taylor 3/(x^2-x-2)

Lösung

taylor

\frac{3}{x ^{2} - x - 2}

- \frac{3}{2} + \frac{3}{4} x - \frac{9}{8} x^{2} + \frac{15}{16} x^{3} - \frac{33}{32} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= - \frac{3}{2} + \frac{\frac{3}{4}}{1 !} x + \frac{- \frac{9}{4}}{2 !} x^{2} + \frac{\frac{45}{8}}{3 !} x^{3} + \frac{- \frac{99}{4}}{4 !} x^{4} + \dots

Fasse zusammen

= - \frac{3}{2} + \frac{3}{4} x - \frac{9}{8} x^{2} + \frac{15}{16} x^{3} - \frac{33}{32} x^{4} + \dots

\int_{1}^{3} ln (2 x) d x

x \to π lim (5)

d er i v a t i v e f (x) = x sec (x)

\frac{d}{d x} (x^{2} x - 4)

t a y l or cos (x)