名校
1 . 已知函数
.
(1)指出函数
的基本性质:定义域,奇偶性,单调性,值域(结论不需证明),并作出函数
的图象;
(2)若关于
的不等式
恒成立,求实数
的取值范围;
(3)若关于
的方程
恰有
个不同的实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d51f20de449bb518d8ccddcd2970a8.png)
(1)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893b785b7c2f2b86a041bbc2317105dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a2f6aa1362f427fa41c9de7110f6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2020-01-30更新
|
652次组卷
|
3卷引用:2015届上海市青浦区高三上学期期终学习质量调研数学试卷
名校
解题方法
2 . 已知复数
,
,(
,
,
),且
.
(1)若
且
,求
的值;
(2)设
,关于
的方程
在
上恰有
解,求实数
的值以及方程的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68500d55d76a20d72701afd11c49c258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b76aba5e1e8b5e594feeaae181b1664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de59a6da1ee210ccf04651ae53275dd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c87874458fabe50aff5e19d586d5d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac06500ca54cb8981de2a69dcd8fccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1639d47583555e889c30159bc85adcb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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15-16高三上·上海浦东新·期中
名校
3 . 已知
.
(1)求
;
(2)对参数
的哪些值,方程
正好有3个实数解;
(3)设
为任意实数,证明:
共有3个不同的实数解
,并且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f674a1b5b697c4fd92267dc24bfe6bd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d227791735377cb0c5644bd895fe4c.png)
(2)对参数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725f66bf5834a7b3cdeca87b18ece516.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4767c9985660f6f836e7e2ef7ecb7e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7a5158e2d7f98058dd210af52e7386.png)
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名校
4 . 已知函数
为偶函数,函数
为奇函数。
对任意实数x恒成立.
(1)求函数
与
;
(2)设
,
,若
对于
恒成立,求实数m的取值范围;
(3)对于(2)中的函数
,若方程
没有实数解,实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca705393a769bcb6f311adc423ae3c94.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45f3071c456623d3ece064a07a1de34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d328eba8ac2f3afba40b751af719252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33ff65cb33635c9219f5673956a83cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c03f7ffe55f0bcc987d3a93e3f3f37fb.png)
(3)对于(2)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff4532f53b62d3d77675f5d5c7f0483.png)
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名校
5 . 已知函数
.
判断
的奇偶性,并作出函数
的图像;
关于
的方程
恰有
个不同的实数解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d51f20de449bb518d8ccddcd2970a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](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/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f2a089bd65b7b1837b5388f9261e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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16-17高一上·上海浦东新·阶段练习
名校
6 . 对于
,
表示
与
中较大的一个值.
(1)求
、
、
、
;
(2)作出函数
的图象;
(3)若方程
在
内有两个解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b8d3f7a166ff5db92d9ee0014a960d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94627984fbca392f9b2e30893baec36.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347bb4ffedcbea2f4c16d047a138d75.png)
(2)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a54ebc9e1876ab54f11d212182a0717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
7 . 定义:若存在常数
,使得对定义域D内的任意两个不同的实数
,均有:
成立,则称
在D上满足利普希茨(Lipschitz)条件.
(1)试举出一个满足利普希茨(Lipschitz)条件的函数及常数
的值,并加以验证;
(2)若函数
在
上满足利普希茨(Lipschitz)条件,求常数
的最小值;
(3)现有函数
,请找出所有的一次函数
,使得下列条件同时成立:
①函数
满足利普希茨(Lipschitz)条件;
②方程
的根
也是方程
的根,且
;
③方程
在区间
上有且仅有一解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9bc59028761bee9de313ee6d5decc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试举出一个满足利普希茨(Lipschitz)条件的函数及常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfa1d9455db388617c1c3d0c5e98e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdfed8d6862125dc1fecfce0322a750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)现有函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
②方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f168b6811f1da5f09db1d9984ad8664f.png)
![](https://img.xkw.com/dksih/QBM/2019/11/12/2332484208558080/2333050301030400/STEM/b968951e37f142de95c41f25a4778494.png?resizew=9)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918d58191d097e04f939343b6d57d07b.png)
③方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298b861acdad2f218a882319c1a3280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e950e8a7181cb37bbddc6010fd87a2.png)
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2012·上海嘉定·一模
8 . 已知函数
(
)在区间
上有最大值
和最小值
.设
.
(1)求
、
的值;
(2)若不等式
在
上有解,求实数
的取值范围;
(3)若
有三个不同的实数解,求实数
的取值范围.
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/41d17618e25342628b0ab9d25b48429b.png?resizew=157)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/01c4fc9f436946ce8716cf33f3306496.png?resizew=39)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/b922825fe2264656a5a1eae856a6e6d0.png?resizew=42)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/10da5539e79742e0890ffbae890f09ef.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/827796b8668a47e6bde9ef300168a4d0.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/21e71419591e4a21b8e1e9a49c298b62.png?resizew=85)
(1)求
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/60db3e0e0f5d49c18bef0815b847d973.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/1fb13e835686469e8bf955f95dfc0083.png?resizew=13)
(2)若不等式
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/689ced6ac58342a687ce648f3d2bd4c1.png?resizew=116)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/9aafe0cc9f06471994955d0971a59e63.png?resizew=70)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/524e2909b5d044c18f1960a3ba27ff1b.png?resizew=13)
(3)若
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/63a24eb90248426fa38e79828a5a00e0.png?resizew=210)
![](https://img.xkw.com/dksih/QBM/2012/1/12/1570689469874176/1570689475551232/STEM/524e2909b5d044c18f1960a3ba27ff1b.png?resizew=13)
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