taylor e^{0.42x}

Lösung

taylor

e^{0.42 x}

1 + 0.42 x + 0.0882 x^{2} + 0.012348 x^{3} + 0.00129654 x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{0.42 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{0.42 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{0.42 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0.42}{1 !} x + \frac{0.1764}{2 !} x^{2} + \frac{0.074088}{3 !} x^{3} + \frac{0.03111696}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + 0.42 x + 0.0882 x^{2} + 0.012348 x^{3} + 0.00129654 x^{4} + \dots

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