maclaurin g(x)= x/(x-1)

Lösung

maclaurin

g (x) = \frac{x}{x - 1}

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

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{- 1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{- 24}{4 !} x^{4} + \frac{- 120}{5 !} x^{5} + \dots

Fasse zusammen

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

f^{^{''}} (x) = \frac{6}{x}

x \to 0 lim (1 - 2 sin^{2} (\frac{x}{2}))

x \to 1 + lim (2 x - 2 - 2)

\int \frac{6 x + 5}{3 x ^{2} + 5 x} d x

\int_{3}^{5} \frac{1}{x ^{2} - 9} d x