taylor 1/((1+x)^3),0

Lösung

taylor

\frac{1}{( 1 + x ) ^{3}}, 0

1 - 3 x + 6 x^{2} - 10 x^{3} + 15 x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 3}{1 !} x + \frac{12}{2 !} x^{2} + \frac{- 60}{3 !} x^{3} + \frac{360}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - 3 x + 6 x^{2} - 10 x^{3} + 15 x^{4} + \dots

in v erse l a pl a ce \frac{3}{s ^{2} + 9}

t an g e n t h (x) = \frac{9}{x}, at x = 2

t a y l or e^{- 5 x - 3}, 5

d er i v a t i v e f (x) = (x^{2} - 10 x) \cdot (x - 14)

\int 3 64 x^{5} d x