taylor e^{-9x},0

Lösung

taylor

e^{- 9 x}, 0

1 - 9 x + \frac{81}{2} x^{2} - \frac{243}{2} x^{3} + \frac{2187}{8} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 9 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 9 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 9 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 9}{1 !} x + \frac{81}{2 !} x^{2} + \frac{- 729}{3 !} x^{3} + \frac{6561}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - 9 x + \frac{81}{2} x^{2} - \frac{243}{2} x^{3} + \frac{2187}{8} x^{4} + \dots

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