taylor e^{-3x}

Lösung

taylor

e^{- 3 x}

1 - 3 x + \frac{9}{2} x^{2} - \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 3}{1 !} x + \frac{9}{2 !} x^{2} + \frac{- 27}{3 !} x^{3} + \frac{81}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - 3 x + \frac{9}{2} x^{2} - \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

x \to 9 - lim (\frac{x ^{9}}{x - 9})

x \to 0 + lim (x ln (x^{6}))

t an g e n t \frac{6 x}{( x + 1 )}

\int \frac{7 x ^{2} + x + 54}{x ^{3} + 9 x} d x

d er i v a t i v e y = x + 2