泰勒 sin(8x)

解答

泰勒

sin (8 x)

8 x - \frac{256}{3} x^{3} + \frac{4096}{15} x^{5} - \frac{131072}{315} x^{7} + \frac{1048576}{2835} x^{9} + \dots

求解步骤

应用泰勒公式

= 0 + \frac{\frac{d}{d x} ( sin ( 8 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( 8 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( 8 x ) ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 0 + \frac{8}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 512}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{32768}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 2097152}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{134217728}{9 !} x^{9} + \dots

整理后得

= 8 x - \frac{256}{3} x^{3} + \frac{4096}{15} x^{5} - \frac{131072}{315} x^{7} + \frac{1048576}{2835} x^{9} + \dots

\frac{d y}{d x} = b - a y

y^{^{'}} = x (1 + y^{2})

t an g e n t y = t^{3} - 36 t + 4, (6, 4)

x \to 0 - lim (e^{\frac{4}{x ^{5}}})

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