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1 . 已知函数
.
(1)求函数
的单调区间;
(2)若
恒成立,求实数
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff7978e698b20c3b12f2e9d3a00c47b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7日内更新
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4卷引用:湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题
湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题安徽省马鞍山市第二中学2023-2024学年高二下学期5月月考数学试题(已下线)第12题 分类讨论法讨论函数的单调性(高二期末每日一题)2024届海南省省直辖县级行政单位琼海市高考模拟预测数学试题
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2 . 已知函数
存在两个极值点
,且
,
.设
的零点个数为
,方程
的实根个数为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019f7f6d8d1bb1b6c365e0cef811f826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc45d00dcc9c1616c14ffb9f739b93ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a5c89d253e763127cc2a9acdd3ebe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.当![]() ![]() | B.当![]() ![]() |
C.![]() | D.![]() |
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解题方法
3 . 数列
,若存在常数
,对任意的
,恒有
,则称数列
为
数列.记
是数列
的前
项和,下列说法错误 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04317d201a1ea6cd583b203b698ef237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68285e96f06a7b2dad33b5ec4a74cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.首项为1,公比为![]() ![]() |
B.存在等差数列![]() ![]() ![]() ![]() |
C.若数列![]() ![]() ![]() ![]() |
D.若数列![]() ![]() ![]() ![]() |
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4 . 已知函数
的导函数为
,若
,设
,
,
.则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01ca8462b0612de856261e4a5d0fbde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a06ce780f4ec6af4d769a09cba08de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6bba85e4c2426061b5c8f53c09b9e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 如图,已知椭圆
(
)的左,右顶点分别为
,
,椭圆的长轴长为4,椭圆上的点到焦点的最大距离为
,
为坐标原点.
的方程;
(2)设过点
的直线
,
与椭圆分别交于点
,
,其中
,
①证明:直线
过定点,并求出定点坐标;
②求
面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e511d8ecf566c5c0730bbe6be0d6347c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.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/58b140e221ddf537b8964fff8557cca0.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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解题方法
6 . 已知抛物线
与椭圆
有公共的焦点.
的标准方程.
(2)如图,过抛物线
的焦点
的直线与抛物线
交于点
,点
,直线AP,BP分别与抛物线
交于点
.证明:
①直线CD过定点;
②
与
的面积之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50996be3c0d950d6ef58110948b7fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82766cfd2b7c59c7fac5b827ae5863b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)如图,过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de77ee0b176035fd3a89edc2ad957a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
①直线CD过定点;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
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7 . 已知函数
(a为常数),则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b89efe08483ed26164fc429b0628459.png)
A.当![]() ![]() |
B.若![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
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8 . 已知函数
,
.
(1)记
,讨论
的单调性;
(2)当
时,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d986f7e47d288006e99ee7dcfe04e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4457c1e88f428c2e98770959f7a2e.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08bcd21775884fe4148b1a249acb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327e81d90543aa594968112a73bfa2ad.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
您最近一年使用:0次
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9 . 函数
是定义在
上的可导函数,其导函数为
,且满足
,若不等式
在
上恒成立,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4c62b70f3e14fe83f770603a6123a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c1134a4f0abdd373bdd7b2268e6a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-04-30更新
|
666次组卷
|
3卷引用:湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题
湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题四川省仁寿第一中学校(北校区)2023-2024学年高二下学期5月期中质量检测数学试题(已下线)模块2专题5 函数同构 化繁为简练
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10 . 帕德近似是法国数学家亨利·帕德发明的用有理多项式近似特定函数的方法.给定两个正整数
,
,函数
在
处的
阶帕德近似定义为:
,且满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46eaf1cdc0ea6f6b18e8fba22ee7ae2.png)
.(注:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51793a343298909a499b0b150660ccb.png)
为
的导数)已知
在
处的
阶帕德近似为
.
(1)求实数
的值;
(2)证明:当
时,
;
(3)设
为实数,讨论方程
的解的个数.
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16563cfb206d0394cac2a0c2595dda6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46eaf1cdc0ea6f6b18e8fba22ee7ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4baac3118da93995e49b29a5d377e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca214aa6276b96d67a451c3fdbc59b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51793a343298909a499b0b150660ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385c9d5f9d6c2c720dd99273021cafd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea7fa65b493fc1bdf84e16d39ae07d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8de781718020ed3f99538b8e25d6186.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccba081685984454ee4fa955dc4f7ea.png)
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