taylor e^{x^2-x}

Lösung

taylor

e^{x^{2} - x}

1 - x + \frac{3}{2} x^{2} - \frac{7}{6} x^{3} + \frac{25}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 1}{1 !} x + \frac{3}{2 !} x^{2} + \frac{- 7}{3 !} x^{3} + \frac{25}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - x + \frac{3}{2} x^{2} - \frac{7}{6} x^{3} + \frac{25}{24} x^{4} + \dots

\int \frac{x}{1} d x

d er i v a t i v e lo g_{10} (x^{3} + 1)

t an g e n t x^{2} + y^{2} = 25, (3, 4)

\frac{\partial}{\partial x} (- 9 x^{2} - 7 y^{2})

y^{^{''}} + 169 y = sec (13 x)