taylor x^2e^x

Lösung

taylor

x^{2} e^{x}

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

a re a y = 4 x, y = x

\frac{d}{d x} (4 + sin (7 x))

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

\int \frac{( x ^{2} - 4 )}{x} d x

y^{^{'}} + y = e^{x} y^{- 2}