taylor e^{-6x},0

Lösung

taylor

e^{- 6 x}, 0

1 - 6 x + 18 x^{2} - 36 x^{3} + 54 x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 6 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 6 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 6 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 6}{1 !} x + \frac{36}{2 !} x^{2} + \frac{- 216}{3 !} x^{3} + \frac{1296}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - 6 x + 18 x^{2} - 36 x^{3} + 54 x^{4} + \dots

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