+图钭学技术大荸数学系 University of Science and Technology of china DEPARTMENT OF MATHEMATICS 由Tayo展开 f(x+h)=f(x0)+hf(x)+f"(x)+∫"(51)x≤51≤x+h h f(x-h)=f(x)-hf(x0)+,f"(x)-f"(52),x-h≤52Sx 因此,有误差 R()=f(ro) f(xo +h)f(xo-h) 2h h If"()+∫"(2)=f"(2)=O(h2) 6数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 由Taylor展开 2 3 0 0 0 0 1 0 1 0 2 3 0 0 0 0 2 0 2 0 ( ) ( ) '( ) ''( ) '''( ), 2! 3! ( ) ( ) '( ) ''( ) '''( ), 2! 3! h h f x h f x hf x f x f x x h h h f x h f x hf x f x f x h x     + = + + +   + − = − + − −   因此，有误差 '''( ) ( ) 6 [ '''( ) '''( )] 12 2 ( ) ( ) ( ) '( ) 2 2 1 2 2 0 0 0 f O h h f f h h f x h f x h R x f x = + = = + − − = −   