1 . 已知函数
.
(1)若
,求
的极值;
(2)若
,设
.证明:
(ⅰ)
;
(ⅱ)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc8c9e209e8fe62fb423a6a0ece34b1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60140b6729628a77ef0a598368e64a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1c15263cbb460891a4af6a9c693060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d1cab7eb5904004b9f28812ca017cf.png)
(ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ad78c48f2947f2b9ae5c7a47bb9440.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51dfc1080ad5a0551f5778ee214c255.png)
您最近一年使用:0次
2024-02-27更新
|
566次组卷
|
3卷引用:山西省部分学校2024届高三下学期一模考试数学试卷
解题方法
2 . 已知椭圆
的左、右焦点分别为
,设点
,在
中,
.
(1)求椭圆C的方程;
(2)设P,Q为C上异于点A的两动点,记直线AP,AQ的斜率分别为
,若
,求证:直线PQ过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e756feec2851b90497421790a7206e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfdab8b0494d22a788fd0a34258abd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fedcf44928a090ad5553edf8a0fd7c.png)
(1)求椭圆C的方程;
(2)设P,Q为C上异于点A的两动点,记直线AP,AQ的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe91cc3bfc93ef1cc3369fa6756bbd4d.png)
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3 . 如图,在三棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/c7e4b942-6b27-4786-a3aa-48b116e85f84.png?resizew=157)
(1)求证:
平面
;
(2)若
,直线AB与平面
所成的角为
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4759c765972e2e039b295a0d0d4fc840.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/c7e4b942-6b27-4786-a3aa-48b116e85f84.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e00a3609e6043af1034761d4d65f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ab602944bedd4fe63d0575178dfdb8.png)
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解题方法
4 . 已知函数
.
(1)判断
的单调性并用定义证明;
(2)求函数
在区间
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389b65da5b415c8be58200d10d13b346.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b9cc5f4baa3b123ee52bdb24f693b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c33b69adc112831fa115b5dffdb616.png)
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)判断
的奇偶性,并说明理由;
(2)判断
在
上的单调性,并证明你的判断;
(3)对任意
,若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd30a699d6b27bbacfa7c9f76697f7a7.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(3)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b745df046d5d409e228cef4766f4c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
6 . 已知椭圆的焦点是椭圆
的顶点,椭圆
的焦点也是
的顶点.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654317ca05d25fee978869723ba8d0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c5db73d81da5525d4d35885dac04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
您最近一年使用:0次
名校
7 . 已知函数.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/0a415767156945ea8ada9ed3756019fc.png)
您最近一年使用:0次
2024-02-14更新
|
1392次组卷
|
5卷引用:山西省晋城市2024届高三一模数学试题
山西省晋城市2024届高三一模数学试题(已下线)重难点2-4 利用导数研究不等式与极值点偏移(8题型+满分技巧+限时检测)陕西省西安市第一中学2024届高三下学期模拟考试文科数学试题(已下线)微专题08 极值点偏移问题(已下线)第9题 导数压轴大题归类(1)(高三二轮每日一题)
8 . 如图,
是边长为2的正六边形
所在平面外一点,
的中点
为
在平面
内的射影,
.
(1)证明:
平面
.
(2)若
,二面角
的大小为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d95a69ba2e982939e3ba0c77df99a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/874c9ce3-22a2-432c-86cf-b40650b25127.png?resizew=161)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6dfed58659a9cab4d1836c3d2effdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5651e38293e0c42a7278af69fa53ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5ff5a2e7663e6a21ccea3149a10113.png)
您最近一年使用:0次
9 . 已知数列
的首项
,且满足
,等比数列
的首项
,且满足
.
(1)求证:数列
是等比数列,并求数列
的通项公式;
(2)求数列
的前
项和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f639aa2fde8c717aa78e22e13daab1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de771c3bd401cb2f90d24e1c58267e4.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d363b6982fee3bf1337d1542137a2f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
.
(1)证明:函数
是奇函数;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2802c53543e37ee05126bb01c09895f7.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e136393c53d7926c26083ba8c9c3c6.png)
您最近一年使用:0次