maclaurin 2/((1-x)^3)

Lösung

maclaurin

\frac{2}{( 1 - x ) ^{3}}

2 + 6 x + 12 x^{2} + 20 x^{3} + 30 x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 2 + \frac{6}{1 !} x + \frac{24}{2 !} x^{2} + \frac{120}{3 !} x^{3} + \frac{720}{4 !} x^{4} + \dots

Fasse zusammen

= 2 + 6 x + 12 x^{2} + 20 x^{3} + 30 x^{4} + \dots

\int \frac{3 r ^{2}}{r + 7} d r

in v erse l a pl a ce \frac{s}{s ^{2} - 2 s - 3}

d er i v a t i v e y = 4 + 9 x

y^{^{'}} = y - y^{3}

l a pl a ce t r an s f or m sin (3 t) cos (5 t)