taylor 5+xe^{3x}

Lösung

taylor

5 + x e^{3 x}

5 + x + 3 x^{2} + \frac{9}{2} x^{3} + \frac{9}{2} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 5 + \frac{\frac{d}{d x} ( 5 + x e ^{3 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 5 + x e ^{3 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 5 + x e ^{3 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 5 + \frac{1}{1 !} x + \frac{6}{2 !} x^{2} + \frac{27}{3 !} x^{3} + \frac{108}{4 !} x^{4} + \dots

Fasse zusammen

= 5 + x + 3 x^{2} + \frac{9}{2} x^{3} + \frac{9}{2} x^{4} + \dots

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