11-12高三·山东潍坊·阶段练习
1 . 已知
,
,
且
,函数
.
(1)求函数
的单调区间;
(2)若函数
的图象在点
,
(2)
处的切线的斜率为
,问:
在什么范围取值时,对于任意的
,
,函数
在区间
上总存在极值?
(3)当
时,设函数
,若在区间
,
上至少存在一个
,使得
成立,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1d0762d3e1431bdf6e0067d53e4fd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e2ea42b5e3534905d8cfff749a8439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f155833b8c37df25a67e628b82ffa2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28b08682efa2692b052f64fe1448fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c8dce55e1df25b6fb286ca415a5bb2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba6841e45d2ab4ee38390b98b538f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb6c6b88c47ffd0a018bf64c5b68a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45340678c2ec1bc8cd68c0a3a2ab8902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e37a0d91fae313345dc21078a162764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a2eafb3dd274dd9b98d83c38e87802.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8703ba8e5650d3b93872074af40f9b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f124fb9eab689c537bb5ddf5012e35f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8c98eefb6fcff10193ba39a6fdb13e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d642a28caeb51a77877ea25b46ddbed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f81694c250c0107d608508c094f27f.png)
(1)当函数
有3个零点,求实数
的取值范围;
(2)当
取条件(1)下的取值时,设函数
有3个零点
,
,
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f81694c250c0107d608508c094f27f.png)
(1)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a42945a6ff4452dfbe550e0f28c82f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcefa1eadaa807e3fe6c61a2f8d2dea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5646305daf3f3a5c135d45dbe51aff69.png)
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3 . 若无穷数列
满足
,
,则称
具有性质
.若无穷数列
满足
,
,则称
具有性质
.
(1)若数列
具有性质
,且
,请直接写出
的所有可能取值;
(2)若等差数列
具有性质
,且
,求
的取值范围;
(3)已知无穷数列
同时具有性质
和性质
,
,且
不是数列
的项,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3567869af3e34bcf1dd5f2124e544785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6518163334e6b56dfa6ae7eb75f9a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bd31185a298a88fb51205d8b67aecd.png)
(3)已知无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0313eea2c65393728d83a287a8b799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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4 . 已知函数
(a为常数).
(1)若函数
是增函数,求a的取值范围;
(2)设函数
的两个极值点分别为
,
(
),求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213611317e843998c672932588cafe21.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e21ac584efecd770c2dd9d2e83803a.png)
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5 . 已知
有两个不同的零点
.
(1)求实数a的取值范围;
(2)若
,且
恒成立,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38572ad4ef879663d599510d64c4020f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aabc96b7433bba077ceac76d8f0d75.png)
(1)求实数a的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a42bb64f8a7ba48cd41e3163c33e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec2e06edc27a6930c32f3450b0fb928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 已知关于
的函数
为
上的偶函数,且在区间
上的最大值为10.设
.
(1)求函数
的解析式.
(2)若不等式
在
上恒成立,求实数
的取值范围.
(3)是否存在实数
,使得关于
的方程
有四个不相等的实数根?如果存在,求出实数
的范围,如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39a21c80ae3e990027ecea33bfb6424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85564659d145e38c0887d186db1c8573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba94b35258a2fbde34d7e26be524fb6e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e567c3e841ba226b51543b0dc43e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4d001c51cf7b47102f641ded56b01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6544efd3f7cea29d879628d508f0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2020-12-26更新
|
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8卷引用:上海市奉贤区致远高级中学2022届高三上学期期中教学评估数学试题
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7 . 若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0937f5a8ad2afa56381cc9d584f6d3.png)
(1)当
时,设
所对应的自变量取值区间的长度为
(闭区间
的长度为
),试求
的最大值;
(2)是否存在这样的
使得当
时,
?若存在,求出
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0937f5a8ad2afa56381cc9d584f6d3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77bd2b5113133614c6ee86d670953565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e669d502287cab6a74d72fb4aa1ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65185cb5d67a482a7c86afc70fdbd230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)是否存在这样的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ede5cb0407ac7f334a726eeac5d89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a916b565f017ddad96d04077568bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e669d502287cab6a74d72fb4aa1ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)令
,已知函数
有两个极值点
,且
,
①求实数
的取值范围;
②若存在
,使不等式
对任意
(取值范围内的值)恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732a081df910f7b85a9d29dd139e2e6c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005f2e6bee90297bd1c2c6533d29a87a.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7006220d33024798081a6f2c1d94c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58c4411628935f2c4a42095c9a644ca.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d001e8728b32aa28b83a9a36e674f9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1b8af65459ae7ef940ef1589ee4d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-03-17更新
|
1114次组卷
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7卷引用:天津市东丽区第一百中学2019-2020学年高三上学期第二次月考数学试题
天津市东丽区第一百中学2019-2020学年高三上学期第二次月考数学试题天津市西青区2019-2020学年高三第一学期期末考试数学试题2020届江苏省南京师大附属扬子中学高三下学期期初数学试题(已下线)强化卷07(3月)-冲刺2020高考数学之拿高分题目强化卷(山东专版)(已下线)专题08 巧辨“任意性问题”与“存在性问题(第一篇)-2020高考数学压轴题命题区间探究与突破天津市蓟州区第一中学2021届高三下学期模拟检测二数学试题(已下线)第七章 导数与不等式能成立(有解)问题 专题四 双变量能成立(有解)问题的解法 微点1 双变量单函数能成立(有解)问题的解法
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9 . 已知函数
,不等式
对
恒成立.
(1)求函数
的极值和函数
的图象在点
处的切线方程;
(2)求实数
的取值的集合
;
(3)设
,函数
,
,其中
为自然对数的底数,若关于
的不等式
至少有一个解
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9627dad36db7d25edad5e4391db232e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdab6cdeadd4f883f1fbd15653d8a649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd9af9d8560a40baa4f081ddcf45452.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4bb5aa475fe2019eb6fa89637738ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a2191c6a5f97bf2a1bbd536a5c9581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1aa6018802b084afcd52baac82aa5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58345bdc3db5c7f1e6b764985bafd6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845dc9e844467074bb2cf8bb95566206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2018-12-21更新
|
787次组卷
|
2卷引用:【校级联考】湖北省黄冈中学等八校2019届高三第一次(12月)联考数学理试题
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10 . 已知函数
,其中
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fca54800d6d494a6ddd1de957efde3c.png)
(1)当
时,求函数
的单调区间;
(2)设
,若
存在极大值,且对于
的一切可能取值,
的极大值均小于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686029b9113496215d521ec89449b5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c83797dcf53cef1ccce1f8ea4d249f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fca54800d6d494a6ddd1de957efde3c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a333323e284662528c56ad5cf1bd8b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2017-10-06更新
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2卷引用:重庆市第一中学2018届高三上学期第一次月考(9月)数学(理)试题