麦克劳林 sin(5x)

解答

麦克劳林

sin (5 x)

5 x - \frac{125}{6} x^{3} + \frac{625}{24} x^{5} - \frac{15625}{1008} x^{7} + \frac{390625}{72576} x^{9} + \dots

求解步骤

应用麦克劳林公式

= 0 + \frac{\frac{d}{d x} ( sin ( 5 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( 5 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( 5 x ) ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 0 + \frac{5}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 125}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{3125}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 78125}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{1953125}{9 !} x^{9} + \dots

整理后得

= 5 x - \frac{125}{6} x^{3} + \frac{625}{24} x^{5} - \frac{15625}{1008} x^{7} + \frac{390625}{72576} x^{9} + \dots

x \to 2 lim (3 x^{2} - x - 2)

d er i v a t i v e 7 x + 8

\int \frac{3}{( 3 x + 4 ) ln ( 3 x + 4 )} d x

x \to 0 lim (sin (3 x) cot (x))

x \to - 7 + lim (\frac{- x ^{2}}{x + 7})