taylor 1/(1-x-x^2)

Lösung

taylor

\frac{1}{1 - x - x ^{2}}

1 + x + 2 x^{2} + 3 x^{3} + 5 x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{1}{1 - x - x ^{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - x - x ^{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - x - x ^{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{4}{2 !} x^{2} + \frac{18}{3 !} x^{3} + \frac{120}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + x + 2 x^{2} + 3 x^{3} + 5 x^{4} + \dots

d er i v a t i v e t - 2

t an g e n t f (x) = x^{2} + 4, at x = - 1

\int \frac{( x ^{2} - x + 18 )}{x ^{3} + 3 x} d x

\int (3 x^{4}) d x

t an g e n t f (x) = x - 3, at x = 7