taylor \sqrt[3]{1+x}

Lösung

taylor

3 1 + x

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

\frac{\partial}{\partial x} (\frac{2 x}{1 + x ^{2} + y ^{2}})

\frac{d}{d x} (x^{3} - 2 x - 5)

\frac{d}{d t} (\frac{3 t}{t - 6})

x \to 0 lim (x^{4} ln (x))

s l o p e (- 2.4) (2.4)