taylor ln(x),7

Lösung

taylor

ln (x), 7

ln (7) + \frac{1}{7} (x - 7) - \frac{1}{98} (x - 7)^{2} + \frac{1}{1029} (x - 7)^{3} - \frac{1}{9604} (x - 7)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= ln (7) + \frac{\frac{d}{d x} ( ln ( x ) ) ( 7 )}{1 !} (x - 7) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( x ) ) ( 7 )}{2 !} (x - 7)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( x ) ) ( 7 )}{3 !} (x - 7)^{3} + \dots

Evaluate Derivatives

= ln (7) + \frac{\frac{1}{7}}{1 !} (x - 7) + \frac{- \frac{1}{49}}{2 !} (x - 7)^{2} + \frac{\frac{2}{343}}{3 !} (x - 7)^{3} + \frac{- \frac{6}{2401}}{4 !} (x - 7)^{4} + \dots

Fasse zusammen

= ln (7) + \frac{1}{7} (x - 7) - \frac{1}{98} (x - 7)^{2} + \frac{1}{1029} (x - 7)^{3} - \frac{1}{9604} (x - 7)^{4} + \dots

x \to - 1 + lim (4 - x)

\frac{d}{d x} (2 (x^{3} + 4)^{2})

\int (4 x - 5) d x

d er i v a t i v e x^{7} (x^{2} - \frac{3}{x ^{3}})

n = 0 \sum \infty \frac{1}{n \cdot 2 ^{n}}