taylor 1/(x^2),1

Lösung

taylor

\frac{1}{x ^{2}}, 1

1 - 2 (x - 1) + 3 (x - 1)^{2} - 4 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 - 2 (x - 1) + 3 (x - 1)^{2} - 4 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

\frac{\partial}{\partial x} (\frac{x ^{2}}{y} - x z)

\frac{\partial}{\partial y} (2 ln (3 x) - 4 ln (2 x y))

d er i v a t i v e \frac{3}{x ^{3}}

\int 15 x^{4} d x

in v erse l a pl a ce \frac{3}{s ^{2} - 4}