泰勒 ln(3x-2)

解答

泰勒

ln (3 x - 2)

3 (x - 1) - \frac{9}{2} (x - 1)^{2} + 9 (x - 1)^{3} - \frac{81}{4} (x - 1)^{4} + \frac{243}{5} (x - 1)^{5} + \dots

求解步骤

应用泰勒公式

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

求导数

= 0 + \frac{3}{1 !} (x - 1) + \frac{- 9}{2 !} (x - 1)^{2} + \frac{54}{3 !} (x - 1)^{3} + \frac{- 486}{4 !} (x - 1)^{4} + \frac{5832}{5 !} (x - 1)^{5} + \dots

整理后得

= 3 (x - 1) - \frac{9}{2} (x - 1)^{2} + 9 (x - 1)^{3} - \frac{81}{4} (x - 1)^{4} + \frac{243}{5} (x - 1)^{5} + \dots

\int \frac{3}{x} d x

d er i v a t i v e ln (\frac{4 x - 4}{5 x + 9})

x y^{^{'}} - 3 y = 6

\frac{\partial}{\partial x} (e^{x^{2} + 2 y})

a re a y = 10 x, y = x^{2}