taylor e^{-x/2},0

Lösung

taylor

e^{- \frac{x}{2}}, 0

1 - \frac{1}{2} x + \frac{1}{8} x^{2} - \frac{1}{48} x^{3} + \frac{1}{384} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{1}{2}}{1 !} x + \frac{\frac{1}{4}}{2 !} x^{2} + \frac{- \frac{1}{8}}{3 !} x^{3} + \frac{\frac{1}{16}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - \frac{1}{2} x + \frac{1}{8} x^{2} - \frac{1}{48} x^{3} + \frac{1}{384} x^{4} + \dots

n = 2 \sum \infty (\frac{1}{2})^{3 n}

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

\frac{d}{d x} (e^{c o s (x)} + cos (e^{x}))

d er i v a t i v e (1 + cos^{2} (x))^{3}

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