taylor x/(1+3x^2)

Lösung

taylor

\frac{x}{1 + 3 x ^{2}}

x - 3 x^{3} + 9 x^{5} - 27 x^{7} + 81 x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 18}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{1080}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 136080}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{29393280}{9 !} x^{9} + \dots

Fasse zusammen

= x - 3 x^{3} + 9 x^{5} - 27 x^{7} + 81 x^{9} + \dots

\int_{0}^{π} (π - x) sin (n x) d x

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

d er i v a t i v e f (x) = (2 x^{3} + 3)^{6}

t an g e n t - 2 x^{2}

\int 9 x^{2} - 8 x d x