taylor 5/(3-2x)

Lösung

taylor

\frac{5}{3 - 2 x}

\frac{5}{3} + \frac{10}{9} x + \frac{20}{27} x^{2} + \frac{40}{81} x^{3} + \frac{80}{243} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{5}{3} + \frac{\frac{d}{d x} ( \frac{5}{3 - 2 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{5}{3 - 2 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{5}{3 - 2 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{5}{3} + \frac{\frac{10}{9}}{1 !} x + \frac{\frac{40}{27}}{2 !} x^{2} + \frac{\frac{80}{27}}{3 !} x^{3} + \frac{\frac{640}{81}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{5}{3} + \frac{10}{9} x + \frac{20}{27} x^{2} + \frac{40}{81} x^{3} + \frac{80}{243} x^{4} + \dots

x \to - 2 lim (x^{2} + 1)

t an g e n t \frac{6 x}{x ^{2} + 1}

x \to + 0 lim ((3 x)^{x^{2}})

\int_{2}^{x} ln (t) d t

a re a x = 2 y - y^{2}, x = y^{2} - 4 y