名校
1 . 若存在直线与曲线
,
都相切,则a的范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf506d939c339a9ba0e88f6f4291718f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577e691feafc7b4972dabb6295788f8b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-11更新
|
983次组卷
|
4卷引用:浙江省东阳市2024届高三5月模拟考试数学试题
浙江省东阳市2024届高三5月模拟考试数学试题(已下线)模块5 三模重组卷 第2套 全真模拟卷(已下线)第7题 切线相关的双变量问题(压轴小题一题多解)浙江省东阳市外国语学校2023-2024学年高二下学期5月月考数学试题
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2 . 已知实数
,
满足
,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd525151afe4656121649b1a7f33ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6d5e85222ac3950da7d27a5d79fb40.png)
您最近一年使用:0次
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3 . 已知函数
.
(1)当
时,证明:
;
(2)
,
,求
的最小值;
(3)若
在区间
存在零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80843579e01c8d79ac853a91db14472.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0bee9c562d944df00bf5b82caff167.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c7a65f44ac570ab84bf43b7d81ed39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
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4 . 已知函数
.
(1)当
时,试求函数图象在点
处的切线方程;
(2)讨论函数
的单调性;
(3)若函数
有两个极值点
,
(
),且不等式
恒成立,其中
,试求整数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e961176258d58dc3c82df5ec8c6ce3aa.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41589c0fcdbff1b98bde4ed6c2c1a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573394d925f221e828978ba5b528dd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-05-12更新
|
493次组卷
|
5卷引用:专题5 导数与不等式恒成立问题【练】
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5 . 已知
的三个角
的对边分别为
且
,点
在边
上,
是
的角平分线,设
(其中
为正实数).
(1)求实数
的取值范围;
(2)设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736d82fce28c323d02a4183610777845.png)
①当
时,求函数
的极小值;
②设
是
的最大零点,试比较
与1的大小.
![](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/fe29c42302504e7fd8577dbc7d130ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9ecf347b1b8b1edd8f354a0fc1f152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736d82fce28c323d02a4183610777845.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f627a70fa1006b30c2db5b1fcfaae82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2024-04-29更新
|
759次组卷
|
4卷引用:压轴题07三角函数与正余弦定理压轴题9题型汇总-2
(已下线)压轴题07三角函数与正余弦定理压轴题9题型汇总-2浙江省东阳市外国语学校2023-2024学年高二下学期5月月考数学试题湖南省岳阳市2024届高三教学质量监测(三)数学试题(已下线)模块5 三模重组卷 第1套 全真模拟卷
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6 . 已知
.
(1)当
时,求
的单调区间;
(2)若
有两个极值点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59fe47b8d4bb6a91c1313a5e1f18c30.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.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/a71c899383cfca8cde9cc07eba832899.png)
您最近一年使用:0次
2024-04-26更新
|
2010次组卷
|
4卷引用:浙江省湖州中学2023-2024学年高二下学期第二次阶段性测试数学试题
7 . 在平面直角坐标系xOy中,过点
的直线
与抛物线
交于M,N两点
在第一象限).
(1)当
时,求直线
的方程;
(2)若三角形OMN的外接圆与曲线
交于点
(异于点O,M,N),
(i)证明:△MND的重心的纵坐标为定值,并求出此定值;
(ii)求凸四边形OMDN的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9192616790cac39e605075941ae408c5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e28faf289d327e5b67e1da974a7b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若三角形OMN的外接圆与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(i)证明:△MND的重心的纵坐标为定值,并求出此定值;
(ii)求凸四边形OMDN的面积的取值范围.
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2024-04-23更新
|
1625次组卷
|
3卷引用:浙江省五校联盟2024届高三下学期3月联考数学试题
8 . 设抛物线
,直线
是抛物线C的准线,且与x轴交于点B,过点B的直线l与抛物线C交于不同的两点M,N,
是不在直线l上的一点,直线
,
分别与准线交于P,Q两点.
(1)求抛物线C的方程;
(2)证明:
:
(3)记
,
的面积分别为
,
,若
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad445f2f16d42d63980353981bdcf48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
(1)求抛物线C的方程;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fd1dc3d012bef0ec559463298f5347.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61098066865164289ca1348b53420cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8503628bad86f077d1f6a4d801314f04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8060a00d925f27135a7baff2d0e9d598.png)
您最近一年使用:0次
2024-04-19更新
|
705次组卷
|
3卷引用:浙江省金华十校2024届高三4月模拟考试数学试卷
名校
解题方法
9 . 已知
的三个内角分别是A,B,C,则下列结论一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() |
B.![]() |
C.“![]() ![]() |
D.![]() |
您最近一年使用:0次
解题方法
10 . 一般地,设函数
在区间
上连续,用分点
将区间
分成
个小区间,每个小区间长度为
,在每个小区间
上任取一点
,作和式
.如果
无限接近于0(亦即
)时,上述和式
无限趋近于常数
,那么称该常数
为函数
在区间
上的定积分,记为
.当
时,定积分
的几何意义表示由曲线
,两直线
与
轴所围成的曲边梯形的面积.如果
是区间
上的连续函数,并且
,那么
.
(1)求
;
(2)设函数
.
①若
恒成立,求实数
的取值范围;
②数列
满足
,利用定积分几何意义,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2779faf49c4c603fdb73ef6f03cc8d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d62698894cd2008bc718645dc5615e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058b6a24dd8207a5bb15af23b536fbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80ab9d17c90844401100376fa2713d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2edc4a53872c30616bca5f3f7ee67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1268e217016ff7e12b9bc51341c4cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8930c962e3b094e1ee2a99c8cc44cead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4eab9145ec5e13b0ae21c135a5b625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436ff3cf58de28b55f7605675a47d818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d4d758bac9a7272c1d40a5ea4176c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d5365888545b29d3850a5eca1b0e54.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb480d935f37cfe76dcb6dcb25a5fb3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f0216d4ec1601bfbc0c642a78491c02.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a48eebe55c30519af8dbc50512a3f41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49afef24cbe3b97b62488510ef5168b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c9d14bfa527b5ba538cc3960e9396f.png)
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