maclaurin x^2e^x-x^3-x^2

Lösung

maclaurin

x^{2} e^{x} - x^{3} - x^{2}

\frac{1}{2} x^{4} + \frac{1}{6} x^{5} + \frac{1}{24} x^{6} + \frac{1}{120} x^{7} + \frac{1}{720} x^{8} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{12}{4 !} x^{4} + \frac{20}{5 !} x^{5} + \frac{30}{6 !} x^{6} + \frac{42}{7 !} x^{7} + \frac{56}{8 !} x^{8} + \dots

Fasse zusammen

= \frac{1}{2} x^{4} + \frac{1}{6} x^{5} + \frac{1}{24} x^{6} + \frac{1}{120} x^{7} + \frac{1}{720} x^{8} + \dots

\frac{d}{d t} (2 e^{3 t})

x^{^{''}} + 4 x = 3

\int \frac{7}{x ^{3} - 27} d x

x \to 4 lim (- \frac{3}{( x - 4 ) ^{2}})

\frac{d y}{d x} = e^{2 - x}