taylor 1/(X-1),12

Lösung

taylor

\frac{1}{X - 1}, 12

\frac{1}{11} - \frac{1}{121} (X - 12) + \frac{1}{1331} (X - 12)^{2} - \frac{1}{14641} (X - 12)^{3} + \frac{1}{161051} (X - 12)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{11} + \frac{\frac{d}{d X} ( \frac{1}{X - 1} ) ( 12 )}{1 !} (X - 12) + \frac{\frac{d ^{2}}{d X ^{2}} ( \frac{1}{X - 1} ) ( 12 )}{2 !} (X - 12)^{2} + \frac{\frac{d ^{3}}{d X ^{3}} ( \frac{1}{X - 1} ) ( 12 )}{3 !} (X - 12)^{3} + \dots

Evaluate Derivatives

= \frac{1}{11} + \frac{- \frac{1}{121}}{1 !} (X - 12) + \frac{\frac{2}{1331}}{2 !} (X - 12)^{2} + \frac{- \frac{6}{14641}}{3 !} (X - 12)^{3} + \frac{\frac{24}{161051}}{4 !} (X - 12)^{4} + \dots

Fasse zusammen

= \frac{1}{11} - \frac{1}{121} (X - 12) + \frac{1}{1331} (X - 12)^{2} - \frac{1}{14641} (X - 12)^{3} + \frac{1}{161051} (X - 12)^{4} + \dots

\frac{d}{d x} (2 x^{3} - 2 x)

\int x sin (s) d x

d er i v a t i v e y = (7) (6^{x - 8})

x^{2} \frac{d y}{d x} + 4 x y - e^{x} = 0

(2 y - 8 x^{2}) d x + x d y = 0