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泰勒 ln(6x+1)

解答

泰勒

ln (6 x + 1)

解答

6 x - 18 x^{2} + 72 x^{3} - 324 x^{4} + \frac{7776}{5} x^{5} + \dots

求解步骤

应用泰勒公式

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

求导数

= 0 + \frac{6}{1 !} x + \frac{- 36}{2 !} x^{2} + \frac{432}{3 !} x^{3} + \frac{- 7776}{4 !} x^{4} + \frac{186624}{5 !} x^{5} + \dots

整理后得

= 6 x - 18 x^{2} + 72 x^{3} - 324 x^{4} + \frac{7776}{5} x^{5} + \dots

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