taylor e^{2x},3

Lösung

taylor

e^{2 x}, 3

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

Schritte zur Lösung

Apply the Taylor Formula

= e^{6} + \frac{\frac{d}{d x} ( e ^{2 x} ) ( 3 )}{1 !} (x - 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{2 x} ) ( 3 )}{2 !} (x - 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{2 x} ) ( 3 )}{3 !} (x - 3)^{3} + \dots

Evaluate Derivatives

= e^{6} + \frac{2 e ^{6}}{1 !} (x - 3) + \frac{4 e ^{6}}{2 !} (x - 3)^{2} + \frac{8 e ^{6}}{3 !} (x - 3)^{3} + \frac{16 e ^{6}}{4 !} (x - 3)^{4} + \dots

Fasse zusammen

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

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