maclaurin 3/(1+x)

Lösung

maclaurin

\frac{3}{1 + x}

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

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 3 + \frac{- 3}{1 !} x + \frac{6}{2 !} x^{2} + \frac{- 18}{3 !} x^{3} + \frac{72}{4 !} x^{4} + \dots

Fasse zusammen

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

\int 4 x^{3} e^{x^{4}} d x

\int ln (y + y^{2}) d y

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

\frac{d}{d x} (x y + y - 1)

\int_{4}^{5} \frac{1}{( x - 4 ) ^{\frac{4}{3}}} d x