1 . 已知函数
且
.
(1)求实数a的值;
(2)若函数
在
上恰有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd535030ec92efe0b1a86a33b7306aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008925a3b60d366297f31efa54aa38c9.png)
(1)求实数a的值;
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5b9f57d3634f8337f1414f8a2a2dc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
2 . 已知函数
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/3d1bd810-67ab-46d9-93e0-a0afa9a3e87b.png?resizew=210)
(1)判断函数
的奇偶性并用定义证明;
(2)用分段函数的形式表示函数
的解析式,并直接在本题给出的坐标系中画出函数
的图像;
(3)用
表示
,
中的较大者,即
,若
,则求
的值 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578b5d562457a6ba731ee5a2dd3b1fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63716f1f42c412f23bfb2f3651638c4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/3d1bd810-67ab-46d9-93e0-a0afa9a3e87b.png?resizew=210)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)用分段函数的形式表示函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c694cf892ee07daa54bdd9f2fb421e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b345ba4baeae1041f7d69ad09dc326c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe57503d720d07a26770942b067d2cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcf4b0cf6235605919cbef4d0b41a1c.png)
(1)若
,求
的值;
(2)若函数
有5个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcf4b0cf6235605919cbef4d0b41a1c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0c63f83d083501b752fc13fb0b4786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
4 . 已知函数
.
(1)当
时,
①求
的值;
②求
的图象与直线
的交点坐标;
(2)若
的值域为R,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136b8fa6ada0d37fc1d4a4fe5658402a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e244d20e919c19caa85d1a83bcf237.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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名校
5 . 已知函数
.
(1)求
和
;
(2)若
,求
的值;
(3)作出函数
的图象;并根据图象写出单调区间;
(4)当方程
有3个解时,直接写出实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2e92fcc7b2d36880047071a0f95e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14348dcf52b54174c7f3cecc63d69e3e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(4)当方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
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名校
解题方法
6 . 道路密度是指该路段上一定时间内通过的车辆数除以时间,车辆密度是该路段一定时间内通过的车辆数除以该路段的长度,现定义交通流量为
,
为道路密度,
为车辆密度,
.已知当道路密度
时,交通流量
,其中
.
(1)求
的值;
(2)若交通流量
,求道路密度
的取值范围;
(3)求车辆密度
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e829a484e6b203719c636c23614851a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2fc8e882b4e76905b05c574322f08c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ae43849c6c6f222cd292d177f7a742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若交通流量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b30e4b464e3ef645fa1780523c56b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)求车辆密度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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名校
解题方法
7 . 黎曼函数是一个特殊的函数,是德国著名数学家波恩哈德·黎曼发现并提出,在数学中有广泛的应用.黎曼函数定义在
上,
.
(1)请用描述法写出满足方程
的解集;(直接写出答案即可)
(2)解不等式
;
(3)探究是否存在非零实数
,使得
为偶函数?若存在,求k,b应满足的条件;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b8e2adb558703f59612bc01f2fb6b5.png)
(1)请用描述法写出满足方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136acbcd8cebcc7153a67f329630b6af.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fead3304932a65d71f88d5002bea5b2b.png)
(3)探究是否存在非零实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceee0ff5c929d67de3c294e027c9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957bd952797bcd94260595386ca07732.png)
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解题方法
8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594e601aae98c805ab55f58e607f31db.png)
(1)若
,则求满足条件的x的值:
(2)解关于x的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594e601aae98c805ab55f58e607f31db.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
(2)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2e0bb6d63b7bcaee92a470d58cc399.png)
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2023-11-28更新
|
120次组卷
|
2卷引用:天津市嘉诚中学2023-2024学年高一上学期期中质量调查数学试卷
名校
解题方法
9 . 设函数
,其中
.
(1)当
时,若
,求
的值;
(2)若
,求函数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726b515b8bf26045b246105f307d64bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d880ccdc807a7e27f1d42c8e2eae1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bb00228e4e58363598fe3dd6efa945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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解题方法
10 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4754564d7b0bb6c49188f363925603.png)
(1)若
求
的值.
(2)若
求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4754564d7b0bb6c49188f363925603.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eabd693631eaffab931d900baa86d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36bac3259a2ea9b563c0d74fc233dabc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次