泰勒 8/(sqrt(x))

解答

泰勒

\frac{8}{x}

8 - 4 (x - 1) + 3 (x - 1)^{2} - \frac{5}{2} (x - 1)^{3} + \frac{35}{16} (x - 1)^{4} + \dots

求解步骤

应用泰勒公式

= 8 + \frac{\frac{d}{d x} ( \frac{8}{x} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{8}{x} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{8}{x} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

求导数

= 8 + \frac{- 4}{1 !} (x - 1) + \frac{6}{2 !} (x - 1)^{2} + \frac{- 15}{3 !} (x - 1)^{3} + \frac{\frac{105}{2}}{4 !} (x - 1)^{4} + \dots

整理后得

= 8 - 4 (x - 1) + 3 (x - 1)^{2} - \frac{5}{2} (x - 1)^{3} + \frac{35}{16} (x - 1)^{4} + \dots

\int tan (9 x se) c^{2} 9 x d x

\int \frac{1}{4 - 5 x} d x

\frac{\partial}{\partial x} (x^{3})

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1) \cdot (y + 4))

\frac{d y}{d x} = y (x y^{3} - 1)