) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 例: 给定点列{x,f(x)=0且x2-x1=x1-x0=h,求 ∫(x2),f(x)(x) 解: X-Xr-x (x) f(x0)+ (x-x0)(x-x2) f(x1)+ x-x0(x-x1) f(x2) 2h h ch x-Xtx-x x-xo+x-x xxo+x-x x1)+ 2h2 2h数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 给定点列   2 0 ( , ( )) i i i= x f x 且 x2 − x1 = x1 − x0 = h ，求 '( ), '( ), '( ) 2 1 0 f x f x f x 解： ( ) 2 ( )( ) ( ) ( )( ) ( ) 2 ( )( ) ( ) 2 2 0 1 2 1 0 2 2 0 1 2 2 f x h x x x x f x h x x x x f x h x x x x L x − − + − − − + − − = ( ) 2 ( ) ( ) ( ) ( ) 2 ( ) ' ( ) 2 2 0 1 2 1 0 2 2 0 1 2 2 f x h x x x x f x h x x x x f x h x x x x L x − + − + − − + − + − + − = 例：