taylor e^{4x},3

Lösung

taylor

e^{4 x}, 3

e^{12} + 4 e^{12} (x - 3) + 8 e^{12} (x - 3)^{2} + \frac{32 e ^{12}}{3} (x - 3)^{3} + \frac{32 e ^{12}}{3} (x - 3)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= e^{12} + \frac{\frac{d}{d x} ( e ^{4 x} ) ( 3 )}{1 !} (x - 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{4 x} ) ( 3 )}{2 !} (x - 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{4 x} ) ( 3 )}{3 !} (x - 3)^{3} + \dots

Evaluate Derivatives

= e^{12} + \frac{4 e ^{12}}{1 !} (x - 3) + \frac{16 e ^{12}}{2 !} (x - 3)^{2} + \frac{64 e ^{12}}{3 !} (x - 3)^{3} + \frac{256 e ^{12}}{4 !} (x - 3)^{4} + \dots

Fasse zusammen

= e^{12} + 4 e^{12} (x - 3) + 8 e^{12} (x - 3)^{2} + \frac{32 e ^{12}}{3} (x - 3)^{3} + \frac{32 e ^{12}}{3} (x - 3)^{4} + \dots

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