⑩天掌 Teaching Plan on Advanced Mathematics 例1求∫(x)=e的阶麦克劳林公式 解∫(x)=∫"(x)=…=∫(x)=e, f(0)=f(0)=f"(0)=…=f"(0)=1 注意到∫(a)=e代入公式,得 e ex=1+x++…++ x"1(0<6<1) n十 2004-4-10Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 例 1 求 x f ( x) = e 的n阶麦克劳林公式. 解 ( ) ( ) ( ) , (n) x  f  x = f  x == f x = e (0) (0) (0) (0) 1 ( )  =  =  = = = n f f f  f n x f x e   = + ( ) 注意到 ( 1) 代入公式,得 (0 1). 2! ! ( 1)! 1 1 2   + = + + + + + +   n n x x x n e n x x e x  2004-4-10