What is taylor e^{-x^2}1 ?

The answer to taylor e^{-x^2}1 is 1-x^2+1/2 x^4-1/6 x^6+1/24 x^8+\ldots

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taylor e^{-x^2}1

taylor

e^{- x^{2}} 1

1 - x^{2} + \frac{1}{2} x^{4} - \frac{1}{6} x^{6} + \frac{1}{24} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{12}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 120}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1680}{8 !} x^{8} + \dots

Refine

= 1 - x^{2} + \frac{1}{2} x^{4} - \frac{1}{6} x^{6} + \frac{1}{24} x^{8} + \dots

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What is taylor e^{-x^2}1 ?
The answer to taylor e^{-x^2}1 is 1-x^2+1/2 x^4-1/6 x^6+1/24 x^8+\ldots