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Popular >

taylor 1/(x-1),0

Solution

taylor

\frac{1}{x - 1}, 0

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 1 of (sin(x))/x

x \to 1 lim (\frac{sin ( x )}{x})

derivative of 3/((1-x^2)^4)derivative of

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

derivative of (1-x^2^{-2})

\frac{d}{d x} ((1 - x^{2})^{- 2})

y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

(\partial)/(\partial x)(x^{y^x})

\frac{\partial}{\partial x} (x^{y^{x}})

Frequently Asked Questions (FAQ)

What is taylor 1/(x-1),0 ?
The answer to taylor 1/(x-1),0 is -1-x-x^2-x^3-x^4+\ldots