taylor 2/(1-x^2)

Lösung

taylor

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

2 + 2 x^{2} + 2 x^{4} + 2 x^{6} + 2 x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{0}{1 !} x + \frac{4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{1440}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{80640}{8 !} x^{8} + \dots

Fasse zusammen

= 2 + 2 x^{2} + 2 x^{4} + 2 x^{6} + 2 x^{8} + \dots

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 7

n = 0 \sum \infty 1 (- \frac{1}{3})^{n}

\int 56 x d x

x \to 0 lim (\frac{1}{x + 2} - \frac{1}{2})

d er i v a t i v e y = 4 x^{- 3}