What is taylor e^{-x^3} ?

The answer to taylor e^{-x^3} is 1-x^3+1/2 x^6-1/6 x^9+\ldots

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taylor e^{-x^3}

taylor

e^{- x^{3}}

1 - x^{3} + \frac{1}{2} x^{6} - \frac{1}{6} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{360}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 60480}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 - x^{3} + \frac{1}{2} x^{6} - \frac{1}{6} x^{9} + \dots

What is taylor e^{-x^3} ?
The answer to taylor e^{-x^3} is 1-x^3+1/2 x^6-1/6 x^9+\ldots