名校
解题方法
1 . 已知函数
(
且
)在
上最大值和最小值的和为
,令
.
(1)求实数a的值,并探究
是否为定值,若是定值,写出证明过程;若不是定值,请说明理由;
(2)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ad2eb4e2649bcaec0a650ed8840314.png)
(1)求实数a的值,并探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3caaf39cc15fc52ecae71ac5bc0e1c5.png)
(2)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebf88145934a10a1dfa614bbfb2cbd7.png)
您最近一年使用:0次
2023-09-18更新
|
242次组卷
|
6卷引用:江苏省南通市如皋中学2021-2022学年高一上学期期末数学试题
江苏省南通市如皋中学2021-2022学年高一上学期期末数学试题江苏省盐城市阜宁中学2022-2023学年高一衔接班上学期第一次学情调研考试数学试题江苏省镇江市扬中市第二高级中学2022-2023学年高一上学期12月月考数学试题(已下线)第6章 幂函数、指数函数和对数函数章末题型归纳总结 (1)-【帮课堂】(苏教版2019必修第一册)(已下线)重难点03函数(15种解题模型与方法)(4)(已下线)4.2.2 指数函数的图象和性质(分层作业)-【上好课】
23-24高一上·江苏南通·阶段练习
2 . 已知函数
对任意的
,都有
,且当
时,
.
(1)判断函数
的单调性并证明;
(2)若
,解关于
的不等式
;
(3)若
,不等式
任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fe667463b55a23c0ef09eb103ba574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4ed37e1a0c5ba92ae64e65fe638ced.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0987f55432e194a56801c1238696850.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002d5fce03e9700db446b31512b2c74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
3 . 已知定义域为R的函数
是奇函数.
(1)判断
的单调性,并证明;
(2)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39027cd6cdc96e73da2e283826dc45c1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2277a65358f2e8c27902170cddac6.png)
您最近一年使用:0次
2023-07-12更新
|
957次组卷
|
3卷引用:江苏省常州市北郊高级中学2022-2023学年高一上学期期末数学试题
名校
4 . (1)锐角三角形
中,
.
,求
的值.
(2)已知
,
,其中
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ee608882881caff2f1e223177424ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fafa5beb70c80533bb17b31fb5416f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6402f1010e94be78552ed4c45548b1b8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da951e45061c4a21b216e04fca76a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bad4c3f9aba47bccdbcc961542c0b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea52ac55e2361a8ccc1664fd91abfb96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dffd51af6a5a4d5e2492d8555fa0c10.png)
您最近一年使用:0次
名校
解题方法
5 . 设a,b为实数,定义在R上的函数
为奇函数,且其图象经过点
.
(1)求
的解析式;
(2)用定义证明
为R上的增函数,并求
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a14ff78575ff72d20376c17b1a5822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7938936a3bcc6db1dd98b714d8112186.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc68350d4a250d83aef73d7e2794816.png)
您最近一年使用:0次
2023-08-08更新
|
511次组卷
|
8卷引用:江苏省常州市教育学会2021-2022学年高一上学期学业水平监测数学试题
名校
解题方法
6 . 设a为实数,给定区间I,对于函数
满足性质P:存在
,使得
成立.记集合
.
(1)设
,
,求证:
;
(2)设
,
,若
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c85eadf1c23b6b46183e978071442a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8af703255327c297eb54bfe318452b9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dfa9363036589c4e93868fe0437a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec84404bbf6cf4a9d992e1760dcfdd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cac663990f61a4a3086c6bea3d51f9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688afe078f708dcdec80f68a1386c041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f412e27806d298e08c365ee16b00f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e74920f57028200604c2691c8f0fb89.png)
您最近一年使用:0次
7 . 已知
.
(1)证明:
;
(2)若函数
,当定义域为
时,值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54b89f1fe624a5678381b2e49301538.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45af01e8048e4948308cb5c41d9235fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d75a3a0ece0a78c9ea606cd6cee712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-10更新
|
328次组卷
|
2卷引用:江苏省苏南八校2023-2024学年高一上学期12月联考数学试卷
名校
解题方法
8 . (1)设
,试比较
和
的大小.
(2)求证:当
时,不等式
成立,当且仅当
等号成立,据此求
的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d229cbec798c9c278a9b5979cb38247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f23db69bdc68433d2db9590fe60550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40901c6ecbde629a554f58db9c0cc677.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8674e0c29d69918736b83bdc8288dc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb2e31608320e989afeeed9a7a8482d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938babc8d8adcabe08f196ef63a36e10.png)
您最近一年使用:0次
名校
9 . 求证:方程
有两个同号且不相等的实根的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f391d487b0808124309ba17df8dd4700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05fc663921c31990daf1211ca1624717.png)
您最近一年使用:0次
2022-10-25更新
|
415次组卷
|
6卷引用:江苏省苏州市第五中学2022-2023学年高一上学期10月阶段性测试数学试题
江苏省苏州市第五中学2022-2023学年高一上学期10月阶段性测试数学试题(已下线)重难点03 从集合的角度理解充分条件、必要条件、充要条件(1)-【帮课堂】(苏教版2019必修第一册)(已下线)第2章 常用逻辑用语综合能力测试-【帮课堂】(苏教版2019必修第一册)(已下线)专题2.2 充分条件、必要条件、充要条件(1)【帮课堂】苏教版2019必修第一册(已下线)1.4 充分必要条件(精练)-《一隅三反》(已下线)高一上学期期末复习【第一章 集合与常用逻辑用语】拔尖-举一反三系列
名校
解题方法
10 . (1)设
,
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
,
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26324941773aadc326cdfd502491484e.png)
您最近一年使用:0次