taylor 1/(1-x),20

Lösung

taylor

\frac{1}{1 - x}, 20

- \frac{1}{19} + \frac{1}{361} (x - 20) - \frac{1}{6859} (x - 20)^{2} + \frac{1}{130321} (x - 20)^{3} - \frac{1}{2476099} (x - 20)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= - \frac{1}{19} + \frac{\frac{d}{d x} ( \frac{1}{1 - x} ) ( 20 )}{1 !} (x - 20) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - x} ) ( 20 )}{2 !} (x - 20)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - x} ) ( 20 )}{3 !} (x - 20)^{3} + \dots

Evaluate Derivatives

= - \frac{1}{19} + \frac{\frac{1}{361}}{1 !} (x - 20) + \frac{- \frac{2}{6859}}{2 !} (x - 20)^{2} + \frac{\frac{6}{130321}}{3 !} (x - 20)^{3} + \frac{- \frac{24}{2476099}}{4 !} (x - 20)^{4} + \dots

Fasse zusammen

= - \frac{1}{19} + \frac{1}{361} (x - 20) - \frac{1}{6859} (x - 20)^{2} + \frac{1}{130321} (x - 20)^{3} - \frac{1}{2476099} (x - 20)^{4} + \dots

\int 6 x y d x

im pl i c i t \frac{d y}{d x}, (4 x + 4 y) 3 = 64 x^{3} + 64 y^{3}

t an g e n t f (x) = - 3 - 5 x^{2}, at x = 3

\frac{d y}{d x} = \frac{( x - y )}{x}

d er i v a t i v e e^{\frac{a ^{2}}{2 a + 1}}