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Beliebt Rechnen >

maclaurin e^{-x},5

Lösung

maclaurin

e^{- x}, 5

Lösung

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

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

Beliebte Beispiele

integral of 1+2/y

\int 1 + \frac{2}{y} d y

derivative 1/(2z^3)

d er i v a t i v e \frac{1}{2 z ^{3}}

y^'=-(2y)/(x+1)+2x

y^{^{'}} = - \frac{2 y}{x + 1} + 2 x

limit as x approaches 4 of x^2-1

x \to 4 lim (x^{2} - 1)

integral of xln^5(x)

\int x ln^{5} (x) d x