名校
1 . 已知
,
是
的导函数,其中
.
(1)讨论函数
的单调性;
(2)设
,
与x轴负半轴的交点为点P,
在点P处的切线方程为
.
①求证:对于任意的实数x,都有
;
②若关于x的方程
有两个实数根
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fe84ecdcafb66c2e3a4dd702503729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5662583ace896ce1f779eaba4911f156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
①求证:对于任意的实数x,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5207aa3a627a574a1e12ae87dd609fdb.png)
②若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1083654e970df6adf6e1c5967501e80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee624bd3ec8c33ac93551432b739af17.png)
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2 . 如图,直线AB经过⊙O上的点C,并且OA=OB,CA=CB,⊙O交直线OB于E,D,连接EC,CD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/b1d868e9-96c8-424a-a0fe-cff93a4fecf9.png?resizew=189)
(1)求证:直线AB是⊙O的切线;
(2)试猜想BC,BD,BE三者之间的等量关系,并加以证明;
(3)若
,⊙O的半径为3,求OA的长.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/b1d868e9-96c8-424a-a0fe-cff93a4fecf9.png?resizew=189)
(1)求证:直线AB是⊙O的切线;
(2)试猜想BC,BD,BE三者之间的等量关系,并加以证明;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219a483b5834a9d8d6bd00fd0458ab01.png)
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名校
解题方法
3 . 如图所示,在直三棱柱ABC-A1B1C1中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/3/9/2932407529332736/2946023371005952/STEM/50a6e23377b94677b1e2de384ab39108.png?resizew=206)
(1)当P为B1C的中点时,求证:A1B1
平面APC1;
(2)试在线段B1C上找一点P(异于B1,C点),使得
,并证明你的结论;
(3)当
时,求多面体A1B1C1PA的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df09d04a0c1a9c47aa547811469a6e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
![](https://img.xkw.com/dksih/QBM/2022/3/9/2932407529332736/2946023371005952/STEM/50a6e23377b94677b1e2de384ab39108.png?resizew=206)
(1)当P为B1C的中点时,求证:A1B1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)试在线段B1C上找一点P(异于B1,C点),使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34b7435f674beb041681fd5615a5b88.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34b7435f674beb041681fd5615a5b88.png)
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2022-03-28更新
|
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2卷引用:四川省南充高级中学2021-2022学年高二上学期入学考试数学(文)试题
名校
解题方法
4 . 把抛物线
沿
轴向下平移得到抛物线
.
(1)当
时,过抛物线
上一点
作切线,交抛物线
于
,
两点,求证:
;
(2)抛物线
上任意一点
向抛物线
作两条切线,从左至右切点分别为
,
.直线
交
从左至右分别为
,
两点.试判断
与
的大小关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ebe959b8ff2bbabce1f0f09a36e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fe004046f183e83376ce219c9d1bb0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194b8ab194c7d299d5c3e0f09ec18384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2007972af3341f27fbc32ce62dfce5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f30acc34f4ee1077532ae6808af2ab2.png)
(2)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cc25bc9e9c48fd18a60b95b64bb499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920ff4e858ac0ed5e5706bb77bfd5c9e.png)
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名校
解题方法
5 . 在如图所示的几何体中,面CDEF为正方形,面ABCD为等腰梯形,AB∥CD,AC=
,AB=2BC=2,AC⊥FB.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/bc07359a-5c0d-43e1-869b-7f39a58b23ea.png?resizew=162)
(1)求证:AC⊥平面FBC;
(2)线段AC上是否存在点M,使EA∥平面FDM?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/bc07359a-5c0d-43e1-869b-7f39a58b23ea.png?resizew=162)
(1)求证:AC⊥平面FBC;
(2)线段AC上是否存在点M,使EA∥平面FDM?证明你的结论.
您最近一年使用:0次
6 . 设
为数列
的前
项和,已知
,
.
(1)求出
,
的值,并证明:数列
为等比数列;
(2)设
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077fe52ca6a0cb41d46f4dbc965af1e5.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83cf578e283612cb8782f67cb5ee11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da72309d2507e2f5e5ed88d8cc08963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5319070a0e6ea62c4216c48d010dce3f.png)
您最近一年使用:0次
7 . 已知在图1所示的梯形
中,
,
于点
,且
.将梯形
沿
对折,使平面
平面
,如图2所示,连接
,取
的中点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/e10d6ad6-6f09-40f9-9c0f-bb3b83868ef8.png?resizew=366)
(1)求证:平面
平面
;
(2)在线段
上是否存在点
,使得直线
平面
?若存在,试确定点
的位置,并给予证明;若不存在,请说明理由;
(3)设
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66418ef39d3081d89411a4907d8599f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24d05b5b9502c2be337f9be84fe4ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ceae9396dc0551b68ac65b5c4648278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306b9504b52df5ad6697fa87200e8a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/e10d6ad6-6f09-40f9-9c0f-bb3b83868ef8.png?resizew=366)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f39524e24db3f7c9e2f49f35b5e660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf910aabe023d18b62268579b6033b18.png)
您最近一年使用:0次
2019-03-06更新
|
535次组卷
|
2卷引用:四川省双流中学2019-2020学年高二上学期入学考试数学(文)试题
名校
解题方法
8 . 已知函数
.
(1)当
时,直接写出
的单调区间(不要求证明),并求出
的值域;
(2)设函数
,若对任意
,总有
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b2d3738f56987d159a343dc160f384.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdabdbbbde9b3ee68df66171b0145785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d5a5e70f64f0933ae1e4ddec5fa2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61761abb364ece2281af24d9b1f008de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2024-03-07更新
|
518次组卷
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11卷引用:四川省德阳市德阳中学校2023-2024学年高一下学期入学考试数学试卷
四川省德阳市德阳中学校2023-2024学年高一下学期入学考试数学试卷安徽省淮南市寿县第一中学2020-2021学年高一下学期入学考试数学试题安徽省淮北市树人高级中学2020-2021学年高一下学期开学考试数学试题安徽省合肥市一中、六中、八中三校2020-2021学年高一上学期期末数学试题安徽省合肥一中、六中、八中2020-2021学年高一上学期期末联考数学试题(已下线)大题好拿分期中考前必做30题(压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)(已下线)第7章 三角函数 单元测试(单元综合检测)(难点)(单元培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)7.3 三角函数的图像和性质(难点)(课堂培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)山东省淄博市美达菲双语高级中学2022-2023学年高一下学期3月月考数学试题湖南省株洲市第二中学2022届高三下学期期中数学试题(已下线)专题17 三角值域问题
9 . 设点
是椭圆
上任意一点,过点
作椭圆的切线,与椭圆
交于
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
;
(2)
的面积是否为定值?若是,求出这个定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e91e565e14d96a20169db44fcde58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b0bec6e780130fbed900fdb153555d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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2024-02-05更新
|
1468次组卷
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6卷引用:四川省成都市第七中学2024届高三下学期入学考试数学(文)试题
10 . 已知函数
.
(1)讨论
的单调性;
(2)设
,求证:当
时,
恰有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae648c38a4f55310db639082bfcca39.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b456391f0ee447887b2091344205f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
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2024-01-24更新
|
873次组卷
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4卷引用:四川省绵阳市南山中学2024届高三下学期入学考试数学(理)试题
四川省绵阳市南山中学2024届高三下学期入学考试数学(理)试题湖南省邵阳市2024届高三第一次联考数学试题(已下线)5.3.1函数的单调性 第二练 强化考点训练(已下线)重难点2-5 利用导数研究零点与隐零点(7题型+满分技巧+限时检测)