What is taylor 1-e^{-x} ?

The answer to taylor 1-e^{-x} is x-1/2 x^2+1/6 x^3-1/24 x^4+1/120 x^5+\ldots

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taylor 1-e^{-x}

taylor

1 - e^{- x}

x - \frac{1}{2} x^{2} + \frac{1}{6} x^{3} - \frac{1}{24} x^{4} + \frac{1}{120} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= x - \frac{1}{2} x^{2} + \frac{1}{6} x^{3} - \frac{1}{24} x^{4} + \frac{1}{120} x^{5} + \dots

What is taylor 1-e^{-x} ?
The answer to taylor 1-e^{-x} is x-1/2 x^2+1/6 x^3-1/24 x^4+1/120 x^5+\ldots