解题方法
1 . 若函数
的定义域为R,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aae4b2e40ca578ac5dbb8f07693dfff.png)
(1)求
的值,并证明函数
是偶函数;
(2)判断函数
是否为周期函数并说明理由,求出
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aae4b2e40ca578ac5dbb8f07693dfff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baeef9267fa2d3de28e70839dc3db48e.png)
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2 . (1)计算
.
(2)已知
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30c70469b77a4cfb8cd65d1c7ce420a.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20499d98e29c917e06824a45253166b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039ec04b0108df3d24a6d3fa7f6bef29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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3 . (1)已知
,求
的值;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbe7ea044718fb7c2c7774f89bc5d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ba4f4450d63609ad3665858d35d82e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb38a67c53abe51ec2929d4431ac99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
4 . 已知角
的终边过点
,求角
的三个三角函数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663e2a3c6f6988e81c4ffcf1bddd1c4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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5 . 已知函数
.
(1)求
的最小正周期和图象的对称轴方程;
(2)当
时,
的最小值和最大值之和为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43f11e4b58c762738de1b0ba5465a1a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c1c1c885e28ef61bf47d1a61a847bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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6 . 已知函数
.
(1)若
是偶函数,求实数
的值;
(2)当
时,
,若关于
的方程
在区间
上恰有1个实数解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06eeb6ee6acf06beac15b9ba0d44cdba.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14f7eb9e5d0d2dc6c8897f6c7863518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa0b6033aba3978ab687ce54d35f58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a13f3df2e1a444f41bc132431848eaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
7 . 已知函数
.(e为无理数,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6efe559625bc3b69b084085fb8777b.png)
(1)若函数
为奇函数,求参数
的值;
(2)在(1)的条件下,求函数
在
上的最大值与最小值之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d56983f0fe19b400e8c15fdfdaf735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6efe559625bc3b69b084085fb8777b.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)在(1)的条件下,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
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8 . 已知全集
,集合
,集合
.
(1)求
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3344b4b2541031b88aa04025bbcd82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500f2d5fbff755afe7b8e64d1f71cd5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e7b8a0677463b01fd0a39ce50461.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81919684bc4047d376c7e57dc6c8f1c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5f52e8d5cf759d2b7e7c4d56419a3e.png)
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9 . 生活中我们用水清洗蔬菜上残留的农药,用水越多,洗掉的农药也越多,但总还有少量的农药残留在蔬菜上.对于某一堆蔬菜,用
个单位量的水清洗一次后,蔬菜上残留的农药量与本次清洗前残留的农药量之比为
,且
.
(1)现要求清洗一次后蔬菜上残留的农药量不超过本次清洗前残留农药量的
,求至少要用多少个单位量的水清洗;
(2)现有
个单位量的水,可以清洗一次,也可以把水平均分成两份后清洗两次,为使清洗后残留的农药量更少,应选择哪种清洗方式?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3fecc7fa9662921384ba13239eb28fa.png)
(1)现要求清洗一次后蔬菜上残留的农药量不超过本次清洗前残留农药量的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca83504e351d7516f61a3052d7a31859.png)
(2)现有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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解题方法
10 . 已知函数
为对数函数,函数
的图象与函数
的图象关于
对称,设函数
,且对任意
都有
恒成立.
(1)求函数
的解析式;
(2)若函数
在
上的最小值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78f50ba34a711fe64198e358b62e0e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd84da85388fcc2b7b74eed6790b9318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f48232ea888fd31e850879c444641f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d786ee0f73092274bce83c0670d5030a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a08521c64aae3d19fe3fe1da35708f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade31f6684e3033e377b90691ec2204d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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