taylor-1/x

Lösung

taylor

- \frac{1}{x}

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= - 1 + \frac{1}{1 !} (x - 1) + \frac{- 2}{2 !} (x - 1)^{2} + \frac{6}{3 !} (x - 1)^{3} + \frac{- 24}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

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

d er i v a t i v e (\frac{2 + 5 z}{5 z}) (15 - 2 z)

\int_{0}^{3} 9 - x^{2} d x

\int \frac{48}{x ^{4} - 10 x ^{2} + 9} d x

\frac{d}{d x} ((3 x) (x + 3))

y^{^{''}} + 25 y = 2 sec (5 t)