1 . 中国数学家华罗庚倡导的“0.618优选法”在各领域都应用广泛,0.618就是黄金分割比
的近似值,古希腊的数学家毕达哥拉斯通过研究正五边形和正十边形的作图,发现了黄金分割率,黄金分割率的值也可以用
表示,即
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8382dcdb655ab1d049f8dba22fa467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3caf448beca2df4d2427360e93b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2268e01c5ae717b00e740bea1f1cc75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d570b6ab83255a9c08707b4eeea81d40.png)
A.![]() | B.1 | C.![]() | D.![]() |
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2 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f27f930806d4ee1a6ac77a0fa6c340.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9df49c32fa5cfd53197f65e1af42a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f27f930806d4ee1a6ac77a0fa6c340.png)
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3 . 数列
、
满足:
,
,
,其中
是数列
的前
项和.
(1)求数列
,
的通项公式;
(2)若
,都有
成立,求实数
的取值范围;
(3)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/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a49ef11731716bd34cef68a697d13c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea552c924173b924a160ce75d8f7dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2532e928dda51e91a70a26b60e309094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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4 . 已知
.
(1)求
的值.
(2)求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536e072eb0439a5e5b430cd55a129374.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c684f5c1cfb58c8729fbc075cee649.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a478e03877fd76050b8af0bf205d0e8c.png)
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5 . 已知
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b80751c98f9991b9cfc03923a98834.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718d8607cabf37d05ac6c02ada39762d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbe2212c10c3da621f550e8c6409bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c40f09bd444276b0e9939f052bfd782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b80751c98f9991b9cfc03923a98834.png)
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6 . 函数
(
,
,
)的一段图象如图所示.
的解析式;
(2)若不等式
在
上恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c830f1abf387dc0a165e9a397d5636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9531427f246890e815b7ed47e78daa78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e988da0b9f8c43f2fc068d71ce6c968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890b9e54643e3bdf813cc1d8a287143c.png)
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7 . 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n项和;
![](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/48f093c61867ee4ce75f951d46b9b123.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)
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8 . 已知数列
满足
,
,且对
,都有
.
(1)设
,证明数列
为等差数列;
(2)求数列
的通项公式.
(3)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3938fc9093a10b040b5ed9d18c876637.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfbfb3bd571b95bdb6a700b443119d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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9 . 已知函数
.
(1)若
,求曲线
在
处的切线方程;
(2)求函数
在
上的单调区间和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df71f8b32945f3915dd2a0b72593bed.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
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7日内更新
|
855次组卷
|
2卷引用:四川成华区某校2023-2024学年高二下学期期中考试数学试题
名校
解题方法
10 . 等差数列
的前
项和为
,且
,则
( )
![](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/2a98d817993ea57b143b0651a7483197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4e70b360f988fdbd92300ab22c4613.png)
A.18 | B.24 | C.27 | D.54 |
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