taylor e^{-h}

Lösung

taylor

e^{- h}

1 - h + \frac{1}{2} h^{2} - \frac{1}{6} h^{3} + \frac{1}{24} h^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 1}{1 !} h + \frac{1}{2 !} h^{2} + \frac{- 1}{3 !} h^{3} + \frac{1}{4 !} h^{4} + \dots

Fasse zusammen

= 1 - h + \frac{1}{2} h^{2} - \frac{1}{6} h^{3} + \frac{1}{24} h^{4} + \dots

s l o p e (- 2, - 7), (2, - 1)

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