What is taylor (1-x)e^{-x} ?

The answer to taylor (1-x)e^{-x} is 1-2x+3/2 x^2-2/3 x^3+5/24 x^4+\ldots

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taylor (1-x)e^{-x}

taylor

(1 - x) e^{- x}

1 - 2 x + \frac{3}{2} x^{2} - \frac{2}{3} x^{3} + \frac{5}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} x + \frac{3}{2 !} x^{2} + \frac{- 4}{3 !} x^{3} + \frac{5}{4 !} x^{4} + \dots

Refine

= 1 - 2 x + \frac{3}{2} x^{2} - \frac{2}{3} x^{3} + \frac{5}{24} x^{4} + \dots

What is taylor (1-x)e^{-x} ?
The answer to taylor (1-x)e^{-x} is 1-2x+3/2 x^2-2/3 x^3+5/24 x^4+\ldots