taylor ln(x),8

Lösung

taylor

ln (x), 8

3 ln (2) + \frac{1}{8} (x - 8) - \frac{1}{128} (x - 8)^{2} + \frac{1}{1536} (x - 8)^{3} - \frac{1}{16384} (x - 8)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 3 ln (2) + \frac{\frac{d}{d x} ( ln ( x ) ) ( 8 )}{1 !} (x - 8) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( x ) ) ( 8 )}{2 !} (x - 8)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( x ) ) ( 8 )}{3 !} (x - 8)^{3} + \dots

Evaluate Derivatives

= 3 ln (2) + \frac{\frac{1}{8}}{1 !} (x - 8) + \frac{- \frac{1}{64}}{2 !} (x - 8)^{2} + \frac{\frac{1}{256}}{3 !} (x - 8)^{3} + \frac{- \frac{3}{2048}}{4 !} (x - 8)^{4} + \dots

Fasse zusammen

= 3 ln (2) + \frac{1}{8} (x - 8) - \frac{1}{128} (x - 8)^{2} + \frac{1}{1536} (x - 8)^{3} - \frac{1}{16384} (x - 8)^{4} + \dots

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