泰勒-2sin(4x)

解答

泰勒

- 2 sin (4 x)

- 8 x + \frac{64}{3} x^{3} - \frac{256}{15} x^{5} + \frac{2048}{315} x^{7} - \frac{4096}{2835} x^{9} + \dots

求解步骤

应用泰勒公式

= 0 + \frac{\frac{d}{d x} ( - 2 sin ( 4 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( - 2 sin ( 4 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( - 2 sin ( 4 x ) ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 0 + \frac{- 8}{1 !} x + \frac{0}{2 !} x^{2} + \frac{128}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 2048}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{32768}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 524288}{9 !} x^{9} + \dots

整理后得

= - 8 x + \frac{64}{3} x^{3} - \frac{256}{15} x^{5} + \frac{2048}{315} x^{7} - \frac{4096}{2835} x^{9} + \dots

d er i v a t i v e y = ln (x^{8})

\frac{d y}{d x} = x^{5} (y - 3), y (0) = 5

\int (x + 1) (x + 2)^{6} d x

\int 5 x^{4} - 4 x^{5} d x

d er i v a t i v e 35 + 35 sin (\frac{- 2 π t - π}{2})