taylor \sqrt[3]{1+x},0

Lösung

taylor

3 1 + x, 0

1 + \frac{1}{3} x - \frac{1}{9} x^{2} + \frac{5}{81} x^{3} - \frac{10}{243} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( 3 1 + x ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 3 1 + x ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 3 1 + x ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{\frac{1}{3}}{1 !} x + \frac{- \frac{2}{9}}{2 !} x^{2} + \frac{\frac{10}{27}}{3 !} x^{3} + \frac{- \frac{80}{81}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + \frac{1}{3} x - \frac{1}{9} x^{2} + \frac{5}{81} x^{3} - \frac{10}{243} x^{4} + \dots

t an g e n t x^{3} + x^{2} + \frac{6}{x}

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