1 . 已知函数
.
(1)求
的最小正周期;
(2)讨论
在
上的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc0afde68848a8c508051fd5f301e5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8a6bc34a61595f56e2c5fc594d0475.png)
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解题方法
2 . 如图,在直三棱柱
中,已知
,D为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/5/70009b7e-e3d6-47af-9655-a87c58e2cea2.png?resizew=163)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf3890578e602df1580b719b0cd4ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/5/70009b7e-e3d6-47af-9655-a87c58e2cea2.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab2deab5e8b990bb6eb99af2d789c9a.png)
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解题方法
3 . 已知以原点O为中心的椭圆标准方程
的离心率为
,焦点F为
.
(1)求椭圆的标准方程;
(2)若过焦点F且倾斜角为
的直线与此椭圆相交于A、B两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
(1)求椭圆的标准方程;
(2)若过焦点F且倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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4 . 如图,在四棱锥
中,底面
是矩形,且
,
,
平面
,
、
分别是线段
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/8a7462c6-c92d-4ed5-a22b-ddd652e46b9b.png?resizew=168)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96127e45e2dd2494fccb1c0905951f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/8a7462c6-c92d-4ed5-a22b-ddd652e46b9b.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d603566c74b1d5de510a2e8f7859010.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0901e2f5cefe6468cbbcaa332287d63.png)
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解题方法
5 . 已知点
,
是椭圆
:
的左右焦点,且椭圆
的短轴长为
,离心率为
.
(1)求椭圆
的方程;
(2)若直线
过点
且斜率为2,与椭圆
交于
两点,求线段
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
6 . 长寿工业园区某工厂产生的废水经过滤后排放,过滤过程中污染物含量y(单位:mg/L)与时间x(单位:h)间的关系为:
, 其中m,k是正实数. 如果在前2h消除了10%的污染物.
(1)求k的值;
(2)若污染物剩余10%就达到排放标准,求污染物达到排放标准至少需要多少时间?
(精确到1h) (参考值:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb9157d53abd1a1d533b4811109e725.png)
(1)求k的值;
(2)若污染物剩余10%就达到排放标准,求污染物达到排放标准至少需要多少时间?
(精确到1h) (参考值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665e939da109084681b765a0daf8e3cb.png)
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解题方法
7 . 已知函数
.
(1)求函数
定义域;
(2)若函数
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de53774745eec3993c1bd4556d3b994.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c82564dd493bf2fe803d0b7f1d44079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
8 . 已知函数
.
(1)求
的最小正周期;
(2)求函数
在区间
上的最小值,并求出函数取得最小值时对应
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48561e845af9e96ee769d3ade9042e11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6b3ff4d2591e8567bdba6ae31c87fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 记
为等差数列
的前
项和,已知
.
(1)求
的通项公式;
(2)若数列
满足
,
,求数列
的前10项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/0c5952ee2dd11e3801cd4275a684b392.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773698999bfd0a6c2d8598551af12e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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10 . 已知直线l的倾斜角为
,且过点
,
(1)求直线l的直线方程;
(2)若以原点为圆心的圆C恰好与直线l相切,求圆C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4c5016bd1fc6582078299b9cf8b392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7cb5891cc7c859eda6e73c17a99a63.png)
(1)求直线l的直线方程;
(2)若以原点为圆心的圆C恰好与直线l相切,求圆C的方程.
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