名校
1 . 已知
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1502aca15b810e295c2841f829c0b41c.png)
(1)若
,求证:函数
恰有一个负零点.(用图像证明不给分)
(2)若函数
恰有三个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f05684f6c0813df9531a9654c6c8c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1502aca15b810e295c2841f829c0b41c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97dd49ae1e7ac427c0a42525dd7d38b3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f49ad7e05f8fada803d5713257d0828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2 . 已知函数
.
(1)当
时,求
,并判断函数
零点的个数;
(2)当
时,
有三个零点
,记
,
,2,3.证明:①
;②
.
参考公式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dc59a1edc821f4cbd77ef908dff3c7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6fb3c74056a4b4ebbda9d2be78de34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e6f74fdd5c57d4454f8e840563771a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722f025aeed67dbc2c16f60c3b06061d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b41b7154250380217e8dc70ff2a7591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4142405dce1c99e4c58474c00b2bd6e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65021f540ac58a37746758611f2fd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69673c72476d11a283eb5e4d1f7a72.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26aa2c8a73ca9a054ed46e16eb5811e5.png)
您最近一年使用:0次
3 . 已知函数
.
(1)若
,求
的取值范围;
(2)若
有两个不相等的实根
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfe72da09a3c70855e5481e5c8eaf80.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a1b101171cf52faf2e3e53d6725aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd25b0aac17082018e89b67803cd6a1.png)
您最近一年使用:0次
4 . 已知函数
,
.
(1)求曲线
在点
处的切线方程.
(2)已知关于
的方程
恰有4个不同的实数根
,其中
,
.
(i)求
的取值范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6233814cb71490dee2b31b2ed87225a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1146b920e21e9b2bf1bb5df6afe7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574824d85f44d42246529ac135c0391c.png)
您最近一年使用:0次
5 . 已知函数
.
(1)证明:当
时,
在
上单调递增;
(2)若
在
上恰有3个零点,求
的值.
参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a05622ee04b5237b746fc15c12a4ef.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1406fead119e695f9720e78e59b9625c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84ce07dcbbcf8e4b7f246649fb3f835.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e955a8ad4c8aaddd5f189559d2e3d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4c7edb4076b60ca8d4ba5213d077d.png)
您最近一年使用:0次
6 . 已知函数
.
(1)设
,证明:当
时,过原点O有且仅有一条直线与曲线
相切;
(2)若函数
有两个零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce0da73f9c18ef1cb4e9646ff201073.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1d1feee09e10e8eceb8a5ff31ba995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
7 . 定义:给定函数
,若存在实数
、
,当
、
、
有意义时,
总成立,则称函数
具有“
性质”.
(1)判别函数
是否具有“
性质”,若是,写出
、
的值,若不是,说明理由;
(2)求证:函数
(
且
)不具有“
性质”;
(3)设定义域为
的奇函数
具有“
性质”,且当
时,
,若对
,函数
有5个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63d7758a927384c13052ae432c20a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe17821ea81c6fec60bd5273901bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ecb084837b614de935871d8f3dd2e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
(1)判别函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d6e08526a91f8dfd160e7da2f92a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.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/86c16d349946f1a9fbc12b28e7e9321c.png)
(3)设定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae15be500f98d647a07fee39c95d041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ca276a67d4eca39a3c57dfab895e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835eec12ec99561a3655c296570d75be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0db56c33be80c68078d92ba0ca47bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
8 . 已知函数
.
(1)若
恰有两个零点,求a的取值范围;
(2)若
的两个零点分别为
(
),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e498dc0ac7b435ae0b600df63b9e2950.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d60d1ff5429bd35707fd80d714dc93.png)
您最近一年使用:0次
2024-04-01更新
|
658次组卷
|
5卷引用:河南省叶县高级中学2023-2024学年高二下学期3月月考数学试题
9 . 已知函数
,其中
且
.
(1)求
的值,判断
的奇偶性并证明;
(2)函数
有零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1ee79efe2e33eacd7eb80c82263e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4266704cf6a09ed98228ee26d91f402c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b77d8fd3ed34166e990b3d79b03b57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
10 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900fc29aaf77c14c9aafce1e06f3dcb5.png)
(1)已知
在
上存在零点,求实数a的取值范围;
(2)若
在定义域上是单调函数,
满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900fc29aaf77c14c9aafce1e06f3dcb5.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b112913b0d7167763e4e4195ca82f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f78ae07b1452e4f9dd8ba93db61d17.png)
您最近一年使用:0次