⑩天掌 Teaching Plan on Advanced Mathematics 3)取x=0, 在0与x之间,令=(0<<1) 则余项Rn(x)= f""( n+1 (n+1) 麦克劳林( Maclaurin)公式 f(x)=f(0)+fY0)x+2702 f"( x-+… 2! 2十 ft(a) (0<6<1) (n+1) ∫(x)=f(0)+f0xJ"(x2+…+f(0 2! +O(x") 2004-4-10Tianjin Polytechnic University Teaching Plan on Advanced Mathematics ( ) ! (0) 2! (0) ( ) (0) (0) ( ) 2 n n n O x x n f x f f x f f x + + +  = +  +  (0 1) ( 1)! ( ) ! (0) 2! (0) ( ) (0) (0) 1 ( 1) ( ) 2   + + + +  = +  + + +   n n n n x n f x x n f x f f x f f x  麦克劳林(Maclaurin)公式 3)取x0 = 0,  在0与x之间,令 = x (0    1) 则余项 1 ( 1) ( 1)! ( ) ( ) + + + = n n n x n f x R x  2004-4-10