What is taylor e^{-4x} ?

The answer to taylor e^{-4x} is 1-4x+8x^2-32/3 x^3+32/3 x^4+\ldots

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taylor e^{-4x}

taylor

e^{- 4 x}

1 - 4 x + 8 x^{2} - \frac{32}{3} x^{3} + \frac{32}{3} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 4}{1 !} x + \frac{16}{2 !} x^{2} + \frac{- 64}{3 !} x^{3} + \frac{256}{4 !} x^{4} + \dots

Refine

= 1 - 4 x + 8 x^{2} - \frac{32}{3} x^{3} + \frac{32}{3} x^{4} + \dots

\frac{d}{d x} (\frac{8 x}{8 + x})

\frac{1}{2 x} y^{^{'}} = \frac{x}{3 y}

\frac{d y}{d x} = (y^{2} - 9)

\frac{\partial}{\partial x} (e^{- 5 t} cos (π x))

x \to - 1 lim (- 1)

What is taylor e^{-4x} ?
The answer to taylor e^{-4x} is 1-4x+8x^2-32/3 x^3+32/3 x^4+\ldots