What is taylor xe^{-x+1}1 ?

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

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taylor xe^{-x+1}1

taylor

x e^{- x + 1} 1

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

(81) (8 - 7)

y = 12 - 7 x - x^{2}, y = 4

cos (y x^{3}) = \frac{1}{6}

\int (\frac{3}{x} + \frac{4}{x ^{5}}) d x

y = \frac{x ^{2}}{x}

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