1.求n次近似多项式pn(x),要求： Pn(xo)=f(xo).Ph(xo)=f(xo).(xo)=f(o) 令 pn(x)=a0+4(x-x0)+a2(x-x0)2+.+an(x-x0)” 则 Pi(x)= a+2a2(x-0)++nan(x-x0)”-1 ph(x)= 2la2+.+n(n-1)an(x-x0)"-2 p(x)= nlan ao=Pn(xo)=f(xo), a=ph(xo)=f'(xo), a=动p%(o)=f"(o),an=pg0(x0)=hfm(x） 故Pn(x)=f(x)+f'(x0x-0)+}f"(x0)(x-x0)2+ +m(xo)(x-xo)”1. 求 n 次近似多项式 要求: ( ) 2! 0 1 2 a p x n =  ( ), 0 = f  x  , ( ) 0 ( ) ! 1 a p x n n = n n ( ) 0 ( ) f x n = 故 pn (x) = ( )0 f x ( )( ) 0 0 + f  x x − x + 2 ! 1 ! 1 n n n f (x )(x x ) 0 0 ( ) + − ! 1 n 2 0 0 + f (x )(x − x ) 2 ! 1 机动 目录 上页 下页 返回 结束 令 pn (x) = 则 pn  (x) = pn (x) =  n an = ! ( ) ( ) p x n n ( ) 0 0 a p x = n ( ), 0 = f x ( ) 1 0 a p x n =  ( ), 0 = f  x a1 2 ( ) 2 0 + a x − x 1 0 ( ) − + + − n n  na x x 2 2!a 2 0 ( 1) ( ) − + + − − n n  n n a x x a0 n n a (x x ) a (x x ) a (x x ) 0 2 + 1 − 0 + 2 − 0 ++ −