taylor ln(x+1),2

Lösung

taylor

ln (x + 1), 2

ln (3) + \frac{1}{3} (x - 2) - \frac{1}{18} (x - 2)^{2} + \frac{1}{81} (x - 2)^{3} - \frac{1}{324} (x - 2)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= ln (3) + \frac{1}{3} (x - 2) - \frac{1}{18} (x - 2)^{2} + \frac{1}{81} (x - 2)^{3} - \frac{1}{324} (x - 2)^{4} + \dots

\frac{\partial}{\partial x} (\frac{x ^{2}}{( y - x ) ^{2}})

n = 1 \sum \infty \frac{2}{n ^{8}}

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