taylor 1/(1-x),7

Lösung

taylor

\frac{1}{1 - x}, 7

- \frac{1}{6} + \frac{1}{36} (x - 7) - \frac{1}{216} (x - 7)^{2} + \frac{1}{1296} (x - 7)^{3} - \frac{1}{7776} (x - 7)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= - \frac{1}{6} + \frac{\frac{d}{d x} ( \frac{1}{1 - x} ) ( 7 )}{1 !} (x - 7) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - x} ) ( 7 )}{2 !} (x - 7)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - x} ) ( 7 )}{3 !} (x - 7)^{3} + \dots

Evaluate Derivatives

= - \frac{1}{6} + \frac{\frac{1}{36}}{1 !} (x - 7) + \frac{- \frac{1}{108}}{2 !} (x - 7)^{2} + \frac{\frac{1}{216}}{3 !} (x - 7)^{3} + \frac{- \frac{1}{324}}{4 !} (x - 7)^{4} + \dots

Fasse zusammen

= - \frac{1}{6} + \frac{1}{36} (x - 7) - \frac{1}{216} (x - 7)^{2} + \frac{1}{1296} (x - 7)^{3} - \frac{1}{7776} (x - 7)^{4} + \dots

\int (x^{7} - 5 x^{- 2} + 4) d x

x \to 0 lim (\frac{8 x}{sin ( x )})

\int \frac{x ^{3}}{x ^{2} + 100} d x

d er i v a t i v e y = - arcsin (5 x^{2} + 4)

f (x) = 3^{2 x + 1}