What is taylor 2/x ,1 ?

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

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taylor 2/x ,1

taylor

\frac{2}{x}, 1

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{- 2}{1 !} (x - 1) + \frac{4}{2 !} (x - 1)^{2} + \frac{- 12}{3 !} (x - 1)^{3} + \frac{48}{4 !} (x - 1)^{4} + \dots

Refine

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

\frac{d y}{d x} = 4 x (x - 1)

\int_{0}^{1} (x 1 - x^{2}) d x

f (x) = e^{2 x - 5} + 4

y^{^{'}} = \frac{y ^{2} + 3 x x ^{2} + y ^{2}}{x y}

\int x (x + 1)^{6} d x

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