What is taylor xe^{-x} ?

The answer to taylor xe^{-x} is x-x^2+1/2 x^3-1/6 x^4+1/24 x^5+\ldots

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taylor xe^{-x}

taylor

x e^{- x}

x - x^{2} + \frac{1}{2} x^{3} - \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{- 4}{4 !} x^{4} + \frac{5}{5 !} x^{5} + \dots

Refine

= x - x^{2} + \frac{1}{2} x^{3} - \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

x \to - 5 lim (x - 5)

X^{2} - 2 X, (0, 3)

\frac{d}{d x} (\frac{1 - 3 x}{6 + x})

B^{^{'}}

y = 2 x^{3} - 2 x, (1, 0)

What is taylor xe^{-x} ?
The answer to taylor xe^{-x} is x-x^2+1/2 x^3-1/6 x^4+1/24 x^5+\ldots