1 . 已知等比数列
的通项公式
,则数列
的公比为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e599af66bf0195b85b43c4be5dba1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.3 | B.2 | C.![]() | D.![]() |
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2 . 设某质点的位移
与时间
的关系是
,则质点在第
时的瞬时速度等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3bde6ef2ee5b749b4d48d706543cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1a48b92c61d209d0556e4cd8fdb70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec4a19f56baeea881b281b58f4429e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3969843b1771e774869ef6fac681269.png)
A.5m/s | B.6m/s | C.7m/s | D.8m/s |
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3 . 下列结论中正确的是( )
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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4 . 已知等差数列
的前
项和为
,且
,
.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,且
.再从条件①、条件②、条件③这三个条件中选择一个作为已知,使得数列
唯一确定,并解答以下问题:
(ⅰ)求
的通项公式;
(ⅱ)若
,求
的最小值.
条件①:
;条件②:
;条件③:
.注:如果选择条件①、条件②和条件③分别解答,按第一个解答计分.
![](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/22c5c4ac959eb2c4b74afabc9cdd3a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dfe5b322577f02fd19caab8cf20170.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a1d79c7172a96f95f6fb3fc1271078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412915890d2cfcf9f639f922826d9a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809bcb2d19fbda33ff39b07358d26543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80bd1a3a5da2db17e41c62fa5bae69b.png)
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5 . 某公园为了美化游园环境,计划修建一个如图所示的总面积为
的矩形花园.图中阴影部分是宽度为1m的小路,中间
,
,
三个矩形区域将种植牡丹、郁金香、月季(其中
,
区域的形状、大小完全相同).设矩形花园的一条边长为
,鲜花种植的总面积为
.
的代数式表示
;
(2)当
的值为多少时,才能使鲜花种植的总面积最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c084f46accb2bd9638261edba4a0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3bde6ef2ee5b749b4d48d706543cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baaa2d65026770c5505f8adeb450e43b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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6 . 函数
的图象如图所示,设
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e63d450091d86d91557f4d39c3de6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0368995a83d85875efe6bb0cd3781fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93707ac95d1b7fe2a672da31b927371.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知等比数列
的前
项和为
,若
,
,则公比
( )
![](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/3e8c45e4c4ab30665338dd87a2258f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41be41a5a4965ebd346e7ee74d21f0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
A.![]() | B.1 | C.![]() | D.3 |
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8 . 已知函数
,则下列结论中错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedb5306174619fe56d3e9438b7134dd.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.存在实数![]() ![]() ![]() |
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解题方法
9 . 已知函数
,则
的极小值等于__________ ;若
在区间
上存在最小值,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4163fd5df0182f4c37d0d586ffb3d85e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea68078761468f2310510e11408d099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 若1,
,2成等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
A.![]() | B.![]() | C.![]() | D.3 |
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