名校
1 . 已知函数
,数列
满足
,则“
为递增数列”是“
”的( )条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbb5429ea1389a06d947ae0fcd74002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44fbf454da8f3c7555e03484f4191e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b3108b3a2a39b0ef539fced4c4b9ce.png)
A.充分不必要 | B.必要不充分 | C.充分必要 | D.既不充分又不必要 |
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解题方法
2 . 若函数
在
上单调,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed93bb6664373ad0c9f2acf2f1f773f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574bdac28b1dcbf03f0fb903e8d0b49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知函数
恰有两个零点,则实数
的取值范围是____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e626aba63d0e1b140650454b9afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知
为等差数列,
为各项均为正数的等比数列,
.
(1)求
和
的通项公式;
(2)求
的前
项和;
(3)若对任意
,有
恒成立,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c441d153bb85e08d02f079496125f4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec8b68d90e55b00b6662a23f851cca89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bd8c5d3cc62cb0d57249d00a585fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
5 . 已知函数
(其中常数
),
,
是函数
的一个极值点.
(1)求
的解析式;
(2)求
在
上的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ddcd70531c74018798d730e00aa5df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d2cbfc4c4eb61b781eaaa6570147af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
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6 . 已知函数
,关于
的性质,有以下四个推断:
①
的定义域是
;
②
的值域是
;
③
是奇函数;
④
是区间
上的增函数.
其中判断正确的选项是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aafb21bf0b3e9040907f773cf4e0610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf620d67c6625a449b5238d61b1c0e3.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d1805dc28d18576b8b49b98d8b438c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e4586d136ad18160316ea6eed15e22.png)
其中判断正确的选项是
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7 . 袋中有大小相同、质量相等的3个白球和2个黑球,若每次抽取1个球,有放回地连续抽取3次,则恰有1次取到黑球的概率为________ ;取到黑球的个数
的数学期望是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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解题方法
8 . 若函数
在区间
内为增函数,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e53c52ba6d187e4be564e7f1cd581b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f26f6cc6cf7d49eeffa37036436bc54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 集合
,集合
,若集合
中元素个数为
,且所有元素从小到大排列后是等差数列,则称集合
为“好集合”.
(1)判断集合
是否为“好集合”;
(2)若集合
是“好集合”,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5578681bed3f7e22b91cfc962045be26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e22e3abe1a2ef8554b4f0f828e4e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d00b592b51981ec491c1a1275593143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db050d01622e491d82b2e809bfc634bc.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90d2e374073f702dbaaa29f34815fd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 已知函数
,其中
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求函数
在
上的最大值;
(3)当
时,求函数
的单调区间;
(4)证明:当
时,函数
有且仅有一个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd87c16c5452e4a6adc228998bc944a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ed49839c4dc0b033431d88a4c1f94.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c0a8155f5a6af42d37856f6c95a0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(4)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db0eb7b60e88da1d807797cb17f85d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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