名校
1 . 已知函数
.
(1)若
,求
的取值范围;
(2)证明:若
有两个零点
,
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df4df8dfa21aa179a98e59bfc7e7225.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](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/b725fdc8de9800f2692f6fea8585b1e9.png)
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解题方法
2 . 已知函数
.
(1)求
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5095035eda4a17fcc5e3eb08e1bbc1e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0be008244415bbd9ed88ce2ce788b48.png)
您最近一年使用:0次
2024高三下·全国·专题练习
解题方法
3 . 已知
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b4bf28a8821e3b58f01ebc5ed3495a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979356078a3322f96656245d1a583541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bdc8d2686a05f12a2ba8a7e3b01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28c41699d9d4f7ddc6cf9088651a816.png)
您最近一年使用:0次
4 . 为方便起见,记一年有365天,并假设每个人的生日在365天中的任意一天都是等可能的. “生日悖论”指:在不少于23个人的群体中,至少有两人生日相同的概率大于50%. 记事件
为“前k人中没有人生日相同”,其中
.
(1)证明:
;
(2)直接写出
的值
,并证明:如果一个班上有不少于23人,则这个班上至少有两人生日相同的概率大于
.
附:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c365eeee68c896623c8a9f4d1a4e0f7.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a975274a249a3930dade65b9e18dc5c.png)
(2)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9608790a944853b9e821ca48524c9f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9eea0153d6a56d88711b4abff1cd006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1065ae0947705c7d16a5a86c78f07e.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff04e1cf282e286ce07c90778f2104b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa16301d1eaa8aa385e0b08645f9dc01.png)
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名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141d819347adf2c2c8f2bd2c99115809.png)
(1)求函数
的极值;
(2)当
时,求证:函数
有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141d819347adf2c2c8f2bd2c99115809.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db8f867196410e2828e2bbd3183b02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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6 . 已知函数
.
(1)
时,证明:
时,
;
(2)讨论
的单调性;
(3)若
有两个零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079bca332f2776ab9d14a684ab8d3673.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfdecc7f8089cb23c20d0a93ee1b601.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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名校
解题方法
7 . 已知函数
在
处取得极大值.
(1)求a的取值集合;
(2)当
时,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e1b7c9639ccc0708bb53ca1cfe9958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(1)求a的取值集合;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1dd527d52b5d03a2ef9e944d8034312.png)
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8 . 数列
满足
,
(
).
(1)计算
,
,猜想数列
的通项公式并证明;
(2)求数列
的前
项和;
(3)设
(
),数列
前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be815a472dbc3112591a3c311750b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109c4b28048ec9e72ba8ecd6311d9f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f87f83fa06ebdc980a6b307d7f54ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ea385391aa939b21c3ce2a1437fac4.png)
您最近一年使用:0次
2024高三下·全国·专题练习
解题方法
9 . 已知函数
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a4e15ae804d351f68e610ffe557b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c944c1c2791f64d1f371d43e9a419983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2484f4dc493a45dae01bb8d385ee14e5.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(1)讨论函数
的单调性;
(2)设
,且
是
的极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd17cccf50bedddbe7cc884859b666de.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb9d122303991da6c5aabcb4bc5ebea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842f26730d4d5544c28dd31f9626c3f9.png)
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2024-05-04更新
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836次组卷
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2卷引用:四川省成都市石室中学2024届高三下期三诊模拟考试文科数学试卷