1 . 如图,已知
是以
为直径的⊙
的一条弦,点
是劣弧
上的一点,过点
作
于
,交
于
,延长线交⊙
于
.
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/a3fbf5dc7aa643f39b48e42a3ccea121.png)
(1)求证:
;
(2)延长
到
,使
,求证:
.
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/fdbee1d6df754523867f44cef568937b.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/794c3363d3e74569b80928f7b7feb58a.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/f83df4fd5f7e496dbd5e71bcdb97d417.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/58db07388afa435d8457bdd816a95dc0.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/fdbee1d6df754523867f44cef568937b.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/58db07388afa435d8457bdd816a95dc0.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/10c515d6b06d4bd0a1fa404cb86ca54c.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/5ed3b3d07cb8422bb1f04090563e3e2e.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/fdbee1d6df754523867f44cef568937b.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/cb8516c16b3f4df89bb988675011deb2.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/f83df4fd5f7e496dbd5e71bcdb97d417.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/c91f6678b3d345289a8ec8d286fd080f.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/a3fbf5dc7aa643f39b48e42a3ccea121.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/4a19ed051191467d97fc60e988943fd5.png)
(2)延长
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/1167344f5c674f23b981778434602cda.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/cd6c932ac14c49699efecc2f1dad603b.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/30c65132883c4e7b8c3216b93b6cb46e.png)
![](https://img.xkw.com/dksih/QBM/2016/9/21/1573035251851264/1573035258470400/STEM/7dc14de2297d43afbea1deceec64e688.png)
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2 . 如图,
是
的直径,弦![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
的延长线相交于点
为
延长线上一点,且
.
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970160136192/1572970166108160/STEM/a71a1b7300a6422ca928673388a58e93.png)
求证:(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970160136192/1572970166108160/STEM/884d7a9d4b2e4897a73103c63da30f64.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970160136192/1572970166108160/STEM/7b3f08daf9384c81b34baf3eb4eca06e.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970160136192/1572970166108160/STEM/370cf3f985a94dfda76ec6e62cc8f8c4.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970160136192/1572970166108160/STEM/a71a1b7300a6422ca928673388a58e93.png)
求证:(1)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970160136192/1572970166108160/STEM/83ed13e1da4b4059b842877acd98a419.png)
(2)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970160136192/1572970166108160/STEM/4ea852c2c3f448f8a839406b38ce984a.png)
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解题方法
3 . 已知数列
中,
.
1.求证:数列
是等比数列,并求
通项公式;
2.设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55efd7c7c534b56c81083a4c19bca82e.png)
1.求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cce1c53146283e962f6ea72aa6b2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
2.设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d218afe8e7141030e5cb050c1362f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e74e5e9a25ef441fa951c314fd8171.png)
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2016-12-04更新
|
734次组卷
|
2卷引用:2016届重庆市巴蜀中学高三3月月考理科数学试卷2
4 . 如图所示,在
中,
是
的平分线,
的外接圆交
于点
,且
.
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/c5d590e3f5a24a71adf7bb847afe9cec.png)
(1)求证:
;
(2)当
,
时,求
的长.
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/39c255be5e4f46b0b7b2d4e0d34c4efb.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/687c2da721e345cb84e9532026dd79ab.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/e0d2d2a870f24698b9048f6c1309cc63.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/7e7b24bad23c4550adffc1ea740849c7.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/977b99bd54134d959883ac56dc4eba71.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/c30852b246da4c5b81b21968a3f853ca.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/33e83275c1a34fc4bcdc096014746d7e.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/c5d590e3f5a24a71adf7bb847afe9cec.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/96ff3b6e3da640e5acf48e08c7647f73.png)
(2)当
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/6c2eeb3452ba4857a46e12d7f4777a21.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/c8468cebe4a4422bac097f69ce7807bf.png)
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572594044583936/1572594050949120/STEM/c92ae7e535df4653a7c7bbc618843eea.png)
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5 . 已知数列{an}满足a1=1,an+1=2an+n﹣1
(Ⅰ)求证:数列{an+n}是等比数列;
(Ⅱ)求数列{an}的通项和前n项和Sn.
(Ⅰ)求证:数列{an+n}是等比数列;
(Ⅱ)求数列{an}的通项和前n项和Sn.
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6 . 已知抛物线C:x2=2py(p>0)的焦点为F,抛物线上一点A的横坐标为x1(x1>0),过点A作抛物线C的切线l1交x轴于点D,交y轴于点Q,当|FD|=2时,∠AFD=60°.
(1)求证:FD垂直平分AQ,并求出抛物线C的方程;
(2)若B位于y轴左侧的抛物线C上,过点B作抛物线C的切线l2交直线l1于点P,AB交y轴于点(0,m),若∠APB为锐角,求m的取值范围.
(1)求证:FD垂直平分AQ,并求出抛物线C的方程;
(2)若B位于y轴左侧的抛物线C上,过点B作抛物线C的切线l2交直线l1于点P,AB交y轴于点(0,m),若∠APB为锐角,求m的取值范围.
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2016-12-04更新
|
533次组卷
|
2卷引用:2015-2016学年重庆市巴蜀中学高二上学期期中考试理科数学试卷
7 . 已知正方体ABCD﹣A1B1C1D1,P是AD1中点,Q是BD中点,E是DD1中点.
![](https://img.xkw.com/dksih/QBM/2016/2/16/1572481269506048/1572481275707392/STEM/1fb65343541d41a28345f36b736d8865.png)
(1)求证:PQ∥平面D1DCC1;
(2)求异面直线CE和DP所成角的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/2/16/1572481269506048/1572481275707392/STEM/1fb65343541d41a28345f36b736d8865.png)
(1)求证:PQ∥平面D1DCC1;
(2)求异面直线CE和DP所成角的余弦值.
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8 . 已知函数
,其中
.
(Ⅰ)讨论
的单调性;
(Ⅱ)设曲线
与
轴正半轴的交点为P,曲线在点P处的切线方程为
,求证:对于任意的正实数
,都有
;
(Ⅲ)若关于
的方程
有两个正实根
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9df5d10a6f1f8d08333d5ba359317e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9678d9630c4df952ce3be68db0a2ac.png)
(Ⅰ)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2dbdf443e1f562404128d004df83992.png)
(Ⅲ)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b42ef7280c8b898aac50cb64aba24f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeeb4e1a1eeeea683c3a780164ba09fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21377ae7c880facfeadae2d9f53007e.png)
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2016-12-03更新
|
6608次组卷
|
14卷引用:2015-2016学年重庆市一中高二4月月考理科数学试卷
2015-2016学年重庆市一中高二4月月考理科数学试卷2015-2016学年河北武邑中学高二下4.24周考理数学卷2015年全国普通高等学校招生统一考试理科数学(天津卷)2020届湖北省武汉中学高三下学期第二次教学质量检测理科数学试题河北省衡水中学2022届高三上学期五调数学试题(已下线)第12讲 双变量不等式:剪刀模型-突破2022年新高考数学导数压轴解答题精选精练(已下线)第29讲 割线法证明零点差大于某值,切线法证明零点差小于某值-突破2022年新高考数学导数压轴解答题精选精练(已下线)第13讲 双变量问题-2022年新高考数学二轮专题突破精练(已下线)专题3-7 导数压轴大题归类:不等式证明归类(2)-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)(已下线)第02讲 一元函数的导数及其应用(二)(练)广东省深圳市福田区红岭中学2023届高三上学期第二次统一考数学试题湖南省张家界市慈利县第一中学2022-2023学年高三上学期第四次月考数学试题(已下线)专题22 导数解答题(理科)-2专题13导数及其应用(第二部分)
9 . 已知椭圆
与
轴交于
两点,
为椭圆
的左焦点,且
是边长为2等边三角形.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于
两点,点
关于
轴的对称点为
(
与
不重合),则直线
与
轴是否交于一个定点?若是,请写出定点坐标,并证明你的结论;若不是,请说明理由 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1497ffc1b18295b5f12c4a566a3285e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eea967ddc26ab20232bfdc970450312.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea68142955809f9f40b15e3fa0f5bdd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
10 . 已知
.
(1)当
为常数,且
在区间
变化时,求
的最小值
;
(2)证明:对任意的
,总存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c2e866288807869ad1dfa7709a46cb.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e1254e772d2e629c810916e7e377be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0f5e152398772be9ec9555664a6407.png)
(2)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2535ecbcc7dea519b632934c5fa650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
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2016-12-04更新
|
190次组卷
|
3卷引用:2017届重庆市第一中学高三上期中数学(文)试卷