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Popular >

taylor 1/((x-1))

Solution

taylor

\frac{1}{( x - 1 )}

Solution

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

Solution steps

Apply the Taylor Formula

= - 1 + \frac{\frac{d}{d x} ( \frac{1}{x - 1} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x - 1} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x - 1} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

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

Refine

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

Popular Examples

limit as x approaches 2 of ln(x/(x^2-4))

x \to 2 lim (ln (\frac{x}{x ^{2} - 4}))

derivative of ay(e^{by})derivative of

a y (e^{b y})

derivative of ln(-x)derivative of

ln (- x)

integral of (12)/(x^{-1)+3}

\int \frac{12}{x ^{- 1} + 3} d x

(dy)/(dx)=3+12x+9y+36xy

\frac{d y}{d x} = 3 + 12 x + 9 y + 36 x y

Frequently Asked Questions (FAQ)

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