名校
1 . 已知数列
满足上:
,
.
(1)若
,证明:数列
是等差数列;
(2)若
,判断数列
的单调性并说明理由;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b66280badd3b6c4cc7629f024d1e67b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87743e3348c037162aa605bb6bb2220c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d27884f5e62dda8dd97ecb5d62f86a0.png)
您最近一年使用:0次
2 . 已知数列
满足
.
(1)若数列
是常数列,求
的值;
(2)当
时,求证:
;
(3)求最大的正数
,使得
对一切整数
恒成立,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7827d2b3caafb7064c6ccce43af3c6d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dab9e79198239cda875305fd6809b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
(3)求最大的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162c0897cdfa67cac5b49becac685e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2017-04-21更新
|
686次组卷
|
2卷引用:2015-2016学年浙江省安吉,德清,长兴三县高一下学期期中考试数学试卷
名校
解题方法
3 . 定义在R上的函数
,当
,且对任意
,有
.
(1)求证:对任意
,都有
;
(2)判断
在R上的单调性,并用定义证明;
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84302e08e2e09d2d62548d35e6a40288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e885000d706e589a10515ff0d93cae55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db7387dec34f24cacb1cd95c433e8a4.png)
(1)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6d0da3cbcaa04a639eaac12c0e29d1.png)
您最近一年使用:0次
2017-02-08更新
|
1129次组卷
|
2卷引用:2016-2017学年浙江杭州西湖高级中学高一上学期期中数学试卷
4 . 如图,四棱锥
中,底面
是正方形,
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
平面
;
(2)证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d4c42112e0a22f240ce2ae432e5b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2016-12-04更新
|
617次组卷
|
7卷引用:2015-2016学年浙江金华等三市部分学校高二下学期期中数学试卷
5 . 已知
,点
在函数
的图象上,其中
…,设
.
(1)证明数列
是等比数列;
(2)设
,求数列
的前
项和;
(3)设
,且数列
的前
项和
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366dfedff1a1a96ec27650375b680059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2aeba7035c6ac1c4aeb153f605be79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5397ee1eb6d157f6ec1e7a878f8d16e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4977e72494aaa1f309d610f41a5613da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3b0e97e830f93adfc494971d57df20.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092304b629c875c81665b7f9322130ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ff128b22e3abab2ba8f4d3012c33ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875d014c95325c8d88ee6de493083865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11913c4302df9c8bdd8b14a3ac576943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb7ced06ce33b36f5f9db367080b76a.png)
您最近一年使用:0次
6 . 已知函数
的定义域是
且
,
,当
时,
.
(1)求证:
是奇函数;
(2)求
在区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bce7c5de6e43a203eb98a7c23f8985.png)
)上的解析式;
(3)是否存在正整数
,使得当x∈
时,不等式
有解?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/a51771f539164b6e9d9eead0303f5eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cda1d250b465616dbc1fd75a2359c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c3cfe479362ebb78ff9951d1d9f083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6c48591cae0bcf7ae6c8d589527c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc4e3775c850f1c1804f9eb7a70153a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bce7c5de6e43a203eb98a7c23f8985.png)
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/0e39cf5721f84387a7307e4ae19b2041.png)
(3)是否存在正整数
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/c0a95e15d16643a2a69d6bd21d5d9265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da7f1da7e1c7aeaf845415de9aec0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54218478418966f351be0d622a834f07.png)
您最近一年使用:0次
2016-12-03更新
|
203次组卷
|
2卷引用:2014-2015学年浙江省东阳中学高二下学期期中考试理科数学试卷
10-11高二下·浙江温州·期中
7 . 已知数列
满足
,
.
(1)求证
;
(2)比较
的大小,并证明;
(3)是否存在
使得
,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937ce158fe772ae70cd797f6514a0779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe50c26147bbdc9874ec6e60f38293a8.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dfdac83e7aaac092e7e7a4e91a2e9d.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d514eb8dff80d4dc3f39de516b63b846.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78816854e432159b3a2adddc45fbdede.png)
您最近一年使用:0次
12-13高二上·浙江杭州·期中
解题方法
8 . 如图,直三棱柱
中,已知
,
,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/1f651409-9fc2-4241-b792-5828526e8e09.png?resizew=181)
(1)求证:
平面
;
(2)当点
在
上什么位置时,会使得
平面
?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47739be8ea23755014d80b408e6a36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/1f651409-9fc2-4241-b792-5828526e8e09.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762b8cac66d86a013ba839266b023e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea124cef7ab3fd8069243e9894d1c59.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431e8bf1a5f9ac9a2ec82c11f31a4afe.png)
您最近一年使用:0次
9 . 已知数列
中,
.
(1)求证:数列
是等差数列;
(2)若
,设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfcdfb924d1edb38139a4030ba5a33a.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3e74fcd0b38bb7bbe6f0d8d2d4a256.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd2a777ca80aba17b6dd45805665540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd2d540aa82078d246c1beedd8a8000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38dfa46a983634a7c520e495b805d324.png)
您最近一年使用:0次