taylor 2/((3x+1)),2

Lösung

taylor

\frac{2}{( 3 x + 1 )}, 2

\frac{2}{7} - \frac{6}{49} (x - 2) + \frac{18}{343} (x - 2)^{2} - \frac{54}{2401} (x - 2)^{3} + \frac{162}{16807} (x - 2)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{2}{7} + \frac{\frac{d}{d x} ( \frac{2}{3 x + 1} ) ( 2 )}{1 !} (x - 2) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{2}{3 x + 1} ) ( 2 )}{2 !} (x - 2)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{2}{3 x + 1} ) ( 2 )}{3 !} (x - 2)^{3} + \dots

Evaluate Derivatives

= \frac{2}{7} + \frac{- \frac{6}{49}}{1 !} (x - 2) + \frac{\frac{36}{343}}{2 !} (x - 2)^{2} + \frac{- \frac{324}{2401}}{3 !} (x - 2)^{3} + \frac{\frac{3888}{16807}}{4 !} (x - 2)^{4} + \dots

Fasse zusammen

= \frac{2}{7} - \frac{6}{49} (x - 2) + \frac{18}{343} (x - 2)^{2} - \frac{54}{2401} (x - 2)^{3} + \frac{162}{16807} (x - 2)^{4} + \dots

(- x y sin (x) + 2 y cos (x)) d x + 2 x cos (x) d y = 0

\frac{d}{d x} (\frac{9}{2} x^{2})

\frac{d}{d x} (73.3 4 x^{3})

\frac{d}{d t} (t^{3} - 12 t^{2} + 45 t)

l a pl a ce t r an s f or m 3 t