taylor (x^2+x)/((1-x)^3)

Lösung

taylor

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

x + 4 x^{2} + 9 x^{3} + 16 x^{4} + 25 x^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{8}{2 !} x^{2} + \frac{54}{3 !} x^{3} + \frac{384}{4 !} x^{4} + \frac{3000}{5 !} x^{5} + \dots

Fasse zusammen

= x + 4 x^{2} + 9 x^{3} + 16 x^{4} + 25 x^{5} + \dots

\int (x - 2)^{2} d x

\frac{\partial}{\partial x} ((- x^{2} + 3)^{2})

x \to 0 + lim (\frac{e ^{- x} - 1}{x})

x \to 0 + lim ((x + e^{x})^{\frac{1}{x}})

a re a y = 4 x^{3}, y = 100 x