名校
1 . 根据多元微分求条件极值理论,要求二元函数
在约束条件
的可能极值点,首先构造出一个拉格朗日辅助函数
,其中
为拉格朗日系数.分别对
中的
部分求导,并使之为0,得到三个方程组,如下:
,解此方程组,得出解
,就是二元函数
在约束条件
的可能极值点.
的值代入到
中即为极值.
补充说明:【例】求函数
关于变量
的导数.即:将变量
当做常数,即:
,下标加上
,代表对自变量x进行求导.即拉格朗日乘数法方程组之中的
表示分别对
进行求导.
(1)求函数
关于变量
的导数并求当
处的导数值.
(2)利用拉格朗日乘数法求:设实数
满足
,求
的最大值.
(3)①若
为实数,且
,证明:
.
②设
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a1d0dba29a77dd111efcde543d6c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4c14935585e8fa61d032730867d771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b6f154c6b2de5695eb1807b98c2c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809615d1f91508e2c6c0cda7e592c479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244021f826099b18e31af1143597bba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5be11a5e6aaf00b2833930b198b4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a1d0dba29a77dd111efcde543d6c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4c14935585e8fa61d032730867d771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c3c1ed4fb65ab9505ad8078d8d0fb5.png)
补充说明:【例】求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7ca0caa9933b7afd4bed2683140a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebdee8d81b048b5aa520f7e8ba56ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e15a54c6122c695239107dd0901bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244021f826099b18e31af1143597bba2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3d9ab2fcf15b94f33cb64f84ed906c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)利用拉格朗日乘数法求:设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c45d8122b61de13875003d00c002c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de725a9fc66f67abbe0015131846a648.png)
(3)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e778f95c72fec00bfbbc63e6dfd0c460.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497d269c30eec393e3f0e877ddbe2983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade042c085bbad8aeaf111b9f4c33408.png)
您最近一年使用:0次
解题方法
2 . 在组合恒等式的证明中,构造一个具体的计数模型从而证明组合恒等式的方法叫做组合分析法,该方法体现了数学的简洁美,我们将通过如下的例子感受其妙处所在.
(1)对于
元一次方程
,试求其正整数解的个数;
(2)对于
元一次方程组
,试求其非负整数解的个数;
(3)证明:
(可不使用组合分析法证明).
注:
与
可视为二元一次方程的两组不同解.
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114b84ba3234b9bb1bf9f64c172292d7.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa38e21db62123319c9557d1bc52825d.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63a043e64f7ed5d168cd2c9384e953b.png)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65fe832c0460e00120d4bc3636aebcaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6c8fe63bb58df1c5a12422e9c9e291.png)
您最近一年使用:0次
2024-03-08更新
|
1125次组卷
|
3卷引用:广东省五粤名校联盟2024届高三第一次联考数学试题
名校
解题方法
3 . 利用方程的方法可以将无限循环小数化为分数,例如将
化为分数是这样计算的:设
,则
,即
,解得
.
这是一种利用方程求解具有无限过程的问题的方法,这种方法在高中计算无限概率、无限期望问题时都有很好的妙用.
已知甲、乙两人进行乒乓球比赛,每局比赛甲获胜的概率为
,乙获胜的概率为
,每局比赛的结果互不影响.规定:净胜
局指的是一方比另一方多胜
局.
(1)如果约定先获得净胜两局者获胜,求恰好4局结束比赛的概率;
(2)如果约定先获得净胜三局者获胜,那么在比赛过程中,甲可能净胜
局.设甲在净胜
局时,继续比赛甲获胜的概率为
,比赛结束(甲、乙有一方先净胜三局)时需进行的局数为
,期望为
.
①求甲获胜的概率
;
②求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f522d1f7a4158bbb09355fcf2ebe1748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd96b78172b97a5fb995bc4fe7a91312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9a257d22b01103a676795f6a6b399e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8567750e1eb0471c3942c1456cdf2299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fae7b60887e1ae9ff3f6b2b959762e.png)
这是一种利用方程求解具有无限过程的问题的方法,这种方法在高中计算无限概率、无限期望问题时都有很好的妙用.
已知甲、乙两人进行乒乓球比赛,每局比赛甲获胜的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)如果约定先获得净胜两局者获胜,求恰好4局结束比赛的概率;
(2)如果约定先获得净胜三局者获胜,那么在比赛过程中,甲可能净胜
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68061f9674fb257c62da194bebd65289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c709117ab1d3ef620883a732aed68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b678dec65a0ca8006cc6828d8cb501.png)
①求甲获胜的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc8a872d7b16187634e8db2571c8cbe.png)
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2024-06-09更新
|
1314次组卷
|
2卷引用:湖北省武汉市武昌区2024届高三下学期5月质量检测数学试卷
解题方法
4 . 大力开展体育运动,增强学生体质,是学校教育的重要目标之一.某校组织全校学生进行了立定跳远训练,为了解训练的效果,从该校男生中随机抽出100人进行立定跳远达标测试,成绩(单位:米)均在
内,整理数据得到如下频率分布直方图.学校规定男生立定跳远2.05米及以上为达标,否则不达标.
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974373271633920/2975164936478720/STEM/e78eef27-5c24-4fa7-b5f5-c354c5e6b86b.png?resizew=397)
(1)若男生立定跳远的达标率低于60%,该校男生还需加强立定跳远训练.请你通过计算,判断该校男生是否还需加强立定跳远训练;
(2)从该校随机抽取的100名立定跳远成绩在
和
内的男生中,用分层抽样的方法抽取7人,再从这7人中随机抽取2人,求这2人来自不同区间的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613af564447c34564fc04450a28598f1.png)
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974373271633920/2975164936478720/STEM/e78eef27-5c24-4fa7-b5f5-c354c5e6b86b.png?resizew=397)
(1)若男生立定跳远的达标率低于60%,该校男生还需加强立定跳远训练.请你通过计算,判断该校男生是否还需加强立定跳远训练;
(2)从该校随机抽取的100名立定跳远成绩在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6da010cdabd6762d8a7796310589c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e32dd67dd6517fc1079a71945d0682d.png)
您最近一年使用:0次
5 . 已知
,不等式
恒成立.
(1)求
的值
;
(2)若方程
有且仅有一个实数解,求ab的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a788b2d8cce011455e549a59ebc5c92b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce9dc4b97804d00d682fed1b04a7eb0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a8eb19e30aa486abf1b0dfb3d3bd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5cbe4c9cd2831801f4a564641b8d90.png)
您最近一年使用:0次
解题方法
6 . 1799年,哥廷根大学的高斯在其博士论文中证明了如下定理:任何复系数一元
次多项式方程在复数域上至少有一根(
).此定理被称为代数基本定理,在代数乃至整个数学中起着基础作用.由此定理还可以推出以下重要结论:
次复系数多项式方程在复数域内有且只有
个根(重根按重数计算).对于
次复系数多项式
,其中
,
,
,若方程
有
个复根
,则有如下的高阶韦达定理:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68be203b2490ecce4c0e2eadeb5d911b.png)
(1)在复数域内解方程
;
(2)若三次方程
的三个根分别是
,
,
(
为虚数单位),求
,
,
的值;
(3)在
的多项式
中,已知
,
,
,
为非零实数,且方程
的根恰好全是正实数,求出该方程的所有根(用含
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b024d78f428194127b5534f948810def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7230de53663c75658c58bbf206a0085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bed25da42194b5a81d123933d5704f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3759b3561834cdc5b499b91f3850d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83590c4a7ea5636843dd4b60c67cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68be203b2490ecce4c0e2eadeb5d911b.png)
(1)在复数域内解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4800c5aa0e5b70b2141541cbd3853e34.png)
(2)若三次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac603c0b3d1d7fd42bd50222b6ab94d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6755cd39b121a0dd2a14da8d43c1fff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddb97874a62bb5530514a467d64af13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8079c5a2d8674d322f7abe6d4ef4a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b024d78f428194127b5534f948810def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb3db0a99f86232e0cf3e55c789ea99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2e2674707c28eddd3f3ab60f73f54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c37d6353f394a5704a92113908a5c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2022·上海·模拟预测
7 . 已知函数
,甲变化:
;乙变化:
,
.
(1)若
,
,
经甲变化得到
,求方程
的解;
(2)若
,
经乙变化得到
,求不等式
的解集;
(3)若
在
上单调递增,将
先进行甲变化得到
,再将
进行乙变化得到
;将
先进行乙变化得到
,再将
进行甲变化得到
,若对任意
,总存在
成立,求证:
在R上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e746284f8292034744ef19606f34ba0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7da1ccb2c68857801d3684316685994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697a2a61d367fe01830b6b5995a2c38d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3deb8eb89eb6be966c64d81acb292b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef23cf7d8c1b7e52a15e052768cd055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b1f3ace6bd767fe4a26dc8098b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b1f3ace6bd767fe4a26dc8098b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf729dc97c117b83cfa0769e02e3ce1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e15191afd613e5d8215bfa73ac86ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
8 . 将2024表示成5个正整数
,
,
,
,
之和,得到方程
①,称五元有序数组
为方程①的解,对于上述的五元有序数组
,当
时,若
,则称
是
密集的一组解.
(1)方程①是否存在一组解
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26725aac8b4a6bf2052893147177a472.png)
等于同一常数?若存在,请求出该常数;若不存在,请说明理由;
(2)方程①的解中共有多少组是
密集的?
(3)记
,问
是否存在最小值?若存在,请求出
的最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9b42973c53907f09f2de384c42fc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73533ed62f52983da9c3f47e0e84d1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c6ecc1d55a020c1c5105b1c5118730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df660c0848f32943b63bbe22189611be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d2f074101ec58868493992814a2ff9.png)
(1)方程①是否存在一组解
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68fb8f0cc81e38b337e8ed4c7e2479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26725aac8b4a6bf2052893147177a472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19482c76310dc031696d73de0894016.png)
(2)方程①的解中共有多少组是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e0c84de10f0f2186313169c3dc997b.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d91750d298e9d685b9eacb994e7a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2024-03-13更新
|
1216次组卷
|
3卷引用:广东省江门市2024届高三一模考试数学试卷
名校
解题方法
9 . 已知
,且
.
(1)解关于
的不等式:
;
(2)求证:对任意
恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976738081afc41550f88aca83861c1b4.png)
(2)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8deae40c582f0759f3d01acb1c0c6c.png)
您最近一年使用:0次
2023-03-30更新
|
336次组卷
|
3卷引用:贵州省2023届高三考前备考指导解压卷数学(理)试题
2022·上海浦东新·模拟预测
名校
解题方法
10 . 已知定义域为
的函数
.当
时,若
(
,
)是增函数,则称
是一个“
函数”.
(1)判断函数
(
)是否为
函数,并说明理由;
(2)若定义域为
的
函数
满足
,解关于
的不等式
;
(3)设
是满足下列条件的定义域为
的函数
组成的集合:①对任意
,
都是
函数;②
,
. 若
对一切
和所有
成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24600bfcfb91c661eb9d237956e011ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0a5af03cc59bf58c1385988a746668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd5f68f8223717c5f9e7a35da919f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5707b77c17eca36e53457fdbc7912ae.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b0cf56d1d3347f1301e42197259c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59df0f69cdcb8bbd1e7369d3b730ab6.png)
(2)若定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72dfa26de75e699e91401e1c7769db70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78db8978ef52545c2d1effc0f52b7f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8528f8c2cefedbaedb13cd43540357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8562a7044c527888e2dd7fa42feda7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8321b2ac0cb0a0d6aa579dcbc9578ec.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac532cbc6695639c3816e49c809aed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2288a34a490fd0c8f4d566959a1e97b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2972af8c65701183de194c358b83256c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7576241e80f3fdd887fed12ebb5d2273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a824bb87d715617e270c800204d7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01d67fd2a155c3dd322dc971370a4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ae7943f38c810776e3dab3a8587f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa10bec00d5ea02234be29a9fd92a647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-07-05更新
|
1753次组卷
|
8卷引用:上海市华东师范大学第二附属中学2022届高三考前模拟数学试题
(已下线)上海市华东师范大学第二附属中学2022届高三考前模拟数学试题2024届高三新高考改革数学适应性练习(九省联考题型)(已下线)考向10函数与导数(重点)-2上海市行知中学2023届高三上学期10月月考数学试题上海市曹杨第二中学2023届高三上学期12月月考数学试题广东省广州市华附2023-2024学年高一上学期期中数学试题(已下线)第三章 函数的概念与性质单元测试基础卷-人教A版(2019)必修第一册广东省茂名市电白区第一中学2023-2024学年高一下学期4月月考数学试题