taylor 1/(1-x),8

Lösung

taylor

\frac{1}{1 - x}, 8

- \frac{1}{7} + \frac{1}{49} (x - 8) - \frac{1}{343} (x - 8)^{2} + \frac{1}{2401} (x - 8)^{3} - \frac{1}{16807} (x - 8)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= - \frac{1}{7} + \frac{\frac{d}{d x} ( \frac{1}{1 - x} ) ( 8 )}{1 !} (x - 8) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - x} ) ( 8 )}{2 !} (x - 8)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - x} ) ( 8 )}{3 !} (x - 8)^{3} + \dots

Evaluate Derivatives

= - \frac{1}{7} + \frac{\frac{1}{49}}{1 !} (x - 8) + \frac{- \frac{2}{343}}{2 !} (x - 8)^{2} + \frac{\frac{6}{2401}}{3 !} (x - 8)^{3} + \frac{- \frac{24}{16807}}{4 !} (x - 8)^{4} + \dots

Fasse zusammen

= - \frac{1}{7} + \frac{1}{49} (x - 8) - \frac{1}{343} (x - 8)^{2} + \frac{1}{2401} (x - 8)^{3} - \frac{1}{16807} (x - 8)^{4} + \dots

\frac{d}{d x} (x^{2} ln (x^{5}))

f (x) = 6 e^{x}

\int \frac{5 x ^{2} - 6}{x ^{2} - 2 x - 8} d x

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

d er i v a t i v e f (x) = c y^{- 7}