taylor 1/((sqrt((3-2x))))

Lösung

taylor

\frac{1}{( ( 3 - 2 x ) )}

\frac{1}{3} + \frac{1}{3 3} x + \frac{1}{6 3} x^{2} + \frac{5}{54 3} x^{3} + \frac{35}{648 3} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{3} + \frac{\frac{1}{3 3}}{1 !} x + \frac{\frac{1}{3 3}}{2 !} x^{2} + \frac{\frac{5}{9 3}}{3 !} x^{3} + \frac{\frac{35}{27 3}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{3} + \frac{1}{3 3} x + \frac{1}{6 3} x^{2} + \frac{5}{54 3} x^{3} + \frac{35}{648 3} x^{4} + \dots

t an g e n t \frac{5 x + 2}{6 x - 4}

\int_{0}^{4} 2 t + 4 d t

a re a x + y = 4, x - y = 0, y + 3 x = 4

\frac{d}{d x} (\frac{4 x}{x ^{2} - 4})

\frac{d y}{d x} + y = e^{x}