What is taylor e^{-2x} ?

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

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taylor e^{-2x}

taylor

e^{- 2 x}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} x + \frac{4}{2 !} x^{2} + \frac{- 8}{3 !} x^{3} + \frac{16}{4 !} x^{4} + \dots

Refine

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

x \to 3 lim (\frac{3 - 27}{x - 3})

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