泰勒 sin(x-x^2)

解答

泰勒

sin (x - x^{2})

x - x^{2} - \frac{1}{6} x^{3} + \frac{1}{2} x^{4} - \frac{59}{120} x^{5} + \dots

求解步骤

应用泰勒公式

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

求导数

= 0 + \frac{1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{- 1}{3 !} x^{3} + \frac{12}{4 !} x^{4} + \frac{- 59}{5 !} x^{5} + \dots

整理后得

= x - x^{2} - \frac{1}{6} x^{3} + \frac{1}{2} x^{4} - \frac{59}{120} x^{5} + \dots

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