名校
1 . 已知函数
,
.
(1)试比较
与
的大小;
(2)若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da03d776579dde13f36c82b72d21c735.png)
(1)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9edd5fb06678dd2cd97d38907b64049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2 . 已知椭圆
的离心率为
分别是G的左、右顶点,F是G的右焦点.
(1)求m的值及点
的坐标;
(2)设P是椭圆G上异于顶点的动点,点Q在直线
上,且
,直线
与x轴交于点M.比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c39d8227c3f373e6dae8e46fd410f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a16354f17e5e6c9943cc721d63f830f.png)
(1)求m的值及点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)设P是椭圆G上异于顶点的动点,点Q在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a3b3ab26376be3df144adc6ec6bbea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea2c1df63a599a774043f6c3b881ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30c8db27f13442553eacf2b144a75ec.png)
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解题方法
3 . 太阳能板供电是节约能源的体现,其中包含电池板和蓄电池两个重要组件,太阳能板通过电池板将太阳能转换为电能,再将电能储存于蓄电池中.已知在一定条件下,入射光功率密度
(E为入射光能量且
为入射光入射有效面积),电池板转换效率
与入射光功率密度
成反比,且比例系数为k.
(1)若
平方米,求蓄电池电能储存量Q与E的关系式;
(2)现有铅酸蓄电池和锂离子蓄电池两种蓄电池可供选择,且铅酸蓄电池的放电量
,锂离子蓄电池的放电量
.设
,给定不同的Q,请分析并讨论为了使得太阳能板供电效果更好,应该选择哪种蓄电池?
注:①蓄电池电能储存量
;
②当S,k,Q一定时,蓄电池的放电量越大,太阳能板供电效果越好.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3aee8bff28232e09d20329385c4f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dff6ed9bba7966f45109293f516e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85298676cc2d8164251caaa0c727cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4199ddf8630e5a3a2ca7bcf52f542c.png)
(2)现有铅酸蓄电池和锂离子蓄电池两种蓄电池可供选择,且铅酸蓄电池的放电量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650ef6e693b37707e2f5918130ff677a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d0b32873983e1f3d86d56040c44dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa16d97ce54701e6d4da2924dfbd6395.png)
注:①蓄电池电能储存量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97102689f3743d1f174d119cc3f0d70e.png)
②当S,k,Q一定时,蓄电池的放电量越大,太阳能板供电效果越好.
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4 . “让式子丢掉次数”:伯努利不等式
伯努利不等式(Bernoulli’sInequality),又称贝努利不等式,是高等数学的分析不等式中最常见的一种不等式,由瑞士数学家雅各布·伯努利提出:对实数
,在
时,有不等式
成立;在
时,有不等式
成立.
(1)猜想伯努利不等式等号成立的条件;
(2)当
时,对伯努利不等式进行证明;
(3)考虑对多个变量的不等式问题.已知
是大于
的实数(全部同号),证明
伯努利不等式(Bernoulli’sInequality),又称贝努利不等式,是高等数学的分析不等式中最常见的一种不等式,由瑞士数学家雅各布·伯努利提出:对实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6339f512d6f801fde040ae9677056d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62a78f2a44f317b65a4d05f0c76a927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb83894d7274b0c36842fa7c51cc466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb986bcbf5c3c17aefc7ac8a1a68b82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267a28b9f6d9e9f5b761a94ca2075bb4.png)
(1)猜想伯努利不等式等号成立的条件;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4360c1b4a506c12bbdce41e73fb74d8.png)
(3)考虑对多个变量的不等式问题.已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206a6f31229c1b9905aca55c50369c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c450723559c1574d3a557bfb7e943fd6.png)
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名校
5 . 已知等比数列
的各项均为正数,且
.
(1)求数列
的通项公式;
(2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff2853ed2252ef24654888b3bea2084.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2597e30850f276a5fe5ae97bee20573a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacabd66c249e6b0b3562056718f7901.png)
您最近一年使用:0次
2024-01-10更新
|
1596次组卷
|
3卷引用:辽宁省沈阳市2023-2024学年高三上学期教学质量监测(一)数学试题
解题方法
6 . 已知
且
.
(1)若
,设
,比较
和
的大小;
(2)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f95dc1d6e605dfbe05b38f19685df87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ecda7bfb0a2043306bf7707a136ad0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f330fbbd672ffc482a77a5cbae0ad76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b23789f5aa1e63e9b40077fc09b8741.png)
您最近一年使用:0次
2023·全国·模拟预测
解题方法
7 . 已知数列
,其前n项和
满足
.
(1)求证:数列
为等差数列;
(2)若
,数列
满足
,
,
,记
为
的前n项和,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec87ad121ff72a3b8f0e266820315f8.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad65d45aa15a5eee838df9cd31c68ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd78c6771e53712d5d7965077c4964a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38ba43826135367d798e714aba0f014.png)
您最近一年使用:0次
2023·全国·模拟预测
解题方法
8 . (1)设a,b为正实数,求证:
.
(2)设a,b,c为正实数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81331a9dc1218bb13758e5e5b45ae366.png)
(2)设a,b,c为正实数,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e2989aee5089e4779c5e34a0c8134.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
,
.
(1)证明:
;
(2)比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d31d07e0e178dd81de9ab409d9475e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e612054a5481a0d6d1e7990be2782f.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b92ed9c28b600f6632dbc1f9fb6d5b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6e131ab54fd300ffe4ea493787d9a1.png)
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解题方法
10 . (1)已知
,求
的取值范围.
(2)比较
与
的大小,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b17fd7892f60c91b03f26fc7f09de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d6df06a5b85848dc4fa33327f8e07.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa92e64c41d5566b8f2388e43401824a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1750a69f0ee1dcb6bbb04d9cd8375791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aef458f2367b76432719f6f56275d8.png)
您最近一年使用:0次
2023-10-07更新
|
208次组卷
|
2卷引用:新疆维吾尔自治区喀什地区2024届高三上学期第一次模考数学试题