名校
1 . 已知
,过函数
与函数
的公共点作
的切线,若存在一条经过原点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f719952d7a0aca7d906be7645b506679.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9f5bab329331795ccf58e444277430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ea070a08757077f748e0b631168483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01568caf37606d5fcfee5d4b8bf3f67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f719952d7a0aca7d906be7645b506679.png)
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2 . 定义一个可导函数
在定义域内一点处
的弹性为
,请写出一个定义在正实数集上且任意一点处的弹性均为
的可导函数___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e7a7523a8174e8d686e1885b1516dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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2022·全国·模拟预测
3 . 已知定义在R上的函数
满足:①曲线
上任意一点处的切线斜率均不小于1;②曲线
在原点处的切线与圆
相切,请写出一个符合题意的函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed582a84139c6d541cf7478621151876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
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名校
4 . 给定正整数
,按照如下规律构成三角形数表:第一行从左到右依次为1,2,3,…,n,从第二行开始,每项都是它正上方和右上方两数之和,依次类推,直到第n行只有一项,记第i行第j项为
,如图所示.现给定
,若
,则i的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b735bb7446bf6bcf6b21a61815311b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3805398b3ea0a1d2e5249877e2a2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b782c104e42c7deb01240334383d7fb.png)
![](https://img.xkw.com/dksih/QBM/2022/5/5/2973090481995776/2973803743289344/STEM/7cb010b5-f067-44bf-ab8d-5525229e9412.png?resizew=364)
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5 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3db364cad05e1e70fb29743351bafc1.png)
(1)当
时,过原点
的函数
的切线方程为__________ ;
(2)当
时,若数列
满足:
.判断下列命题是否正确,正确的在括号内写正确,错误的写错误.
①
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
( )
②
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf06dcd2cef3226b0663f5562eb423f.png)
( )
③
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fa384c97d499ae7ca08320f684c432.png)
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3db364cad05e1e70fb29743351bafc1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9dc8a749985e8aae334a15da6d70f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75369db7afe5feec5c95e960136cbf3b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15aa2314541715f6be69251653ebf6da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf06dcd2cef3226b0663f5562eb423f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15aa2314541715f6be69251653ebf6da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fa384c97d499ae7ca08320f684c432.png)
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6 . 在复平面内,设点A、P所对应的复数分别为πi、cos(2t﹣
)+isin(2t﹣
)(i为虚数单位),则当t由
连续变到
时,向量
所扫过的图形区域的面积是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdaf49f9611922348aa2784465da614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edc29e6f02468674c8b1e9e54e15109.png)
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2021-06-07更新
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689次组卷
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6卷引用:重庆市第一中2021届高三高考数学押题卷试题(四)
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