taylor e^{1/θ}

Lösung

taylor

e^{\frac{1}{θ}}

e - e (θ - 1) + \frac{3 e}{2} (θ - 1)^{2} - \frac{13 e}{6} (θ - 1)^{3} + \frac{73 e}{24} (θ - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= e + \frac{- e}{1 !} (θ - 1) + \frac{3 e}{2 !} (θ - 1)^{2} + \frac{- 13 e}{3 !} (θ - 1)^{3} + \frac{73 e}{4 !} (θ - 1)^{4} + \dots

Fasse zusammen

= e - e (θ - 1) + \frac{3 e}{2} (θ - 1)^{2} - \frac{13 e}{6} (θ - 1)^{3} + \frac{73 e}{24} (θ - 1)^{4} + \dots

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