1 . 已知二次函数
(
均为实数)满足
,对于任意实数
都有
,并且当
时,有
.
(1)求
的值;
(2)证明
;
(3)当
时,函数
(
为实数)是单调的,求证:
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a431537df789febf4bc45e3dc23cefaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5480f15ca0864627e652e67784fc4b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58427d5aa7deeca47c8789241913f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e08b4f3fa330e70f9d28bc866b5ddc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8c25a0a31b41ea8aa9a8658af4953d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6785823721fb2e288b417ba2d617ef04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a878fd5a7104a7f42770a19097d56457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
您最近一年使用:0次
2021-08-23更新
|
82次组卷
|
2卷引用:陕西省咸阳百灵学校2020-2021学年高二下学期第一次月考文科数学试题
解题方法
2 . 已知函数
是方程
的实数根,且
.
(1)求证:
;
(2)判断
值的正负,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475633da702813f09a8c018f2ee6dd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f20cb1947941fd2722c4a9c7aa987e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb61406d17f93df42862e75365ac5ff.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3096936439b16630e55991e16924c04e.png)
您最近一年使用:0次
3 . 设函数
是定义在
上的偶函数,且
对任意的
恒成立,且当
时,
.
(1)求证:
是以2为周期的函数(不需要证明2是
的最小正周期);
(2)对于整数
,当
时,求函数
的解析式;
(3)对于整数
,记
在
有两个不等的实数根},求集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545931b962cf570712d04888b57093f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1300fc4664b019bef578d4500b401b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a38b7245804665589963db957fad702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1300fc4664b019bef578d4500b401b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b868278dd071dc5117550ad17454ec2.png)
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名校
4 . 已知函数
的图象上有两点
,
.函数
满足
,且
.
(1)求证:
;
(2)求证:
;
(3)能否保证
和
中至少有一个为正数?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4753463638237ed69779fff0c66746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2d666c964eaf1879e069d971b0d636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431521d6928b08a6d75e17676219dd64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5089dc8320c35b7068b66001e2b69f8.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe716b3a010661bc2ffd99a6263c5108.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90e8d5d7fed033f48270b1ff825fcd5.png)
(3)能否保证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6ae35ea314b3b3c56dc3500e14aa8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d145687ec9531a97ab689a0a17023f.png)
您最近一年使用:0次
5 . 已知二次函数
(
均为实数),满足
,对于任意实数
都有
,并且当
时,有
.
(1)求
的值;并证明:
;
(2)当
且
取得最小值时,函数
(
为实数)单调递增,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd0587f5d6a3b5db9e4a93e0dbc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c766352f0be38b719621052de92615bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fffcb16e0156bb695b6f97b5c654661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff133c17652425c22f0b367e002797df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd53e5d21d735d3d2dfb6ee01ec2650c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17d9b0379b2b27da73d525d61de9093.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bde2e500fd5386e355db9040a1946d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461d9ebddd8fd839073485e9dc113256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434e938638cced59180fb39abbf78b95.png)
您最近一年使用:0次
名校
6 . 已知二次函数
(
均为实数),满足
,对于任意实数
都有
,并且当
时,有
.
(1)求
的值;并证明:
;
(2)当
且
取得最小值时,函数
(
为实数)单调递增,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd0587f5d6a3b5db9e4a93e0dbc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c766352f0be38b719621052de92615bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fffcb16e0156bb695b6f97b5c654661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff133c17652425c22f0b367e002797df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd53e5d21d735d3d2dfb6ee01ec2650c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17d9b0379b2b27da73d525d61de9093.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bde2e500fd5386e355db9040a1946d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461d9ebddd8fd839073485e9dc113256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434e938638cced59180fb39abbf78b95.png)
您最近一年使用:0次
2017-09-02更新
|
51次组卷
|
2卷引用:贵州省铜仁一中2016-2017学年高二下学期期末数学(文)试题
真题
解题方法
7 . 设函数
.
上画出函数
的图象;
(2)设集合
,
.试判断集合
和
之间的关系,并给出证明;
(3)当
时,求证:在区间
上,
的图象位于函数
图象的上方.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958d83c38fd1f4804df2dd7ce6146dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4af5195336841d2264ee3a00ae43f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91522a897fd4b8ce8c92bbb1ddd7f896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ab25013a9111e850d7258a5f1cd625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9589f30699d1a766f1e700cc88a344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0581fcaa2dcf917479091fded7f5b21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41825f0c6368611094133ee11b9638cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2016-12-04更新
|
466次组卷
|
5卷引用:2006年普通高等学校春季招生考试数学试题(上海卷)
2006年普通高等学校春季招生考试数学试题(上海卷)2017届江西南昌新课标高三一轮复习训练三数学试卷(已下线)专题02+二次函数-2020-2021学年新教材高一数学寒假辅导讲义(沪教版2020)北京名校2023届高三一轮总复习 第2章 函数与导数 2.8 函数的图象(已下线)专题11 不等式中的恒成立问题的求解策略(一题多变)
2024高三·全国·专题练习
解题方法
8 . 正四棱锥
的外接球半径为R,内切球半径为r,求证:
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff3606c7bf728b4f539261461cde677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
您最近一年使用:0次
解题方法
9 . 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)
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名校
10 . 已知函数
,(
,a为常数).
(1)讨论函数
的奇偶性;
(2)若函数
有3个零点,求实数a的取值范围;
(3)记
,若
与
在
有两个互异的交点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a39a5005c53d0e72546c0dfda5fdd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b348ef9ae62245f05324c52dc03e53.png)
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