1 . 如图,在直四棱柱
中,底面
为菱形,
为
的中点.
(1)证明:直线
平面
;
(2)若
,且
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/533c27d9-b490-4d35-b107-c60cb120ade0.png?resizew=160)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7542b49ab149f2be8ba6b48392bef1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa3d0db9ad31d33c2883a6efed1dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9c4666ac5098d6cf61af1c82dab681.png)
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解题方法
2 . 已知函数
,关于
的方程
的实数根的个数为
,则
的所有可能取值组成的集合为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46cdf3be718ae88a923d5a1d64e9076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b14bd9b01ef01720d4b1cb9d90721a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
3 . 已知函数
是偶函数,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/6861a383-11d8-4f4e-b49d-9b7656e39d6a.png?resizew=240)
(1)求
的值,并作出函数
在区间
上的大致图象;
(2)根据定义证明
在区间
上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7b4162be068735915bfb30b315632c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/6861a383-11d8-4f4e-b49d-9b7656e39d6a.png?resizew=240)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a57e7e65245a4d173c5d0bc3c34e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16a685cbaf10f04e6bbe3d585c9298a.png)
(2)根据定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9099a75c433e97bbe05052a00110571.png)
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4 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59bb6539f03daf9ab48ea262586fddf.png)
(2)已知
是第二象限角,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59bb6539f03daf9ab48ea262586fddf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f04ae821930016c324ef80c1cc05c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a65ec6ff0e83185adf8cfa41b17245.png)
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5 . 已知函数
的最小正周期为
.
(1)求
的值,并求
的单调递减区间;
(2)求
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae19befa90729c2ffd8f57365fa0c76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
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6 . 已知函数
,将
图象上所有的点向右平移
个单位长度,得到函数
的图象,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d20e503e66086d64de7bbcbd6e9e339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c48e8b4a3e2ef13de1ad88f8ed2b4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
A.![]() |
B.![]() ![]() |
C.直线![]() ![]() |
D.若![]() ![]() ![]() |
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7 . 定义在
上的函数
满足:
①
,且
,都有
;
②
,都有
.
若
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5d9a0f5e3cbc65ea723d7d95a64265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c37532eee686de2828ce0c17ed8ad8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a61137add4c8583b26f47988be15bf.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01df857351773a26d9a7a3092bc67873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd09f80733a8c98bd8c51905d15fe5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知等比数列
的前
项和为
,数列
的前
项和为
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614306cc3f34bdee4d5d885b79667645.png)
__________ .
![](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/41cf1da18d91f7c98086553d157d1a87.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/120df84d1991d54f2a37ccf087f9546b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614306cc3f34bdee4d5d885b79667645.png)
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9 . 已知
,则正数
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbc019befb7b0c7f758ad64ea56d06c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 六盘水红心猕猴桃因富含维生素
及
等多种矿物质和18种氮基酸,被誉为“维
之王”.某收购商为了了解某种植基地的红心猕猴桃品质,从该基地随机摘下100个猕猴桃进行测重,其重量分布在区间
内(单位:克),根据样本数据作出频率分布直方图如下图所示.
的猕猴桃中抽取5个,再从这5个猕猴桃中随机抽取2个,求这2个猕猴桃重量均不小于90克的概率;
(2)已知该基地大约还有6000个猕猴桃,该收购商准备收购这批猕猴桃,提出了以下两种收购方案:方案一:所有猕猴桃均以20元每千克收购;方案二:小于90克的猕猴桃以10元每千克收购,不小于90克的猕猴桃以30元每千克收购;请你就这两种方案,通过计算为该猕猴桃基地选择最佳的出售方案.(同一组中的数据用该组区间的中点值代表,视频率为概率)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31b860524956257664abb6d410e9b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e2f5652e34ab5921c8086f3afa1500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84847f6b494ba78afce1e4001fc3d367.png)
(2)已知该基地大约还有6000个猕猴桃,该收购商准备收购这批猕猴桃,提出了以下两种收购方案:方案一:所有猕猴桃均以20元每千克收购;方案二:小于90克的猕猴桃以10元每千克收购,不小于90克的猕猴桃以30元每千克收购;请你就这两种方案,通过计算为该猕猴桃基地选择最佳的出售方案.(同一组中的数据用该组区间的中点值代表,视频率为概率)
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