taylor e^{x-1},1

Lösung

taylor

e^{x - 1}, 1

1 + (x - 1) + \frac{1}{2} (x - 1)^{2} + \frac{1}{6} (x - 1)^{3} + \frac{1}{24} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} (x - 1) + \frac{1}{2 !} (x - 1)^{2} + \frac{1}{3 !} (x - 1)^{3} + \frac{1}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 1 + (x - 1) + \frac{1}{2} (x - 1)^{2} + \frac{1}{6} (x - 1)^{3} + \frac{1}{24} (x - 1)^{4} + \dots

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