What is taylor 1/(x-1),2 ?

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

taylor 1/(x-1),2

taylor

\frac{1}{x - 1}, 2

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 1}{1 !} (x - 2) + \frac{2}{2 !} (x - 2)^{2} + \frac{- 6}{3 !} (x - 2)^{3} + \frac{24}{4 !} (x - 2)^{4} + \dots

Refine

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

\frac{d}{d x} (in (3 x + 1) (x + 2) 2)

f a c t or a x^{n} + b x^{n - 1}

\int 2 x^{3} - 6 x^{2} d x

\frac{d y}{d x} + y = \frac{1 - e ^{- 2 x}}{e ^{x} + e ^{- x}}

\frac{d}{d x} (x^{- 4} + cos (x))

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