What is maclaurin e^{-3x^2} ?

The answer to maclaurin e^{-3x^2} is 1-3x^2+9/2 x^4-9/2 x^6+27/8 x^8+\ldots

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maclaurin e^{-3x^2}

maclaurin

e^{- 3 x^{2}}

1 - 3 x^{2} + \frac{9}{2} x^{4} - \frac{9}{2} x^{6} + \frac{27}{8} x^{8} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 6}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{108}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 3240}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{136080}{8 !} x^{8} + \dots

Refine

= 1 - 3 x^{2} + \frac{9}{2} x^{4} - \frac{9}{2} x^{6} + \frac{27}{8} x^{8} + \dots

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What is maclaurin e^{-3x^2} ?
The answer to maclaurin e^{-3x^2} is 1-3x^2+9/2 x^4-9/2 x^6+27/8 x^8+\ldots