maclaurin 1/(1+2x)

Lösung

maclaurin

\frac{1}{1 + 2 x}

1 - 2 x + 4 x^{2} - 8 x^{3} + 16 x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} x + \frac{8}{2 !} x^{2} + \frac{- 48}{3 !} x^{3} + \frac{384}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - 2 x + 4 x^{2} - 8 x^{3} + 16 x^{4} + \dots

\int \frac{x ^{3} - 1}{x} d x

\frac{d y}{d x} = 21 x^{2} e^{- y}

a re a x + y = 2, x = y^{2} - 2 y

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{125})

x \to \infty lim (\frac{k}{x})