taylor 1/(|1-x|)

Lösung

taylor

\frac{1}{∣ 1 - x ∣}

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 + x + x^{2} + x^{3} + x^{4} + \dots

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

\int_{- \infty}^{1} e^{x} d x

\int cos (x) 3 2018 + sin (x) d x

\frac{\partial}{\partial x} (x^{0.5} y^{0.5})

\frac{\partial}{\partial x} (sin (- 6 x - 3 y))