What is taylor e^{-9x} ?

The answer to taylor e^{-9x} is 1-9x+81/2 x^2-243/2 x^3+2187/8 x^4+\ldots

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taylor e^{-9x}

taylor

e^{- 9 x}

1 - 9 x + \frac{81}{2} x^{2} - \frac{243}{2} x^{3} + \frac{2187}{8} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 9 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 9 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 9 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 9}{1 !} x + \frac{81}{2 !} x^{2} + \frac{- 729}{3 !} x^{3} + \frac{6561}{4 !} x^{4} + \dots

Refine

= 1 - 9 x + \frac{81}{2} x^{2} - \frac{243}{2} x^{3} + \frac{2187}{8} x^{4} + \dots

x \to 1 + lim (\frac{7}{x - 1})

x ln (x) \frac{d y}{d x} + y = x e^{x}

\int ∣ x - 1 ∣ d x

\int \frac{- 2}{x ^{2} + 16} d x

e^{\frac{y}{x}} \frac{( - y d x + x d y )}{x ^{2}} = 0

What is taylor e^{-9x} ?
The answer to taylor e^{-9x} is 1-9x+81/2 x^2-243/2 x^3+2187/8 x^4+\ldots