taylor e^{2x},5

Lösung

taylor

e^{2 x}, 5

e^{10} + 2 e^{10} (x - 5) + 2 e^{10} (x - 5)^{2} + \frac{4 e ^{10}}{3} (x - 5)^{3} + \frac{2 e ^{10}}{3} (x - 5)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= e^{10} + \frac{\frac{d}{d x} ( e ^{2 x} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{2 x} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{2 x} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

Evaluate Derivatives

= e^{10} + \frac{2 e ^{10}}{1 !} (x - 5) + \frac{4 e ^{10}}{2 !} (x - 5)^{2} + \frac{8 e ^{10}}{3 !} (x - 5)^{3} + \frac{16 e ^{10}}{4 !} (x - 5)^{4} + \dots

Fasse zusammen

= e^{10} + 2 e^{10} (x - 5) + 2 e^{10} (x - 5)^{2} + \frac{4 e ^{10}}{3} (x - 5)^{3} + \frac{2 e ^{10}}{3} (x - 5)^{4} + \dots