1 . 已知直线
与椭圆
:
交于
、
两点,直线
不经过原点
.
(1)求
面积的最大值;
(2)设
为线段
的中点,延长
交椭圆
于点
,若四边形
为平行四边形,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
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2 . 已知a,b∈R,函数
,
.
(1)当a=1,b=0时,求方程
的根;
(2)设函数
在[-2,2]上的最大值为G(a,b),当G(a,b)取得最小值时,求2a-b的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f53dca784e409fc6b92d060be2067f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055fd1d9cd5048a39e76f56215efba19.png)
(1)当a=1,b=0时,求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8bfb563f79688d136e0cb958b5153c.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71607511fdd4faa9e832345ceb2a817d.png)
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3 . 已知数列
满足
,
,数列
的前
项和为
,则使不等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed52052b02762c35a651572215d0826.png)
成立的最小正整数
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5b1b1cbd3544ae1812b9f65e957784.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed52052b02762c35a651572215d0826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b11cd2083a38e421928fea51168e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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4 . 已知1<a≤2,函数
.
(1)证明:函数
在(0,+
)上有唯一零点;
(2)设
是函数
在(0,+
)上的零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffda632a87178328b0d6be3319a69b4.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229e67dd9fe978e48c221b0b9dc57f1c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229e67dd9fe978e48c221b0b9dc57f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5f5c64af78dbe4d1200c5201f1477f.png)
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5 . 已知单位向量
,
的夹角为60°,向量
,且
,
,设向量
与
的夹角为
,则
的最大值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b04618e5b2db68f2de6ba68972c505c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97169074b37d4b914ecd271e311c0211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95842ad442c7f6d5ec4b32939b929e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54eff1aaacb1ba98b5e379789f6d47a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 已知实数a,b满足:对于任意的实数x,不等式
恒成立,则
的取值范围为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f67e4eb752ced56c45f326cd39a40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761a4034330ec48e65d5a627c4184760.png)
A.[1,+![]() | B.[![]() ![]() | C.[![]() ![]() | D.[![]() ![]() |
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7 . 已知函数
的图象向左平移
个单位后得到函数g(x)的图象,则g(0)=_________ ,若实数x1,x2满足
,则|
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca26d7dac38b616203456afcaac690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdaf49f9611922348aa2784465da614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6edc010b2238d6a35b48213bfebabe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
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8 . 若集合A={(m,n)|(m+1)+(m+2)+…+(m+n)=2020,m∈Z,n∈N*},则集合A中的元素个数为( ).
A.8 | B.10 | C.12 | D.16 |
您最近一年使用:0次
9 . 已知数列{
}的前n项和为
,且满足
.
(1)求数列{
}的通项公式;
(2)设数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b5b92877484c401bc2c56c43c41fb7.png)
(1)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b191044f5c024f377d999910b78b422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc63f77d5522a0853c9d7d7158987c88.png)
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10 . 已知函数
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9183df9b3f276abc8a9b279ea35dc7.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce020353e4314fe1e1cfe2d84b91221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41695a4b39b662183ebc8092c06bf034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b75b95500ecdd45377847255bcd5302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d661ea1afb474d15f37b8a2378d764ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9183df9b3f276abc8a9b279ea35dc7.png)
您最近一年使用:0次