maclaurin 1/(x-1)

Lösung

maclaurin

\frac{1}{x - 1}

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

Schritte zur Lösung

Apply the Maclaurin 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

\frac{\partial}{\partial x} (x^{4} + y^{4} - 4 x + 1 y)

t an g e n t f (x) = 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 4

im pl i c i t \frac{d y}{d x}, y^{3} + y = x

\int \frac{1}{x ^{13}} d x

\int sec (x) \cdot tan (x) d x