第一章总练习题 - 1 5x 8 1 2 3 | 5x 8 | 14 2 2 | 5 x...

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第一章总练习题 2 2 1. : 5 8 1 2. 3 |5 8| 14 2 2.| 5 8| 6,5 8 6 5 8 6, . 3 5 5 2 (2) 3 3, 5 2 3 3 3,0 15. 5 (3) | 1| | 2 | 1 ( 1) ( 2) ,2 1 4 4, . 2 2 | 2 |, . 2 , 2, 4, 2; 2 , 3 x x x x x x x x x x x x x x x x x y x x x y x y x y x y x y x     求解下列不等式 () 试将 表示成 的函数 2. 2 2 2 3 1 2 3 1 2, 4, ( 2). 3 2, 4 1 ( 2), 4. 3 1 3. 1 1 . 2 1. 2 1 2,4(1 ) 4 4, 0. 1, 0. 4. : 1 2 3 2 (1) 2 . 2 2 2 2 2 1 2 1 1 , . 2 2 1 2 3 2 2 2 n n y x y y y x y y x x x x x x x x x x x x n n n n     L 求出满足不等式 的全部 用数学归纳法证明下列等式 , 2- , 等式成立设等式对于 成立 则 1 2 3 1 1 1 1 1 2 1 2 1 1 2 2 2 1 1 2 3 1 2 2 2 2 2 2 2 1 2 4 ( 1) ( 1) 3 2 2 2 , 2 2 2 2 1 . . 1 ( 1) (2)1 2 3 ( 1). (1 ) 1 (1 1) 1 (1 ) 1, (1 ) (1 ) n n n n n n n n n n n n n n n n n n n n n x nx x x nx x x x x x n x x L L L 即等式对于 也成立故等式对于任意正整数皆成立 1 , 1 2 1 2 . 1 ( 1) 1 2 3 ( 1) ( 1) (1 ) n n n n n n n x nx x x nx n x n x x L 等式成立 , 设等式对于 成立 则
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1 2 2 1 2 2 1 1 2 2 1 1 2 2 1 2 2 1 ( 1) (1 ) ( 1) (1 ) 1 ( 1) (1 2 )( 1) (1 ) 1 ( 1) ( 2 )( 1) (1 ) 1 ( 1) ( 2 )( 1) (1 ) 1 ( 2) ( 1) , (1 ) 1 n n n n n n n n n n n n n n n n n n n x nx x n x x n x nx x x n x x n x nx x x x n x n x nx x x x n x n x n x x n 即等式对于 成立 . , . | 2 | | | 2 5. ( ) (1) ( 4), ( 1), ( 2), (2) ; (2) ( ) ; (3) 0 ( ) (4) 2 2 4 2 1 1 2 2 2 4 2 2 (1) ( 4) 1, ( 1) 2, ( 2) 2, (2) 0. 4 1 2 2 4/ , 2 (2) ( ) x x f x x f f f f f x x f x x f f f f x x f x         由归纳原理 等式对于所有正整数都成立 的值 表成分段函数 : 是否有极限 ? 时是否有极限 0 0 0 2 2 2 2 2 2 2 2 ; 2, 2 0; 0, 0. (3) . lim ( ) 2, lim ( ) 0 lim ( ). (4) . lim ( ) lim ( 4/ ) 2, lim ( ) lim 2 2 lim ( ), lim ( ) 2. 6. ( ) [ 14], ( ) 14 (1) (0), x x x x x x x x x x x f x f x f x f x x f x f x f x f x x f x x f                  无因为 . 是不超过 的最大整数 0 0 2 2 3 , ( 2) ; 2 (2) ( ) 0 ?
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