f x f x f x x f x f a a a b x a b a x a x b b a b x b k-1 k-1 k k k-1 k-1 k k k k k-1 k-1 k-1,2 ( ) 0, ( ) (a ) 0, a b k a b a b a b x x f x x f x f x x ???? k k k k k k 3. 继续运算, 由区间[ , ]构造区间[ , ] 并得到: 若则为所求的根; 若则取[a ,b ]= [ , ]; 否则, 可取[a ,b ]= [ , ]. 1 1 * * * * (a) ( ) ( ) 0 1 (b) ( ) 2 (c) ... ..., ... ...; [ , ] [ , ] , ( ) 0, ( , ), lim , lim k k k k k k k k k k k k k k f a f b b a b a a b a b x f x x a b a x b ? ??? ???? ? ?? ? ?? ?? ??? 0 0 1 1 k k 0 1 k 0 1 k 这样就得到一系列闭区间: [a ,b ], [a ,b ], ...[a ,b ],...,k= 0,1,2,...., 并满足: a a a b b b 即满足并且* * , lim k k k x x x ??? ?
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