名校
1 . 新教材人教B版必修第二册课后习题:“求证方程
只有一个解”.证明如下:“化为
,设
,则
在
上单调递减,且
,所以原方程只有一个解
”.解题思想是转化为函数.类比上述思想,不等式
的解集是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c18c032d75893db45e61e6c4eb0d4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cfb1e9557770560280b5248ae2d0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856491b01dab707170d83a1bc4b1f257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec65a2bec3d4296c613a80b3ae41d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb24655f40cd3200323b4f920c9f473.png)
您最近一年使用:0次
2020-11-04更新
|
706次组卷
|
7卷引用:湖北省黄冈市麻城一中2019-2020学年高三上学期期末数学(理)试题
湖北省黄冈市麻城一中2019-2020学年高三上学期期末数学(理)试题辽宁省抚顺市二中、旅顺中学2019-2020年高三上学期期末考试数学试题辽宁省辽南协作体2019-2020学年高三上学期期末考试数学文试题辽宁省辽南协作体2019-2020学年高三上学期期末考试数学理试题安徽省六安市舒城中学2020-2021学年高二下学期开学考试数学(理)试题(已下线)第18讲 数学思想选讲(二)-【提高班精讲课】2021-2022学年高一数学重点专题18讲(沪教版2020必修第一册,上海专用)内蒙古海拉尔第二中学2021-2022学年高三上学期第一次阶段考数学(文科)试题
解题方法
2 . 被誉为“数学之神”之称的阿基米德(前287~前212),是古希腊伟大的物理学家、数学家、天文学家,他最早利用逼近的思想证明了如下结论:抛物线的弦与抛物线所围成的封闭图形的面积,等于抛物线的弦与经过弦的端点的两条切线所围成的三角形面积的三分之二,这个结论就是著名的阿基米德定理,其中的三角形被称为阿基米德三角形.在平面直角坐标系
中,
是焦点为
的抛物线
上的任意一点,且
的最小值是
.若直线
与抛物线
交于
,
两点,则弦
与抛物线
所围成的封闭图形的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165bb2c55562cc390b1940aa899f6e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd9b7b70528182066ca934427d74f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314bf8f0ce875b4dd66ba692fd6a75c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
3 . 给出下列命题:
用反证法证明命题“设a,b,c为实数,且
,
,则
,
,
”时,要给出的假设是:a,b,c都不是正数;
若函数
在
处取得极大值,则
或
;
用数学归纳法证明
,在验证
成立时,不等式的左边是
;
数列
的前n项和
,则
是数列
为等比数列的充要条件;
上述命题中,所有正确命题的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee08def7a24d4255453ad40a77cd4e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd92e0bbdc7a5fd3d604160cf4306ba.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36a91b78ea833d5b09c11366324a845.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052c6cf4517966ecebd39354490b1723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c9d7f7f9a3e9ec476f5cf7fda97c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb989bea4883060e495e03e709593361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8b8edd94bc4d5d517ec77e56800e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f13167b6a291eeb91bd9a796745f6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d493ee368a6be6e8de57368520c8cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
上述命题中,所有正确命题的序号为
您最近一年使用:0次
4 . 对于三次函数
,定义
是
的导函数
的导函数,若方程
有实数解
,则称点
为函数
的“拐点”,可以证明,任何三次函数都有“拐点”,任何三次函数都有对称中心,且“拐点”就是对称中心,请你根据这一结论判断下列命题:
①任意三次函数
都关于点
对称:
②存在三次函数有两个及两个以上的对称中心;
③存在三次函数
,若
有实数解
,则点
为函数
的对称中心;
④若函数
,则:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f890d263fb7ec680993048607ead5e46.png)
其中所有正确结论的序号是____________________ (把所有正确命题的序号都填上).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641790f25de4850d4dde3e370db820c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
①任意三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/335fdba7c29341e200ebbb000f5c2121.png)
②存在三次函数有两个及两个以上的对称中心;
③存在三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbadbb09da422f97c3757082869fa50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641790f25de4850d4dde3e370db820c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dbf5abbfd8097f70365f4750199d730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f890d263fb7ec680993048607ead5e46.png)
其中所有正确结论的序号是
您最近一年使用:0次
2011·贵州遵义·一模
5 . 已知函数
在
上最小值是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c996bcd14149792beddc817232d5223d.png)
(1)求数列
的通项公式;
(2)令
,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ecc4b17102dcc3e61b62601088a8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdfed8d6862125dc1fecfce0322a750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c996bcd14149792beddc817232d5223d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f735dc3f470a63d8cd5b6010be01c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f74802491f0cae0f258ae2babb8f71c.png)
您最近一年使用:0次
6 . 定义
是
的导函数
的导函数,若方程
有实数解
,则称点
,
为函数
的“拐点”.可以证明,任意三次函数
都有“拐点”和对称中心,且“拐点”就是其对称中心,请你根据这一结论判断下列命题:
①存在有两个及两个以上对称中心的三次函数;
②函数
的对称中心也是函数
的一个对称中心;
③存在三次函数
,方程
有实数解
,且点
为函数
的对称中心;
④若函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac322fc4206da717226ad89530effdd5.png)
.
其中正确命题的序号为_______ (把所有正确命题的序号都填上).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b589732202941f828016f982c92996b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60a6d986c80039124c8a869b0e481af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
①存在有两个及两个以上对称中心的三次函数;
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c087948f0abff7f6b3218860c973f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efc139f70df469a51f530e03c98abaa.png)
③存在三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a42dfca9f27abe558892fc0b7db96df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb0c68f6e69ab9da3ea2c8c2f48f683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed0aa12ed308e80e35f1bb6101d36d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b8df99b8a0839cba0eb04427c0a1b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac322fc4206da717226ad89530effdd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb688d1f5aa60c67b53486b84f0aa432.png)
其中正确命题的序号为
您最近一年使用:0次