名校
解题方法
1 . 已知函数
,下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0174c661f9122201cd489d4e3dd702.png)
A.![]() |
B.![]() |
C.若![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() |
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2024-06-15更新
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240次组卷
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2卷引用:广东省东莞高级中学、东莞第六高级中学2023-2024学年高二下学期5月联合教学质量检测数学试卷
名校
2 . 已知函数
.
(1)当
时,求
的最大值;
(2)讨论函数
在区间
上零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d7abebebf906a845461e157c5c9a0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf613d5ed2a4b75ee70638f28fd9f44f.png)
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解题方法
3 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)设
是
的两个极值点,
是
的一个零点,且
.是否存在实数
,使得
按某种顺序排列后构成等差数列?若存在,求
;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763bf20d6c376dbf15f344294ea2cdea.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0d7fbcc396c7b646c31f60e32d9e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b202920f8532a7a3e9f1d7775a9361e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
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4 . 将函数
的图象向右平移
个单位长度,得到函数
的图象,则函数
的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4201223cfcf158b600f5c72407e32b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2660bdb91f09c1a2a719bb54539f59f1.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2024-06-15更新
|
123次组卷
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2卷引用:湖南省娄底市第三中学2023-2024学年高二下学期5月月考数学试题
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5 . 帕德近似是利用分式有理函数逼近任意函数的一种方法,定义分式函数
为
的
阶帕德逼近,其分子是m次多项式,分母是n次多项式,且满足
,
,
,…,
时,
为
在
处的帕德逼近.
(1)求函数
在
处的
阶帕德逼近
;
(2)已知函数
.
①讨论
的单调性;
②若
有3个不同零点
,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbfee67d1c1cb26b67ef0fe3169e6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd909ba3e40f03e2f58a4eed2e05f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcb8c6a69df1a0deaba265e204d5f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a8c1ed551fccee1c1848746c5f282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72029562177dfc99a171c9013eb90227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4573475f70860a3d99b92a329d0d07f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b1868d9850b7103e1326eb001dfbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58de4362237a2a719cde7c9049903da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adc63ce466d20e93f7d09d8b0bf9076.png)
①讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.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/d79fc0ce080b8ad8b63ba63259c680b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e03829b4bbd1148c7f479ca409d436.png)
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6 . 定义 如果函数
和
的图像上分别存在点
和
关于
轴对称,则称函数
和
具有
关系.
(1)若
,试判断函数
和
是否具有
关系;
(2)若函数
和
不具有
关系,求实数
的取值范围;
(3)若函数
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04f47dc0f7298b89b4d9f6195686f85.png)
在区间
上具有
关系,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166703f700475d6bcd4b8ee7c71f2c7f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7c95672da462203194363bb292dbcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166703f700475d6bcd4b8ee7c71f2c7f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b524386c37301f3cfad5f28ef7883ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c95bc37ed65d74fba895bf21c4db925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166703f700475d6bcd4b8ee7c71f2c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545ac68beedab0a5490f97c88437a317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04f47dc0f7298b89b4d9f6195686f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e5b56723fc6f8297356195e084fd9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23efa380a58dc9663ba06dc249ce721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166703f700475d6bcd4b8ee7c71f2c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . 已知函数
,其中
为常数且
,
(1)当
时,求曲线
在点
处的切线方程,
(2)若函数
在区间
上有且只有一个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba34726226022b3356d5a7a2323b67a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd69684b91e09f501685cb6672c19ea.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a8b597825ec5cc308ca3450676c1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94a8d21fec01cd2f2cf3b1f62eb6515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 已知函数
.
(1)求函数
的单调区间;
(2)若
,满足
.
(ⅰ)求
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712744afe565a9fa6d29d3dd12cedf3f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e71b7cc594da8081cc8599f6e2c529.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b2a373bc2e3fc7fadfc551f06c3f4b.png)
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9 . 已知函数
,
是函数
的一个极值点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9c1fce9fa39cabf241d72fee10dd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
A.![]() | B.函数![]() ![]() |
C.过点![]() ![]() | D.函数![]() |
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10 . 若函数
在区间
内有两个零点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32273aa2c863a64e2944cb6467054b7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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