maclaurin xe^x

Lösung

maclaurin

x e^{x}

x + x^{2} + \frac{1}{2} x^{3} + \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

= x + x^{2} + \frac{1}{2} x^{3} + \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

x \to - 4 lim (16 - x^{2})

\int \frac{x}{( x - 1 ) ( x ^{2} + 2 x + 2 ) ^{2}} d x

x \to 0 + lim (\frac{2}{x})

x \frac{d y}{d x} + 8 y = e^{x^{8}}

x \to 0 + lim (1 + \frac{1}{x - 1})