泰勒 cot(x)

解答

泰勒

cot (x)

cot (1) - csc^{2} (1) (x - 1) + csc^{2} (1) cot (1) (x - 1)^{2} + \frac{4 csc ^{2} ( 1 ) - 6 csc ^{4} ( 1 )}{6} (x - 1)^{3} + \frac{- 8 csc ^{2} ( 1 ) cot ( 1 ) + 24 csc ^{4} ( 1 ) cot ( 1 )}{24} (x - 1)^{4} + \dots

求解步骤

应用泰勒公式

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

求导数

= cot (1) + \frac{- csc ^{2} ( 1 )}{1 !} (x - 1) + \frac{2 csc ^{2} ( 1 ) cot ( 1 )}{2 !} (x - 1)^{2} + \frac{4 csc ^{2} ( 1 ) - 6 csc ^{4} ( 1 )}{3 !} (x - 1)^{3} + \frac{- 8 csc ^{2} ( 1 ) cot ( 1 ) + 24 csc ^{4} ( 1 ) cot ( 1 )}{4 !} (x - 1)^{4} + \dots

整理后得

= cot (1) - csc^{2} (1) (x - 1) + csc^{2} (1) cot (1) (x - 1)^{2} + \frac{4 csc ^{2} ( 1 ) - 6 csc ^{4} ( 1 )}{6} (x - 1)^{3} + \frac{- 8 csc ^{2} ( 1 ) cot ( 1 ) + 24 csc ^{4} ( 1 ) cot ( 1 )}{24} (x - 1)^{4} + \dots

\int - 2 e^{3 x} d x

\int \frac{3}{2} ln x^{3} + 1 d x

d er i v a t i v e f (x) = \frac{x}{x - 1}

t an g e n t f (x) = 3 - 5 x + 2 x^{2}, (- 9, 210)

(x + y)^{2} d x + (2 x y + x^{2} - 9) d y = 0