1 . 已知函数
,若函数
恰有6个零点,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e205ba02c6f9795f0de51775cdd17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d274a9a2bfafc648ec0e420a5777b9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:天津市静海区第一中学2021-2022学年高三上学期第一次阶段检测数学试题
2 . 已知数列
为等差数列,数列
为等比数列,且
,
,
,
.
(1)求
,
的通项公式.
(2)已知
,求数列
的前2n项和
.
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f81b63fc0cffb75cc6aeae64591277c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a72a928a6bcde50c7e502669880892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c72dc9034f1aca2b4ef5afb4475c66.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd37f8bb8b52db13ba5c48b878de23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5e7f98ec8f4ea9b9492405094c5380.png)
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解题方法
3 . 已知正实数a,b满足
,则
的最小值为___________ .
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d66a894fe1c8dddb41d9e4885e979a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c36723680999121c79ad8ee75d2b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b098834e9a4a77cb48ffcaa17858a8.png)
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4 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c5c8af0f6d0a59247ed2f4ae1b90c2.png)
(1)若函数
在
上单调递增,求
的最小值.
(2)证明:当
时,
;
(3)若对于任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c5c8af0f6d0a59247ed2f4ae1b90c2.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468955192675ea33da77c042bb5664e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d74217631c5420650c5746bc9300e47b.png)
(3)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08972617a44cef00eca0d4f98f4a383c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:天津市静海区第一中学2021-2022学年高三上学期第二次阶段检测数学试题
天津市静海区第一中学2021-2022学年高三上学期第二次阶段检测数学试题天津市实验中学2022-2023学年高三上学期第二阶段学习质量检测数学试题(已下线)江西省九所重点中学2023届高三第二次联考联合考试数学(文)试题变式题21-23
5 . 已知数列
是公差为2的等差数列,其前8项的和为64.数列
是公比大于0的等比数列,
,
.
(1)求数列
和
的通项公式;
(2)记
,求数列
的前
项和
;
(3)记
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd86fd3108963fbf87c75d504fa40cf.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9037368a39bb0bff26415939c77359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cf77695058b0b8e6b8ac8fd090137d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
6 . 在三棱锥
中,
底面
,
,
,
为
的中点,球
为三棱锥
的外接球,
是球
上任一点,若三棱锥
体积的最大值是
,则球
的体积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c924e35451cb9e54f9dfc60c0c061052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790c0a17ee2d7181ee95da741694bd1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae1de3f5eb55a078a2dc8d2a585b86a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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9卷引用:天津市静海区第一中学2021届高三下学期三模数学试题
天津市静海区第一中学2021届高三下学期三模数学试题湖北省“宜荆荆恩”2022-2023学年高三上学期起点考试数学试题江苏省扬州中学2022-2023学年高二上学期开学质量检测数学试题(已下线)专题3 空间几何体的体积运算(提升版)辽宁省铁岭市六校协作体2022-2023学年高三上学期第一次联考数学试题(已下线)专题15 立体几何(讲义)-2广东省广州市铁一,广附,广外2023届高三上学期三校联考数学试题(已下线)第5题 立体几何中以外接球为背景的最值问题(压轴小题)(已下线)重难点08 玩转外接球、内切球、棱切球经典问题-【帮课堂】(苏教版2019必修第二册)
7 . 设函数
.
(1)若
,求
在点
处的切线方程;
(2)求
的单调区间;
(3)若
,求证:在
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4011837b3c81c04499dc7fa1edafbed3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd13d230c1af5ec3772f7ff5bef35ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea59cee971344ed593ff082a65d177c2.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cf62a02057141c8d8665aea1bd9ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
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名校
解题方法
8 . (1)已知函数
,若对
都有
,求实数
的取值范围.
(2)设函数
,若对任意
,
,不等式
恒成立,求实数t的取值范围.
(3)若函数f(x)、g(x)分别为R上的奇函数、偶函数,且满足f(x)+g(x)=2x,若不等式
对任意![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d535fecb9688b6a07901bcceb0f338e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa2686060312ed2221ad9de62c260c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f9c1637fcfca0a2be89a6f7bc4f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0237ce2177500476b13b709e0370564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4f4a5c7d050086cd21767c37e17670.png)
(3)若函数f(x)、g(x)分别为R上的奇函数、偶函数,且满足f(x)+g(x)=2x,若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5380cc894eeb8405fbfd30e5a629d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02afb6613b182e45f56cd05e5fe838c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . (1)已知
若
使得
成立 ,求实数a的取值范围.本题解题的关键是应把“
”这一条件转化为
(2)
,
均有
成立,求实数
的取值范围.请写出本题的转化过程,不用计算结果.
(3)已知函数
,
,
是函数
的极值点,若对任意
的,总存在的
,使得
成立,求实数
的取值范围.本题解题的关键是应把“
”这一条件转化为
(4)已知函数
,若存在
,
,使得
,求
的取值范围.
(5) 已知函数
.若
,
是
的两个极值点,且
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d889aed83eb3de697e4941cc172d65d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c20cebe242708e2e5be1041bdea2e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c368430c7da48f551da8e33aeb3ec0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c368430c7da48f551da8e33aeb3ec0dd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9edacf657300060f533d04cd839bd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e3b2e97106a0651d6756f471e0a610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9435bef426cc8838bfe7511c5e5e7c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1deedac12588a3152e165475dfbaa5ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a61d77911527508524874b212a0937d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36bfb9e7afc6c1a6a5a5dca07d984517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4672f1227c57dd7b11339df9dcdd86b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eca5c282908fef3f0481e376f42c490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eca5c282908fef3f0481e376f42c490.png)
(4)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b62eeec71822417b38cae64d9c43620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2e078c61be9422d603d19368f10f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbf8da534490147db4fee75f71a4c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03bcc0761987a294cda9ca59f5d7e2e.png)
(5) 已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c73eb4532373dc5f9e3408b8b9640c.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/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795ed79c2a310d99c9111255d0dc4f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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10 . 已知
,若
的图象与
轴有3个不同的交点,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb1e9e95264ce1975c8290a25ca8ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982162499da753ce02dc03b0b61185fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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