taylor e^xcos(x)

Lösung

taylor

e^{x} cos (x)

1 + x - \frac{1}{3} x^{3} - \frac{1}{6} x^{4} - \frac{1}{30} x^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 2}{3 !} x^{3} + \frac{- 4}{4 !} x^{4} + \frac{- 4}{5 !} x^{5} + \dots

Fasse zusammen

= 1 + x - \frac{1}{3} x^{3} - \frac{1}{6} x^{4} - \frac{1}{30} x^{5} + \dots

\int 6 e^{2} d x

\int_{- 8}^{27} \frac{1}{3 x} d x

l a pl a ce t r an s f or m e^{- 5 t} sin (2 t)

(2 x y - sec^{2} (x)) d x + (x^{2} + 2 y) d y = 0

\frac{d}{d x} (x y e^{- x^{2} - y^{2}})