taylor 1/(x+1)

Lösung

taylor

\frac{1}{x + 1}

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

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{1}{x + 1} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x + 1} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x + 1} ) ( 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 (t + 4) e^{t^{2} + 8 t + 1} d t

y^{^{''}} + 8 y^{^{'}} = - 256 cos (8 x)

y^{^{'}} + 2 x^{- 1} y = 6 x^{4} y^{2}

\int 3 x^{- \frac{2}{3}} - 2 x^{\frac{5}{3}} d x

\int e^{\frac{- 1}{2} l n (x)} d x