taylor x^{11/2},1,x=1.4

Lösung

taylor

x^{\frac{11}{2}}, 1, x = 1.4

1 + \frac{11}{2} (x - 1) + \frac{99}{8} (x - 1)^{2} + \frac{231}{16} (x - 1)^{3} + \frac{1155}{128} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( x ^{\frac{11}{2}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{11}{2}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{11}{2}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{\frac{11}{2}}{1 !} (x - 1) + \frac{\frac{99}{4}}{2 !} (x - 1)^{2} + \frac{\frac{693}{8}}{3 !} (x - 1)^{3} + \frac{\frac{3465}{16}}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 1 + \frac{11}{2} (x - 1) + \frac{99}{8} (x - 1)^{2} + \frac{231}{16} (x - 1)^{3} + \frac{1155}{128} (x - 1)^{4} + \dots