taylor e^{3x},9

Lösung

taylor

e^{3 x}, 9

e^{27} + 3 e^{27} (x - 9) + \frac{9 e ^{27}}{2} (x - 9)^{2} + \frac{9 e ^{27}}{2} (x - 9)^{3} + \frac{27 e ^{27}}{8} (x - 9)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= e^{27} + \frac{\frac{d}{d x} ( e ^{3 x} ) ( 9 )}{1 !} (x - 9) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{3 x} ) ( 9 )}{2 !} (x - 9)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{3 x} ) ( 9 )}{3 !} (x - 9)^{3} + \dots

Evaluate Derivatives

= e^{27} + \frac{3 e ^{27}}{1 !} (x - 9) + \frac{9 e ^{27}}{2 !} (x - 9)^{2} + \frac{27 e ^{27}}{3 !} (x - 9)^{3} + \frac{81 e ^{27}}{4 !} (x - 9)^{4} + \dots

Fasse zusammen

= e^{27} + 3 e^{27} (x - 9) + \frac{9 e ^{27}}{2} (x - 9)^{2} + \frac{9 e ^{27}}{2} (x - 9)^{3} + \frac{27 e ^{27}}{8} (x - 9)^{4} + \dots