名校
1 . 在
平面上有一点列
、
、
、
、
,对每个正整数
,点
位于函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0588f0857e7a5e6312d5c49c3d17519d.png)
的图像上,且点
、点
与点
构成一个以
为顶角顶点的等腰三角形;
(1)求点
的纵坐标
的表达式;
(2)若对每个自然数
,以
、
、
为边长能构成一个三角形,求
的取值范围;
(3)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd67df25b5ec4927f554716b2ae6eaf.png)
,若
取(2)中确定的范围内的最小整数,问数列
的最大项的项数是多少?试说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c13955f18e011796d8c19a1b3cdca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4dedec1be0ecb7414f6333bcddbc0c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92129b48a5926f91d87d5c259af60741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0588f0857e7a5e6312d5c49c3d17519d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cf588c9f3d87ade316c899ded48edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae3a88c614758672f5d2f2149236476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9264ace0f81ad6261b83c6777722ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)若对每个自然数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a61a13583a33aea4b957969b35f858f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd67df25b5ec4927f554716b2ae6eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d307ec71820b6536453fbdb5069da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc5d10484bd7ecd36924b654e80090d.png)
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名校
解题方法
2 . 已知数列
满足
,
,
,n为正整数.
(1)证明:数列
是等比数列,并求通项公式;
(2)证明:数列
中的任意三项
,
,
都不成等差数列;
(3)若关于正整数n的不等式
的解集中有且仅有三个元素,求实数m的取值范围;
![](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/c4ceb3142d785fe846a8935df2e45500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d280d7c7637028f59649b3025e553cb7.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86177a9ae8baa220750bf7c7f2f41eae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ac33c2fdec7345569781f9e5f6227d.png)
(3)若关于正整数n的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18f925d1944df03865d6c45d2cdd130.png)
您最近一年使用:0次
2022-01-22更新
|
549次组卷
|
4卷引用:上海市川沙中学2023-2024学年高一下学期数学5月月考数学试卷
上海市川沙中学2023-2024学年高一下学期数学5月月考数学试卷上海市曹杨第二中学2021-2022学年高二上学期期末数学试题(已下线)第03讲 等比数列(核心考点讲与练)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)河北省邯郸市部分学校2023届高三上学期11月月考数学试题
名校
解题方法
3 . 已知二次函数
满足以下两个条件:①不等式
的解集是
②函数
在
上的最小值是3.
(Ⅰ)求
的解析式;
(Ⅱ)若点
在函数
的图象上,且
.
(ⅰ)求证:数列
为等比数列
(ⅱ)令
,是否存在正实数
,使不等式
对于一切的
恒成立?若存在,指出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc8350b12974ffc8d06fce36d158f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda688e214d77aa259c18afc0275b555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80a3d6ab4c74543c703a71926826dd6.png)
(ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136eaf36d164bf5ac378a4401c25263b.png)
(ⅱ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/816d808dd830e644b83910757c5d90b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4489542f50a9d4768ca3dd38e543c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2020-04-20更新
|
272次组卷
|
3卷引用:四川省绵阳南山中学实验学校2019-2020学年高一下学期开学考试数学(理)试题
四川省绵阳南山中学实验学校2019-2020学年高一下学期开学考试数学(理)试题四川省绵阳南山中学实验学校2019-2020学年高一下学期开学考试数学(文)试题(已下线)高一数学下学期开学摸底卷-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)
4 . 在数列
中,
对任意
成立,其中常数
.若关于
的不等式
的解集为
,则实数
的取值范围是_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596f2f87cdc40f3f24b8048d53b0d141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a0eb18734749893f5b26cd0be58a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4d7ef9279801234aa4c07724d923e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
5 . 下列说法中,正确的有__________ .(写出所有正确说法的序号)
①已知关于
的不等式
的解集为
,则实数
的取值范围是
.
②已知等比数列
的前
项和为
,则
、
、
也构成等比数列.
③已知函数
(其中
且
)在
上单调递减,且关于
的方程
恰有两个不相等的实数解,则
.
④已知
,且
,则
的最小值为
.
⑤在平面直角坐标系中,
为坐标原点,
则
的取值范围是
.
①已知关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/123c15869608f974b89771202442d3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9059219044592024f63637984f86be30.png)
②已知等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5188d6760683a860adab0cda195cdf80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd6fe11dfa538e67bfd63478fc428a1.png)
③已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d97ad2720a77862202ac613e9e77e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1e1c54b1a07850afba46754a27b32a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cdd93d95a9fb5f5cd7e8be3800ecdf.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0cb6220005e5dbd9999e537aa90d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3aa69c18639f94f0635ea4c07dc2dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b90f08f3dcf9f9c7fe7c0fced28bc9a.png)
⑤在平面直角坐标系中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04872f980977d25187ae6b80c2f04c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafb698ab3b41359de48221799569bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a35d07184600690b812ac5885ee66a.png)
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