名校
解题方法
1 . 设
,
,
是不全相等的实数,随机变量
取值为
,
,
的概率都是
,随机变量
取值为
,
,
的概率也都是
,则( )
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4cdd0dbc2da1b63c3718d7e4aed12f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4976036205aef7be17bd77d381735ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeae74ffd434af867c7a08a87259d4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2 . 在数列
中,
,
.给出下列三个结论:
①存在正整数
,当
时,
;
②存在正整数
,当
时,
;
③存在正整数
,当
时,
.
其中所有正确结论的序号是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9871684eaddd74a5ffa9f907790acdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec8e838690c44786ee8343b57904b3e.png)
①存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65fe91daf4622edddc49cf828e132432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/facdd0916180bd028327e523bdcd3f52.png)
②存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65fe91daf4622edddc49cf828e132432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd3e65f0f4bf3e5fb6570df7fb60510.png)
③存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65fe91daf4622edddc49cf828e132432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b034b89c013225cb2117287dc0a8c61.png)
其中所有正确结论的序号是
您最近一年使用:0次
3 . 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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名校
解题方法
4 . 将椭圆
上所有点的横坐标伸长为原来的
倍,纵坐标伸长为原来的
倍得到椭圆
,设
的离心率分别为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e48d1edbfb6a5a48f9a95551d1dbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee74315c62da704465b46d9baaf26c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d45e896826de39e9704cb71b508224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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名校
解题方法
5 . 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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名校
解题方法
6 . 某同学参加一次测试,该测试共有10道选择题,每做对1道得10分,做错1道扣10分,不做得0分,60分及格.该同学已经完成了5道题的作答,且都正确,已知剩下的每道题他做对的概率均为
.记该同学做
道题且及格的概率为
.
(1)求
;
(2)试求
取得最大值时n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
(2)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
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7 . 设正整数
,有穷数列
满足
,且
,定义积值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36bd11e8ffb70eac461dc4768b840a.png)
(1)若
时,数列
与数列
的S的值分别为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a1568c0bf07f285b2e01c3a3a55900.png)
①试比较
与
的大小关系;
②若数列
的S满足
,请写出一个满足条件的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcaa1756eafc97696d69068689892c8.png)
(2)若
时,数列
存在
使得
,将
,
分别调整为
,
,其它2个
,令
数列
调整前后的积值分别为
,写出
的大小关系并给出证明;
(3)求
的最大值,并确定S取最大值时
所满足的条件,并进行证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83056c039e255d1ca7e26b756f3a6d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b99718e1bce4057550e1aef19c82b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36bd11e8ffb70eac461dc4768b840a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b801f41875296c26e893f492af633bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a422e11339ddc763ada97021f03722a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a1568c0bf07f285b2e01c3a3a55900.png)
①试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5769559be3487868d334c66d130360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcaa1756eafc97696d69068689892c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a58d2f2ef54bddedcb3ca40b1b43bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c973c75e2e9209e2a22e3deb453e0cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e57093fadaaa08e9ac73e855221525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711e95f069a685da11ff70b16504578a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d03382cb64aca02dd52d8196abb804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c5515db76e233bad7f418cfbcbc0b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f021e668a3bb0b84447138c33a6ca188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a3fc7a52b6b15e855cd22bdf8d00bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a58d2f2ef54bddedcb3ca40b1b43bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab93d9afb14d07b81567d47207c4be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab93d9afb14d07b81567d47207c4be0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c11e6c8be2cb8384953b3f19f7b77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
您最近一年使用:0次
8 . “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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9 . 已知数列
的前n项和为
,且
,
,则( )
![](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/e31fb9cdc11d44c3dcab0488366ad458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6691617159667fcfc3f6ce9146cd075a.png)
A.当![]() ![]() | B.![]() |
C.数列![]() ![]() | D.当![]() ![]() |
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10 . 已知等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8430c0f580ff69646229842c38fab9.png)
(1)若
均为正整数,求
的值;
(2)设
,
分别是分式
中的
取
(
>
>2)时所对应的值,试比较
的大小,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8430c0f580ff69646229842c38fab9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6703fce72e701fd5d9be3e25448d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9724cf149ccc974596673c8aaae9558f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e327c14ae50f0f10478a6c751c26fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a550c916c64f621010e604a30ef67566.png)
您最近一年使用:0次