}{3 !} (x + 1)^{3} + \frac{\frac{93}{2}}{4 !} (x + 1)^{4} + \dots

Refine

= 1 + \frac{3}{2} (x + 1) + \frac{7}{4} (x + 1)^{2} + \frac{15}{8} (x + 1)^{3} + \frac{31}{16} (x + 1)^{4} + \dots

\int 2 x + 8 x^{- 2} d x

f (x) = x^{2} + 10 x, at x = 8

x \to \infty lim (x^{2} e^{2 x})

x \to - 2 lim (\frac{x ^{3} + 1}{x + 1})

y^{^{''}} - 3 y^{^{'}} + 2 y = 14 sin (2 x) + 18 cos (2 x)

What is taylor 2/(x^2-x) ?
The answer to taylor 2/(x^2-x) is 1+3/2 (x+1)+7/4 (x+1)^2+15/8 (x+1)^3+31/16 (x+1)^4+\ldots