maclaurin 1/(1+x)

Lösung

maclaurin

\frac{1}{1 + x}

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

Schritte zur Lösung

Apply the Maclaurin 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

\int \frac{13}{x 1 + 2 x} d x

d er i v a t i v e (30 + x) (230 - 10 x)

\frac{d}{d x} (\frac{5 x}{e ^{x}})

\frac{d}{d x} (arcsin (\frac{x}{1 + x ^{2}}))

\frac{d}{d x} (\frac{( 2 π - x cos ( x ) )}{x - 2 π})