1 . 已知如图,在直三棱柱ABC﹣A1B1C1中,AA1=AC,且AB⊥AC,M是面CC1的中点,N是BC的中点,点P在直线A1B1上.
![](https://img.xkw.com/dksih/QBM/2016/4/27/1572605640695808/1572605646790656/STEM/465544bbe958498293870b6ac70c3cfc.png)
(Ⅰ)若P为A1B1中点,求证:NP∥平面ACC1A1;
(Ⅱ)证明:PN⊥AM.
![](https://img.xkw.com/dksih/QBM/2016/4/27/1572605640695808/1572605646790656/STEM/465544bbe958498293870b6ac70c3cfc.png)
(Ⅰ)若P为A1B1中点,求证:NP∥平面ACC1A1;
(Ⅱ)证明:PN⊥AM.
您最近一年使用:0次
2 . 已知数列{an}的前n项和Sn,a1=﹣
,Sn+
(n≥2).
(1)计算S1,S2,S3,猜想Sn的表达式并用数学归纳法证明;
(2)设bn=
,数列的{bn}的前n项和为Tn,求证:Tn>﹣
.
![](https://img.xkw.com/dksih/QBM/2016/2/25/1572499600531456/1572499606601728/STEM/b8244919cde24479b7f81d9cd38e1dec.png)
![](https://img.xkw.com/dksih/QBM/2016/2/25/1572499600531456/1572499606601728/STEM/e81c4514dc144f75beac4c90b80cbe19.png)
(1)计算S1,S2,S3,猜想Sn的表达式并用数学归纳法证明;
(2)设bn=
![](https://img.xkw.com/dksih/QBM/2016/2/25/1572499600531456/1572499606601728/STEM/0f083b9f1d064e29a7bd5ae8bd842c82.png)
![](https://img.xkw.com/dksih/QBM/2016/2/25/1572499600531456/1572499606601728/STEM/48f8a4ad543445d5b478d0a447cdd06e.png)
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2012高二下·浙江嘉兴·学业考试
名校
解题方法
3 . 已知函数
.
(1)求函数
的极值;
(2)对于曲线上的不同两点
,如果存在曲线上的点
,且
使得曲线在点
处的切线
,则称
为弦
的伴随直线,特别地,当
时,又称
为
的
—伴随直线.
①求证:曲线
的任意一条弦均有伴随直线,并且伴随直线是唯一的;
②是否存在曲线
,使得曲线
的任意一条弦均有
—伴随直线?若存在,给出一条这样的曲线,并证明你的结论;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aca3bb4e25eaef56fb7ba9c79da0944.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对于曲线上的不同两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a00dc6f0af494437c9f98223f3e861f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752e086b85f9fbb95010bf771072af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69264c1535cf0ccdac2d186da669df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1635f56ef7fb304920f253f30fbba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0429adcf685c47f2d97d567387385461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
①求证:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②是否存在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
您最近一年使用:0次
2016-12-01更新
|
986次组卷
|
4卷引用:2020届辽宁省大连市高三上学期第二次模拟考试数学(理)试卷
2020届辽宁省大连市高三上学期第二次模拟考试数学(理)试卷(已下线)2011-2012学年浙江省嘉兴一中高二下学期摸底考试理科数学试卷2016-2017学年湖南省长沙市第一中学高二下学期第一次月考数学(理)试卷(已下线)江苏省苏锡常镇四市2023届高三下学期3月教学情况调研(一)数学试题变式题17-22
名校
解题方法
4 . 如图所示,M、N、P分别是正方体ABCD-A1B1C1D1的棱AB、BC、DD1上的点.
(1)若,求证:无论点P在DD1上如何移动,总有BP⊥MN;
(2)棱DD1上是否存在这样的点P,使得平面APC1⊥平面ACC1?证明你的结论.
您最近一年使用:0次
2016-12-04更新
|
626次组卷
|
4卷引用:2015-2016学年辽宁师大附中高一上12月月考数学试卷
解题方法
5 . 已知数列
的前
项和为
,
,满足
.
(1)计算
,猜想
的一个表达式(不需要证明)
(2)设
,数列
的前
项和为
,求证:
.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0a53b6755b419e78cb64cc193ce826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8489821754dcda77ce79ad337f27206.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd44027bdc6a6e4e5fa2168c34f50dc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/a0358e59b474fd18fac4797f3506a0ac.png)
您最近一年使用:0次
2016-12-03更新
|
354次组卷
|
2卷引用:2015-2016学年辽宁省实验中学分校高二上学期期末考试文科数学试卷
6 . .对于函数
,若
,则称
为
的“不动点”,若
,则称
为
的“稳定点”.函数的“不动点”和“稳定点”的集合分别记为
和
,即
,
.
(1)求证:
;
(2)若
,且
,求实数
的取值范围;
(3)若
是
上的单调递增函数,
是函数的稳定点,问
是函数的不动点吗?若是,请证明你的结论;若不是,请说明的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccf2afc8b9479e16dfaf6b86d3d962d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/0b164ca7a43db8ed2958a9a9b5a21369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e60faa38dfd9c8001edd62b2d089204.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfac30eb449e17bbee48dd07c7ab385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d02e5de0c92487382f4b98376e9740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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14-15高一上·湖南张家界·期末
解题方法
7 . 设函数
满足
且
.
(1)求证
,并求
的取值范围;
(2)证明函数
在
内至少有一个零点;
(3)设
是函数
的两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d0b83762279e1e6d818d3999201fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39675659305a1b59862e5f222083f6f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a1f987b14c075c1ca923de99be51449.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
(2)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbfd0c7caacb8f926dbc857f913a6dd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be837b55c392129d22e35a0b97921c5.png)
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10-11高二下·内蒙古赤峰·阶段练习
名校
8 . 已知三角形ABC的三边长为a、b、c,且其中任意两边长均不相等.若
成等差数列.(1)比较
与
的大小,并证明你的结论;(2)求证B不可能是钝角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f81b8a02e231884bc36fdc4870830cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe34b1cc3a3cfcfad66fb03b9e22c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c147d6cbd7cbaeb8ec08a0ba69cd59dd.png)
您最近一年使用:0次
2016-12-01更新
|
827次组卷
|
8卷引用:辽宁省铁岭市六校协作体2022-2023学年高三质量检测数学试题
辽宁省铁岭市六校协作体2022-2023学年高三质量检测数学试题(已下线)2010-2011年内蒙古赤峰市田家炳中学高二下学期4月月考考试数学文卷(已下线)2011-2012学年河南省周口市高二下学期四校第一次联考文科数学试卷河南南阳一中2015-2016学年高二下第二次月考文科数学试题内蒙古巴彦淖尔市杭锦后旗奋斗中学2017-2018学年高二下学期第一次月考数学(文)试题2018-2019学年人教版高中数学选修1-2 模块综合评价(一)黑龙江省海林市朝鲜族中学人教版高中数学选修1-2同步练习:模块终结测评(二)河南省郑州市巩义中学2019-2020学年高二下学期期中考试数学(文)试题
11-12高二上·浙江金华·阶段练习
名校
9 . 若直线l:x+my+c=0与抛物线y2=2x交于A、B两点,O点是坐标原点.
(1)当m=﹣1,c=﹣2时,求证:OA⊥OB;
(2)若OA⊥OB,求证:直线l恒过定点;并求出这个定点坐标.
(3)当OA⊥OB时,试问△OAB的外接圆与抛物线的准线位置关系如何?证明你的结论.
(1)当m=﹣1,c=﹣2时,求证:OA⊥OB;
(2)若OA⊥OB,求证:直线l恒过定点;并求出这个定点坐标.
(3)当OA⊥OB时,试问△OAB的外接圆与抛物线的准线位置关系如何?证明你的结论.
您最近一年使用:0次
2016-12-01更新
|
856次组卷
|
4卷引用:辽宁省锦州市联合校2021-2022学年高二上学期期末模拟数学试题(锦州五高命题)
辽宁省锦州市联合校2021-2022学年高二上学期期末模拟数学试题(锦州五高命题)(已下线)2011-2012学年浙江省东阳中学高二12月阶段性检测理科数学试卷(已下线)2011-2012学年山东省汶上一中高二12月月考理科数学安徽省池州市东至县第二中学2020-2021学年高二下学期3月月考文科数学试题
2011·辽宁沈阳·模拟预测
10 . 已知二次函数
和“伪二次函数”![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a9b750094486e1eefebcd02c22eec.png)
(
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50f9c6eac4df8472e6a7446ebde7230.png)
),
(I)证明:只要
,无论
取何值,函数
在定义域内不可能总为增函数;
(II)在二次函数
图象上任意取不同两点
,线段
中点的横坐标为
,记直线
的斜率为
,
(i)求证:
;
(ii)对于“伪二次函数”
,是否有(i)同样的性质?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e73001005c51065ad1315be7a4175d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a9b750094486e1eefebcd02c22eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb7dd8a018719c13d39eafdd39b59bd.png)
![](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/d50f9c6eac4df8472e6a7446ebde7230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9173f81cce498276001b0285454972e0.png)
(I)证明:只要
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bc334305133ac2b4b8d21efeb3324c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
(II)在二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e73001005c51065ad1315be7a4175d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4268b18eccd4761ec42b59508b913e8.png)
(ii)对于“伪二次函数”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d943bb3fbdc91b5097b7e34270e5c37.png)
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