taylor x/(1-x^2)

Lösung

taylor

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

x + x^{3} + x^{5} + x^{7} + x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{120}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{5040}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{362880}{9 !} x^{9} + \dots

Fasse zusammen

= x + x^{3} + x^{5} + x^{7} + x^{9} + \dots

n = 0 \sum \infty \frac{1}{n ln ( n )}

\frac{\partial}{\partial x} (x^{2} y + 2 y^{2} - 4 x y + 6)

\int \frac{y ^{2} + 20 y + 100}{( y ^{2} + 100 ) ^{2}} d y

y^{^{''}} - 8 y^{^{'}} + 19 y = 0

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + a ^{2}})