taylor x/(1+x)

Lösung

taylor

\frac{x}{1 + x}

x - x^{2} + x^{3} - x^{4} + x^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{- 24}{4 !} x^{4} + \frac{120}{5 !} x^{5} + \dots

Fasse zusammen

= x - x^{2} + x^{3} - x^{4} + x^{5} + \dots

t an g e n t y = \frac{- 1 e ^{x}}{x}, (1, - 1 e)

x^{2} y^{^{'}} + x y = 4, y (1) = 3

f (x) = 2 x^{\frac{1}{3}}

\int \frac{x ^{4}}{( 1 + x ^{2} ) ^{\frac{3}{2}}} d x

d er i v a t i v e x^{3} + y^{3}