真题
1 . 设计一幅宣传画,要求画面面积为
,画面的宽与高的比为
,画面的上、下各留
空白,左、右各留
空白.怎样确定画面的高与宽尺寸,能使宣传画所用纸张面积最小?如果要求
,那么
为何值时,能使宣传画所用纸张面积最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c499d124da675401cd05fd2d9d724ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a4203ef7b8c021445f213baa9950b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbdcf4d4784de11ae2331cf54ffa9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9938aea41f03701b233dee15809f2126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59818d80a7a3c77e1a58cb005a0d31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 设函数
.
(1)证明:当
,且
时,
;
(2)点
在曲线
上,求曲线在点P处的切线与x轴和y轴的正向所围成的三角形面积表达式(用
表达).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb1c53efea67064ff2ddac3ceea3378.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea134f599285e3d32d2ab3e7186990.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab66ffc45b32fa9189415b1edfab9b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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真题
解题方法
3 . 设
,数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ac63c45383e1b0a80afbe8cb0adcbb.png)
(1)求数列
的通项公式;
(2)证明:对于一切正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5e02bef0f92246b375f559143bc9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ac63c45383e1b0a80afbe8cb0adcbb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:对于一切正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19b8ef4193d4c8c4c8944f8c02d7f37.png)
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