名校
解题方法
1 . 已知函数
.
(1)若
,求
在点
处的切线方程;
(2)令
,判断
在
上极值点的个数,并加以证明;
(3)令
,定义数列
. 当
且
时,求证:对于任意的
,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb46a163897842c1fe507d8fca253bc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa80a12751a326ffabe3115ff779983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0138235d884d203490107787ea2e2830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff61248b4e57f4f9f5b2d9ab74a82ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06b9066e5f16f7a4c2ccc88d48fbea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fee9e71a4c714607f4b7af44337c411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad94568bce23439be8ded967d870c98.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(Ⅰ)求曲线
在点
处的切线方程;
(Ⅱ)求证:存在唯一的
,使得曲线
在点
处的切线的斜率为
;
(Ⅲ)比较
与
的大小,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f150d5ef78b3298229880b5e327685.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(Ⅱ)求证:存在唯一的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0573a6bcc480a91a43126d01bc19eeae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd30bbe4130d3161d55011d4cf9a3d0.png)
(Ⅲ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554231a67ae07a50e2510f42c3250136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b708034aa1e680d6b14ce2133650a85.png)
您最近一年使用:0次
2018-01-21更新
|
1255次组卷
|
10卷引用:北京市第一零一中学2023届高三三模数学统考四试题
名校
3 . (1)请根据对数函数
来指出函数
的基本性质(结论不要求证明),并画出图象;
(2)拉普拉斯称赞对数是一项“使天文学家寿命倍增”的发明.对数可以将大数之间的乘除运算简化为加减运算,请证明:
;
(3)2017年5月23日至27日,围棋世界冠军柯洁与DeepMind公司开发的程序“AlphaGo”进行三局人机对弈,以复杂的围棋来测试人工智能.围棋复杂度的上限约为
,而根据有关资料,可观测宇宙中普通物质的原子总数约为
.甲、乙两个同学都估算了
的近似值,甲认为是
,乙认为是
.现有两种定义:
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237086720/STEM/2c179cd798bc431f94b813641b8a2aec.png?resizew=190)
①若实数
满足
,则称
比
接近
;
②若实数
,且
,满足
,则称
比
接近
;请你任选取其中一种定义来判断哪个同学的近似值更接近
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3808314697be51e2ff72179fb6556374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b8eea00910cad6239a29a85991f925.png)
(2)拉普拉斯称赞对数是一项“使天文学家寿命倍增”的发明.对数可以将大数之间的乘除运算简化为加减运算,请证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8734005d48f1e77eeaebe832058dee.png)
(3)2017年5月23日至27日,围棋世界冠军柯洁与DeepMind公司开发的程序“AlphaGo”进行三局人机对弈,以复杂的围棋来测试人工智能.围棋复杂度的上限约为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f610f3ed73c02ddc0fd21b34d12ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/013492f5b66a5b5b9169222c524474b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0b4b553124abf972a92af238b80480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10e3a8a2bd5a1fd799f8640d31d826d.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237086720/STEM/2c179cd798bc431f94b813641b8a2aec.png?resizew=190)
①若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b782dd2de9c9caa840838cd63d817de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413915a68960106812e6577dedac2f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376218b0e2c4b0bc42f54573c5703a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5892a5def700f49245c7389aae50a68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
您最近一年使用:0次
名校
4 . 设数列
的前
项和为
,且
.
(1)求证:数列
为等比数列;
(2)设数列
的前
项和为
,求证:
为定值;
(3)判断数列
中是否存在三项成等差数列,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/3ec5876debe2d19fc86125efcf9003d0.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea49f8a2b98b542b1ebb2ac813346c90.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/7b87635913b4f90a784edd6ef79f2aec.png)
(3)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85849759030b70f4645bc3fdd2721e22.png)
您最近一年使用:0次
2017-09-14更新
|
1951次组卷
|
7卷引用:2020届江苏省南通市如皋中学高三创新班下学期4月模拟考试数学试题
2020届江苏省南通市如皋中学高三创新班下学期4月模拟考试数学试题江苏省盐城市第一中学2020届高三下学期第一次调研考试数学试题甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(文)试题江苏省海安县2018届高三上学期第一次学业质量测试数学试题江苏省徐州市第三中学2017~2018学年度高三第一学期月考(理科)数学试卷(已下线)《2018届优等生百日闯关系列》【江苏版】专题二 第六关 以新定义数列为背景的解答题(已下线)第02章+章末复习课(重点练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版必修5)
名校
5 . 如图,已知曲线
,曲线
,
是平面上一点,若存在过点
的直线与
都有公共点,则称
为“
型点”.
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237242368/STEM/e2692fbc1f4647a0a8b17efc77414ca8.png?resizew=212)
(1)证明:
的左焦点是“
型点”;
(2)设直线
与
有公共点,求证:
,进而证明原点不是“
型点”;
(3)求证:
内的点都不是“
型点”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f63dee0fb484e63eb3a8baebcdf46f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88956e6ba9a7e1d23fabc6707fc3da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880248fa1259b2600a87f09a61287d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237242368/STEM/e2692fbc1f4647a0a8b17efc77414ca8.png?resizew=212)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1f54ccf474ea17a7fe62a1b6f0e87.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db94a845b19c6ee907a2e566cc4da9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1f54ccf474ea17a7fe62a1b6f0e87.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fac7fedc3d5ebe2e396075e7d2caa51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1f54ccf474ea17a7fe62a1b6f0e87.png)
您最近一年使用:0次
名校
6 . 已知函数
,设
.
(1)判断函数
零点的个数,并给出证明;
(2)首项为
的数列
满足:①
;②
.其中
.求证:对于任意的
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446f4d677ccf4584a39e1fe080956e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8725228907c7a0c353309d88aa3385be.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779b28641c18eacbceca96d4e4ad9710.png)
(2)首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff64232ae491cbd3590890a0752f39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754ded041cb75fee4d0bc0ac54a264f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae495bf57e8d3fea4b95ff0ef20d02dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a82caca991a9f313f3d17537fb41be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e86c62c29f5960b6018bae6189fbf2d.png)
您最近一年使用:0次
2017-06-06更新
|
1732次组卷
|
3卷引用:湖南省长沙市雅礼中学2017届高考模拟试卷(二)数学(理)试题
名校
解题方法
7 . 如图,在四棱锥
中,
为正三角形,平面
平面
,
//
,
,
.
![](https://img.xkw.com/dksih/QBM/2019/6/7/2220515209068544/2220763683184640/STEM/0ad9b1c0afd04d89bce4301d90237f4b.png?resizew=118)
(1)求证:平面
平面
.
(2)求三棱锥
的体积.
(3)在棱
上是否存在点
,使得
//平面
?若存在,请确定点
的位置,并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43dfede0d7e17c2ad89ab51349e6bf0.png)
![](https://img.xkw.com/dksih/QBM/2019/6/7/2220515209068544/2220763683184640/STEM/0ad9b1c0afd04d89bce4301d90237f4b.png?resizew=118)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2017-08-07更新
|
1421次组卷
|
5卷引用:北京市昌平区2017届高三第二次统一练习数学(文科)试题
8 . 已知四棱台
的下底面是边长为4的正方形,
,且
面
,点
为
的中点,点
在
上,
,
与面
所成角的正切值为2.
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/6e3d1c174c68482dacf02fedb5be4125.png?resizew=234)
(Ⅰ)证明:
面
;
(Ⅱ)求证:
面
,并求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/d88cd0caee424dd7b5b7e613451e1e8f.png?resizew=119)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/02a34008e38b48868aab49bc73fb3ac1.png?resizew=53)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/f4005f91998e4d48bd313ce75b5ed179.png?resizew=44)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/7b469e3683f3499eb5667bafea560131.png?resizew=48)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/fcdd0823aa4b4d67864b42de2e1bc03c.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/392bd2ccb6a2481b80a317fb8fea0a55.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/641b2f927cc749ddbc999bfabe8dd3db.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/2159f82842c74b8891d03d8d5ccef65b.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/3752f3e007be4b1abacc7a9e63f322f8.png?resizew=73)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/1065a71f857d402a9d5dba0c43798749.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/7b469e3683f3499eb5667bafea560131.png?resizew=48)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/6e3d1c174c68482dacf02fedb5be4125.png?resizew=234)
(Ⅰ)证明:
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/f22dfced01694498af37b49858dddcdc.png?resizew=39)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/f8c4a18ecffb42ee88eb12e9569d97ae.png?resizew=52)
(Ⅱ)求证:
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/0e4aebe48b824c7f9ba331405853b053.png?resizew=44)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/5e10df256d444157a88df238a066cda2.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2017/6/4/1701753905446912/1701893112143872/STEM/8c5ee610ec474657b72f559ba23ecd79.png?resizew=63)
您最近一年使用:0次
名校
9 . (1)证明:当
时,
;
(2)若不等式
对任意的正实数
恒成立,求正实数
的取值范围;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7e5b12719915c134ab756cb09f75c1.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a264a7259b8956b59ef9ef37c9af8855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a0805acb0016f9851d5d1a49e2b553.png)
您最近一年使用:0次
2017-05-22更新
|
507次组卷
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3卷引用:湖北省襄阳第四中学2017届高三下学期第一次模拟考试数学(文)试题
10 . (1)当
时,试用分析法证明:
;
(2)已知
,
.求证:
中至少有一个不小于0.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6c5526947e9bef051bc3bdf7fd186d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b1411bbc505b5056e68e077d18e06b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003fe3cdffd8338cf5766dd287b0c5e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
您最近一年使用:0次
2017-05-03更新
|
834次组卷
|
5卷引用:河南省豫西名校2017-2018学年高二下学期第一次联考数学(文)试题