taylor ln(x),5

Lösung

taylor

ln (x), 5

ln (5) + \frac{1}{5} (x - 5) - \frac{1}{50} (x - 5)^{2} + \frac{1}{375} (x - 5)^{3} - \frac{1}{2500} (x - 5)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= ln (5) + \frac{\frac{1}{5}}{1 !} (x - 5) + \frac{- \frac{1}{25}}{2 !} (x - 5)^{2} + \frac{\frac{2}{125}}{3 !} (x - 5)^{3} + \frac{- \frac{6}{625}}{4 !} (x - 5)^{4} + \dots

Fasse zusammen

= ln (5) + \frac{1}{5} (x - 5) - \frac{1}{50} (x - 5)^{2} + \frac{1}{375} (x - 5)^{3} - \frac{1}{2500} (x - 5)^{4} + \dots