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

Lösung

taylor

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

1 + 2 x + \frac{5}{2} x^{2} + \frac{8}{3} x^{3} + \frac{65}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{5}{2 !} x^{2} + \frac{16}{3 !} x^{3} + \frac{65}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + 2 x + \frac{5}{2} x^{2} + \frac{8}{3} x^{3} + \frac{65}{24} x^{4} + \dots

\int (x^{2} + 1) e^{- 2 x} d x

\int (\frac{sec ( x ) tan ( x )}{sec ( x ) - 7}) d x

\int \frac{2}{3 x ^{2}} d x

\frac{d}{d x} (arctan (2 x^{2}))

\frac{\partial}{\partial y} (\frac{y}{2 x ^{2} + y ^{2}})