maclaurin x-e^{3x}

Lösung

maclaurin

x - e^{3 x}

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

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

d er i v a t i v e \frac{3 t}{t - 9}

x \to 1 lim (\frac{x + 2}{x ^{3} + 8})

\frac{\partial}{\partial x} (x^{4} ln (yz))

n = 1 \sum \infty \frac{1}{1 0 ^{n}}

n = 1 \sum \infty (\frac{2}{7}) \cdot n