What is taylor e^{-5x} ?

The answer to taylor e^{-5x} is 1-5x+25/2 x^2-125/6 x^3+625/24 x^4+\ldots

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taylor e^{-5x}

taylor

e^{- 5 x}

1 - 5 x + \frac{25}{2} x^{2} - \frac{125}{6} x^{3} + \frac{625}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 5}{1 !} x + \frac{25}{2 !} x^{2} + \frac{- 125}{3 !} x^{3} + \frac{625}{4 !} x^{4} + \dots

Refine

= 1 - 5 x + \frac{25}{2} x^{2} - \frac{125}{6} x^{3} + \frac{625}{24} x^{4} + \dots

\int_{1}^{9} \frac{1}{2 x} d x

\frac{d}{d x} (7 (2 x e^{x} + e^{x} x^{2}))

\int y + x e^{y} d y

x \to \infty lim (1 \cdot x)

\frac{d}{d x} (\frac{x ^{3} - 8}{x ^{3} + 8})

What is taylor e^{-5x} ?
The answer to taylor e^{-5x} is 1-5x+25/2 x^2-125/6 x^3+625/24 x^4+\ldots