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

Lösung

taylor

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

x^{2} + x^{4} + x^{6} + x^{8} + x^{10} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \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} + \frac{0}{9 !} x^{9} + \frac{3628800}{10 !} x^{10} + \dots

Fasse zusammen

= x^{2} + x^{4} + x^{6} + x^{8} + x^{10} + \dots

\frac{\partial}{\partial x} (x y^{2} arctan (z))

y^{^{''}} - 2 y - 3 y = 3 e^{2 x}

d er i v a t i v e y = x^{7 x}

l a pl a ce t r an s f or m t^{3} e^{- 3 t}

x \to 0 lim (6^{x})