taylor 1/(1-x^2)

Lösung

taylor

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

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{40320}{8 !} x^{8} + \dots

Fasse zusammen

= 1 + x^{2} + x^{4} + x^{6} + x^{8} + \dots

\int csc (\frac{v - π}{2}) cot (\frac{v - π}{2}) d v

\frac{d y}{d x} + (\frac{4}{x}) y = - 4 x - 5

\int_{0}^{1} \frac{1}{x ( x + 1 )} d x

\frac{\partial}{\partial x} (4 x^{4} y^{5} - 3 x^{2})

\frac{\partial}{\partial x} (x - y^{2} + 3 x y)