名校
1 . 已知函数
,
,其中
.
(1)若
,求实数a的值
(2)当
时,求函数
的单调区间;
(3)若存在
使得不等式
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cd20be84d4a5c153adc0dcaeffcf84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f09d8c5f6875b04965d79e787dca3ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67bad806be39af278f3cb7f77da2645a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d101c4394ba31350bfdadf5b25c4e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
您最近一年使用:0次
7日内更新
|
239次组卷
|
2卷引用:天津市蓟州区第一中学2023-2024学年高二下学期第二次月检测(6月)数学试题
名校
解题方法
2 . 已知函数
,其中
为实数.
(1)当
时,
①求函数
的图象在
(
为自然对数的底数)处的切线方程;
②若对任意的
,均有
,则称
为
在区间
上的下界函数,
为
在区间
上的上界函数.若
,且
为
在
上的下界函数,求实数
的取值范围.
(2)当
时,若
,
,且
,设
,
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4d96931977f6f5462acb196bcd417e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea4d74f476f741b75a448ee01c0e86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f121036d30c000b01b7be98d9c8a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f121036d30c000b01b7be98d9c8a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e75907a1b513cdf63614b4b68ece89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb0aa7bf71da74a9b3d4a022812290a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f861459b5e5a3ce298f205d9677e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd34bc2979bfed0fa99269635dde578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9499b9c4b5292d3f28799d1e96653ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253fe46f6392ea2a63475453fbe5b16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cce18618decec25cc47f40f2f7478f.png)
您最近一年使用:0次
7日内更新
|
81次组卷
|
2卷引用:天津市蓟州区第一中学2023-2024学年高二下学期第二次月检测(6月)数学试题
3 . 从包含甲、乙2人的7人中选4人参加4×100米接力赛,求在下列条件下,各有多少种不同的排法?(结果用数字作答,否则无分)
(1)甲、乙2人都被选中且必须跑中间两棒;
(2)甲、乙2人只有1人被选中且不能跑中间两棒;
(3)甲、乙2人都被选中且必须跑相邻两棒;
(4)甲、乙2人都被选中且不能相邻两棒;
(5)甲、乙2人都被选中且甲不能跑第一棒,乙不能跑第四棒.
(1)甲、乙2人都被选中且必须跑中间两棒;
(2)甲、乙2人只有1人被选中且不能跑中间两棒;
(3)甲、乙2人都被选中且必须跑相邻两棒;
(4)甲、乙2人都被选中且不能相邻两棒;
(5)甲、乙2人都被选中且甲不能跑第一棒,乙不能跑第四棒.
您最近一年使用:0次
名校
4 . 已知函数
.
(1)求曲线
在
处的切线方程;
(2)若
,讨论函数
的单调性.
(3)记函数
,设
是函数
的两个极值点,若
,且
恒成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b276d8b7113c704d6a063a45a27dc334.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13e17d17a186d57f60bcb5d88f892c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(3)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a5ac79c78d796958e609ff87f5af60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52be8ca37591d8606e8796d2dadbc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5197924c11272156c4635ee3e8242c6.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
,
.
(1)求函数
的极值;
(2)令
是函数
图像上任意两点,且满足
,求实数a的取值范围;
(3)若
,使
成立,求实数a的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c0b471c9a4ff941c65b0dc3b7605b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70cf3adcbbb5705690e7f27305c76c76.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b229881b13d72d0fe3be1ed2593ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87c2e6a41fbe97b9f28f5b77bd94787.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e1f61457b8457b8c6e27014adf0d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2f64c0b155bc323c22a190f871395d.png)
您最近一年使用:0次
2024-04-02更新
|
311次组卷
|
2卷引用:天津市蓟州区第一中学2023-2024学年高二下学期第一次月考检测数学试题
名校
6 . 在如图所示的多面体中,四边形
为正方形,平面
平面
,且
和
均为等腰直角三角形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/99a30976-2144-46f9-a92c-2cae6956aabf.png?resizew=145)
(1)求证:直线
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)若点
在线段
上,若直线
与平面
所成角为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ec3f44cd7f4689920e5df628177737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aaab1426cea05dd8fdfa4aed6e5c3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/99a30976-2144-46f9-a92c-2cae6956aabf.png?resizew=145)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603c7e98deecdba0cf3773757a9b8304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9efe66d99f813c6b1387392186822bb.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.
(1)判断函数
的奇偶性;
(2)若
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc25f25645503e2792a3a2662738da8.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b222dc2a68d433409cae95997a7f0c4d.png)
您最近一年使用:0次
2023-12-26更新
|
1056次组卷
|
4卷引用:天津市蓟州区下营中学2023-2024学年高一上学期12月月考数学试题
名校
解题方法
8 . 在
中,内角
的对边分别为
且满足
.
(1)求角
;
(2)若
,
,求
的面积;
(3)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389189cdee5472d4e3432403f6c54a96.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783d6adfa8fb1352679c5185258d842a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e876b53581904085bbc4e00fad0c718f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f4f8020bef636dcb3b8dc5fa2bdbb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc90eb7e72622d0665504a09286fa26.png)
您最近一年使用:0次
名校
9 . (1)在数列
中,
,
,且满足
,求数列
的通项公式;
(2)在数列
中,
,
,求数列
的通项公式;
(3)若数列
是正项数列,且
,求数列
的通项公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdf53108bee755f5aa9a34ea4d163e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d77060931748cee8c21b43d15033b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dfb585f199d747ebe4dc2dd8511716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4745b37f852bf8a03cb9b78573d76691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab4a34614de1ff243fed859c11c5d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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10 . (1)
;
(2)
;
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85b1735db422a7d27e886d4c207291.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d24c9e39cce3a08fccf0c10fb072cce0.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be7839e890978ced725ca682e6b6770.png)
您最近一年使用:0次