What is taylor e^{-7x},0 ?

The answer to taylor e^{-7x},0 is 1-7x+49/2 x^2-343/6 x^3+2401/24 x^4+\ldots

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taylor e^{-7x},0

taylor

e^{- 7 x}, 0

1 - 7 x + \frac{49}{2} x^{2} - \frac{343}{6} x^{3} + \frac{2401}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 7 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 7 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 7 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 7}{1 !} x + \frac{49}{2 !} x^{2} + \frac{- 343}{3 !} x^{3} + \frac{2401}{4 !} x^{4} + \dots

Refine

= 1 - 7 x + \frac{49}{2} x^{2} - \frac{343}{6} x^{3} + \frac{2401}{24} x^{4} + \dots

What is taylor e^{-7x},0 ?
The answer to taylor e^{-7x},0 is 1-7x+49/2 x^2-343/6 x^3+2401/24 x^4+\ldots