taylor x^{2/3},1

Lösung

taylor

x^{\frac{2}{3}}, 1

1 + \frac{2}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{4}{81} (x - 1)^{3} - \frac{7}{243} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{2}{3}}{1 !} (x - 1) + \frac{- \frac{2}{9}}{2 !} (x - 1)^{2} + \frac{\frac{8}{27}}{3 !} (x - 1)^{3} + \frac{- \frac{56}{81}}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 1 + \frac{2}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{4}{81} (x - 1)^{3} - \frac{7}{243} (x - 1)^{4} + \dots

t an g e n t y = (x^{3} + 1) (3 x^{2} - 4 x + 2), (1, 2)

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{8}{y ^{4}}) (y + 2 y^{3})

in v erse l a pl a ce \frac{5}{s ^{2} + 1}

\frac{d}{d x} ((x + \frac{1}{x ^{3}})^{2})

\int (\frac{x ^{2} + 1}{x ^{3} + 3 x}) d x