maclaurin sqrt(1-x/3)

Lösung

maclaurin

1 - \frac{x}{3}

1 - \frac{1}{6} x - \frac{1}{72} x^{2} - \frac{1}{432} x^{3} - \frac{5}{10368} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{1}{6}}{1 !} x + \frac{- \frac{1}{36}}{2 !} x^{2} + \frac{- \frac{1}{72}}{3 !} x^{3} + \frac{- \frac{5}{432}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - \frac{1}{6} x - \frac{1}{72} x^{2} - \frac{1}{432} x^{3} - \frac{5}{10368} x^{4} + \dots

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