taylor ln(x),3

Lösung

taylor

ln (x), 3

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

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