taylor ln(s)

Lösung

taylor

ln (s)

(s - 1) - \frac{1}{2} (s - 1)^{2} + \frac{1}{3} (s - 1)^{3} - \frac{1}{4} (s - 1)^{4} + \frac{1}{5} (s - 1)^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} (s - 1) + \frac{- 1}{2 !} (s - 1)^{2} + \frac{2}{3 !} (s - 1)^{3} + \frac{- 6}{4 !} (s - 1)^{4} + \frac{24}{5 !} (s - 1)^{5} + \dots

Fasse zusammen

= (s - 1) - \frac{1}{2} (s - 1)^{2} + \frac{1}{3} (s - 1)^{3} - \frac{1}{4} (s - 1)^{4} + \frac{1}{5} (s - 1)^{5} + \dots

y^{^{'}} = \frac{3 y ^{2} + 4 x}{2 x y}

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