taylor ln(x)5

Lösung

taylor

ln (x) 5

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

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( ln ( x ) \cdot 5 ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( x ) \cdot 5 ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( x ) \cdot 5 ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 0 + \frac{5}{1 !} (x - 1) + \frac{- 5}{2 !} (x - 1)^{2} + \frac{10}{3 !} (x - 1)^{3} + \frac{- 30}{4 !} (x - 1)^{4} + \frac{120}{5 !} (x - 1)^{5} + \dots

Fasse zusammen

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

x \to 0 lim (\frac{( ln ( 1 + x ) )}{x})

\int (3 x - 2)^{4} d x

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