1 . 已知函数
在区间
内有两个极值点.
(1)求实数
的取值范围;
(2)若
的极大值和极小值的差为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085f6e0545853d86ec16f679a674ca0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5239e374894f95da60c5cb35a2a718.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
2 . 已知
为坐标原点,对于函数
,称向量
为函数
的相伴特征向量,同时称函数
为向量
的相伴函数.
(1)记向量
的相伴函数为
,求当
且
时,
的值;
(2)设函数
,试求
的相伴特征向量
,并求出与
共线的单位向量;
(3)已知
,
,
为
的相伴特征向量,
,请问在
的图象上是否存在一点
,使得
.若存在,求出
点坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(1)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe91c3b3290e5eb048b0028b0a5686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6197fc9360bc260883f303f344dce62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f5a04aef63712bb14cd11854ab79b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8c56d09485b718a85ed23f637e2d77.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bda80f584d122194e5da3ab8445320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd9c7231464c17b412d8ee08848f095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25953bf09041ebbd17e08f8bd243c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8995dd0d46aa3505185b312b37d2654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc45ae56d0d739339059deff9106093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d0f698f257914921dae5b31f9051e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b929fe0f9c13dd6dfabca91a1a4aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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7日内更新
|
140次组卷
|
2卷引用:江苏省连云港市海州高级中学2023-2024学年高一下学期期中学情调查考试数学试题
名校
解题方法
3 . 在棱长均为2的正三棱柱
中, E为
的中点.过AE的截面与棱
分别交于点F, G.
(1)若F为
的中点,求三棱柱被截面AGEF分成上下两部分的体积比 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301709b97852b4c2b951cfa2b2cfa2d2.png)
(2)若四棱锥
的体积为
求截面 AGEF 与底面ABC所成二面角的正弦值;
(3)设截面AFEG的面积为
面积为S₁,△AEF面积为
当点F在棱
上变动时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770abdd10660689c605577f9cb6d9db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa717be2a43918b9eb13655f86042a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b828011b4a0be31af4f30d829d7e30b1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/18/c1fc03ae-c978-409e-8fa2-9e23147b9838.png?resizew=123)
(1)若F为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5fb47a5caaa26007a7606acf05c52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301709b97852b4c2b951cfa2b2cfa2d2.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04eb4a437f9aee581cb2d0fff0d9d588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c181e33261a6c8df1e5291b0a119dc9.png)
(3)设截面AFEG的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431bceebfd7dbb3dcbd0348e486a97fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c9821bd2db0d34acbd7acd0fb2bb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5fb47a5caaa26007a7606acf05c52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17646ce1c1499a928584904d416a2a2.png)
您最近一年使用:0次
4 . 已知向量
,
,设函数
.
(1)求函数
的最小正周期;
(2)解不等式
;
(3)若对
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845305c95afc278738c29ce8bdc4b15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e404eed46e092c00b47db9b231c3ef1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab63c5b5d4a95127d3e2853e6fde9541.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(3)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12442aac32ca3cdec8ead596f0db327d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c4340db2a136a5f66f20e4eeff70ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
5 . 已知
,
(1)若
,求
的值;
(2)在三角形ABC中,若
,求
的最大值;
(3)若关于x的不等式
在
上恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7ac529db355de5d6f84b66ab748dfd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37ae6d0fb13ff62d4f9ae4da903f3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ba9745c01bcc7c3b62a4ee6dd60a3a.png)
(2)在三角形ABC中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9665922679187aa5f4961188509f5c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a5801e8be81aae66c47cc058fe370c.png)
(3)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a8c86ace105fc98a7eca98e0bbcf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18cf6fd97502bd971747cf25ce00de0.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
和
的定义域分别是A和B,若函数
和
同时满足下列两个条件:
①对任意的
,都有
或对任意的
,都有
;
②存在
,使得
.
则称
和
互为“依偎函数”,记作
,其中,
叫做“依偎点”.
(1)是否存在
有无数个“依偎点”?若存在,请举例说明;若不存在,请说明理由;
(2)若函数
,
,是否存在k,使得
如果存在,求出k的值;如果不存在,请说明理由;
(3)求证:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
①对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479511a50da604b2fc7398617db8387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479511a50da604b2fc7398617db8387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18165b24e85935b2d036eb6ba4aa0125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099adf32792e7334032a80084e0cb584.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0e49c46c9fb222376736229da4e80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0e49c46c9fb222376736229da4e80b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacd6155ac43dbd8aa73d03740c24af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f084386fd408381964398bf8c907a7.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a487acd081800a523a236a1337261e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
您最近一年使用:0次
2024-04-23更新
|
322次组卷
|
2卷引用:江苏省南京市南京师范大学附属中学2023-2024学年高二下学期期中考试数学试卷
名校
7 . 已知函数
,且
.
(1)求
的值及曲线
在点
处的切线方程;
(2)求函数
在区间
上的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c56eb056e2289654ae4944f38117225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6d8799983510bb2f6332b8a54805e9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
您最近一年使用:0次
2024-04-19更新
|
638次组卷
|
3卷引用:江苏省连云港高级中学2023-2024学年高二下学期期中考试数学试卷
8 . 布劳威尔不动点定理是拓扑学里一个非常重要的不动点定理,它可运用到有限维空间并构成了一般不动点定理的基石,得名于荷兰数学家鲁伊兹·布劳威尔(L.E.J.Brouwer).简单地讲就是:对于满足一定条件的连续函数
,存在实数
,使得
,我们就称该函数为“不动点”函数,实数
为该函数的不动点.
(1)求函数
的不动点;
(2)若函数
有两个不动点
,且
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d468b616235df122370cf58f03bb678f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249ae140f4c699e463b914aa0a25a260.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493db98b5e52328db4dd952e589b3cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cfc6ebbd5ab3be6a65a553e9da0f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2024-04-16更新
|
385次组卷
|
2卷引用:江苏省徐州市沛县中学、中国矿业大学附属中学2023-2024学年高二下学期4月联考数学试题
名校
解题方法
9 . 已知O为坐标原点,对于函数
,称向量
为函数
的伴随向量,同时称函数
为向量
的伴随函数.
(1)设函数
,试求
的伴随向量
;
(2)记向量
的伴随函数为
,在
中,
,
,求
的值;
(3)记向量
的伴随函数为
,函数
,函数
在区间
上的最大值为
,最小值为
,设函数
,若
,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897afa1737ad49e3911d913a9677284c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(2)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38938a4057a43a64fdcc42911f2a68ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe7a93172d308a58200e3c722fe1072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a67c529d3e81a79c4e4409953d316f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21bdea15993d7447c9bee28f7318bc9.png)
(3)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea58aa816188f75602b875a163ae1e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c691f19308f093ef6c3a77a519fb79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07286db2a5af137e599d59ea52b08a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e93d044f7bde4330e206b4edd2bd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26c2d48c264304810689c150770f681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ad48f39539154d0844c87d0ff3ed63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f356419f670193d39741a41fb5d89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e91406484c332ac8fc96a54c7e187b.png)
您最近一年使用:0次
解题方法
10 . 如图,三棱锥
中,
,且平面
平面
,
,
为平面
的重心,
为平面
的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/0a763d76-8a5c-4170-9bdc-c86b3c6a19a1.png?resizew=142)
(1)棱
可能垂直于平面
吗?若不可能,说明理由;
(2)求
与
夹角正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eaf10b924a42867329185ad83c85cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/0a763d76-8a5c-4170-9bdc-c86b3c6a19a1.png?resizew=142)
(1)棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
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