taylor 1+(1+x)/(1-x)

Lösung

taylor

1 + \frac{1 + x}{1 - x}

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{2}{1 !} x + \frac{4}{2 !} x^{2} + \frac{12}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \dots

Fasse zusammen

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

\frac{\partial}{\partial x} (x^{3} e^{x} + cos (y))

\frac{d}{d x} (a - x)

\int 3 x ln (6 x) d x

\int \frac{ln ( x + a )}{x + a} d x

x \to + (- 2) lim (- 4 x + a)