解题方法
1 . 数值线性代数又称矩阵计算,是计算数学的一个重要分支,其主要研究对象包括向量和矩阵.对于平面向量
,其模定义为
.类似地,对于
行
列的矩阵
,其模可由向量模拓展为
(其中
为矩阵中第
行第
列的数,
为求和符号),记作
,我们称这样的矩阵模为弗罗贝尼乌斯范数,例如对于矩阵
,其矩阵模
.弗罗贝尼乌斯范数在机器学习等前沿领域有重要的应用.
(1)
,
,矩阵
,求使
的
的最小值.
(2)
,
,,矩阵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880f9f9ab3fcb2dfdfc14d0ab8582fb9.png)
求
.
(3)矩阵
,证明:
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860fc1db2edc066188f8d24e35dbf205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332153dce658c8cc26984e355b7c15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c529cf68fc1e9a4f9ab4dfbadcfe01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bb39d4f4036ceed78844592288c408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5550d8659980c02488a57afd5964ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747bedda3150eb258ffb25c923a47614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c297fac2721a2c7bbaa60b0274dbc34f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de651a4843a0cdbf9e26e51f9c53e837.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83986d667f7618313804888470393a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6abaf4851fb819b325eb5d21cd0260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7013adffb807e769979945ba9aa0809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83986d667f7618313804888470393a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880f9f9ab3fcb2dfdfc14d0ab8582fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f922593fce42b4d7e592e51873aa2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8a93d9cf3359a0ad6106ea5360acb.png)
(3)矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6bed24376a5b1ea247ffb1552eaaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83986d667f7618313804888470393a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f823d5ffe45a61c388710e7a67fd02.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
是定义在R上的奇函数,其图象经过点
.
(1)求实数
,
的值并指出
的单调性(不必证明);
(2)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412242f68a30b1099aa3f56b1e806eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64e8f8505ae8d4e3fa214e588c710d.png)
(1)求实数
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672e7080c77d9811dd7482380e0d94f0.png)
您最近一年使用:0次
2024高三·全国·专题练习
3 . 设二次函数f(x)=3ax2+2bx+c.若a+b+c=0,f(1)f(0)>0.
(1)求证:方程f(x)=0有实根;
(2)设x1,x2是方程f(x)=0的两个实数根,求|x1-x2|的取值范围.
(1)求证:方程f(x)=0有实根;
(2)设x1,x2是方程f(x)=0的两个实数根,求|x1-x2|的取值范围.
您最近一年使用:0次
名校
解题方法
4 . 已知函数
为奇函数.
(1)求
,判断
的单调性,并用定义证明;
(2)若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ca09548bb2ade976e4db708ff209c4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2a56a3dbc9d402e33f172d90694b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-02-18更新
|
342次组卷
|
4卷引用:山东省临沂市2023-2024学年高一上学期期末学科素养水平监测数学试题
5 . 我们知道:设函数
的定义域为D,那么“函数
的图象关于原点成中心对称图形”的充要条件是“
,
”.有同学发现可以将其推广为:设函数
的定义域为D,那么“函数
的图象关于点(m,n)成中心对称图形”的充要条件是“
,
”已知
.
(1)利用上述结论,证明:
的图象关于点
成中心对称图形;
(2)判断
的单调性(无需证明),并解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57eb010ff662d57396d079222c0cdad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0381746695cc95095bd5f248b707ea1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8f7c92dca9e48db1da75fbad2a7287.png)
(1)利用上述结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49a26cf164e6f90fbd6fadd34bb82fc.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5246be48b0389b4a60952950875d352d.png)
您最近一年使用:0次
6 . 已知函数
,
.
(1)判断函数
的奇偶性,并说明理由;
(2)当
时,证明:函数
在
上单调递减;
(3)若对任意的
,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0cb86fc09ac3f21b960718acf51c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cfada8fd642ddf968bfd4228d48ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40beaf3b21a8d7d06b46d473e99d1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c91f17f6001a1341711dc4d0473035c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
7 . 已知函数
,
.
(1)函数
在
上单调递增,求实数a的取值范围;
(2)当
时,对任意
,关于x的不等式
恒成立,求实数a的取值范围;
(3)当
,
时,若点
,
均为函数
与函数
图象的公共点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f779eb0eb4e0ca4a92b20fe9b77be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f588722d20a51f2e43f9318589b3d6.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b2856045b940760ebabe6606df19a6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ed427e67d7d27d53df7039cca81038.png)
您最近一年使用:0次
名校
解题方法
8 . 已知
是二次函数,不等式
的解集是
,且
在区间
上的最大值是12.
(1)求
的解析式;
(2)试判断函数
在
上的单调性,并用单调性的定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c76c41773aae617db1c0cc04bcf836f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9430ded94aee51af5a5de91fef1d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef1b322a7e2dbe40f17a0f9c61ec4aa.png)
您最近一年使用:0次
2024-01-10更新
|
293次组卷
|
4卷引用:3.2.1单调性与最大(小)值(第2课时)
(已下线)3.2.1单调性与最大(小)值(第2课时)重庆市开州区临江中学2023-2024学年高一上学期第二阶段性(12月期中)考试数学试题江西省上饶艺术学校2023-2024学年高一上学期12月月考数学试题(已下线)专题04 函数的性质与应用2-期末复习重难培优与单元检测(人教A版2019)
2024·全国·模拟预测
9 . 已知
.证明:
(1)当
时,
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b8b32dd4e8910769e4176362d7b40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e84dbb03e8c627ff11d5c7aeb0c8b5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7ad23e894950eb21a3da9f40433e6f.png)
您最近一年使用:0次
名校
解题方法
10 . 已知定义在
上的函数
,对于
,恒有
.
(1)求证:
是奇函数;
(2)若
是增函数,解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70e0db0174a2c05b28fb6d0c2508778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1cdb84948a62fecaec0e17018ddf08.png)
您最近一年使用:0次
2024-01-21更新
|
596次组卷
|
4卷引用:辽宁省丹东市2023-2024学年高一上学期期末教学质量监测数学试题