taylor x^{1/3}

Lösung

taylor

x^{\frac{1}{3}}

1 + \frac{1}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{5}{81} (x - 1)^{3} - \frac{10}{243} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{3}}{1 !} (x - 1) + \frac{- \frac{2}{9}}{2 !} (x - 1)^{2} + \frac{\frac{10}{27}}{3 !} (x - 1)^{3} + \frac{- \frac{80}{81}}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 1 + \frac{1}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{5}{81} (x - 1)^{3} - \frac{10}{243} (x - 1)^{4} + \dots

\frac{d}{d x} (- e^{x} (x + 6))

x \to 3 + lim (\frac{4 - x}{9 - x ^{2}})

\int \frac{sin ( 3 x )}{3 + 3 cos ( 3 x )} d x

im pl i c i t \frac{d y}{d x}, 3 x y = 6

\int_{- 1}^{2} (x^{3}) d x