泰勒 3/((x^2-x-2))

解答

泰勒

\frac{3}{( x ^{2} - x - 2 )}

- \frac{3}{2} + \frac{3}{4} x - \frac{9}{8} x^{2} + \frac{15}{16} x^{3} - \frac{33}{32} x^{4} + \dots

求解步骤

应用泰勒公式

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

求导数

= - \frac{3}{2} + \frac{\frac{3}{4}}{1 !} x + \frac{- \frac{9}{4}}{2 !} x^{2} + \frac{\frac{45}{8}}{3 !} x^{3} + \frac{- \frac{99}{4}}{4 !} x^{4} + \dots

整理后得

= - \frac{3}{2} + \frac{3}{4} x - \frac{9}{8} x^{2} + \frac{15}{16} x^{3} - \frac{33}{32} x^{4} + \dots

\frac{d}{d x} ((2 + x)^{\frac{1}{3}} (1 - x)^{\frac{2}{3}})

\int \frac{9}{( x - 1 ) ( x + 8 )} d x

t a y l or 4 x^{4} + 3 x^{3} + 2 x^{2} + x + 1

\frac{d}{d t} (6 ln (cos (t)))

\int \frac{( x + 4 )}{2 x + 3} d x