泰勒 cos(pi-6x)

解答

泰勒

cos (π - 6 x)

- 1 + 18 x^{2} - 54 x^{4} + \frac{324}{5} x^{6} - \frac{1458}{35} x^{8} + \dots

求解步骤

应用泰勒公式

= - 1 + \frac{\frac{d}{d x} ( cos ( π - 6 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( π - 6 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( π - 6 x ) ) ( 0 )}{3 !} x^{3} + \dots

求导数

= - 1 + \frac{0}{1 !} x + \frac{36}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 1296}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{46656}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 1679616}{8 !} x^{8} + \dots

整理后得

= - 1 + 18 x^{2} - 54 x^{4} + \frac{324}{5} x^{6} - \frac{1458}{35} x^{8} + \dots

d er i v a t i v e y = 2 sin (x) + c e^{- x} cos (x)

18 y^{^{''}} + 9 y^{^{'}} - 2 y = 0

y^{^{'}} = 3 x^{2} + 1

in v erse l a pl a ce \frac{5 s - 2}{7 s ^{2} - s - 11}

x \to - \infty lim (x - 2)