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1 . 已知定义在R上的奇函数f(x)=
(a>0,且a≠1).
(Ⅰ)求k的值;
(Ⅱ)当m∈[0,1],n∈[-1,0]时,不等式f(2n2-m+t)+f(2n-mn2)>0恒成立,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89830df2d24530877907c7cc35e41ba.png)
(Ⅰ)求k的值;
(Ⅱ)当m∈[0,1],n∈[-1,0]时,不等式f(2n2-m+t)+f(2n-mn2)>0恒成立,求t的取值范围.
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2 . 已知
分别为椭圆C:
的左、右焦点,点
在椭圆上,且
轴,
的周长为6.
(Ⅰ)求椭圆的标准方程;
(Ⅱ)E,F是椭圆C上异于点
的两个动点,如果直线PE与直线PF的倾斜角互补,证明:直线EF的斜率为定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882651b776851f3f0665de12da6ed47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0e2297e289632ffc211bd20e2e772e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1434a7398f22cb12bd74b8837628232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a846139a5dee6762bb7193273da66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7155284dd936a234de37b151850503d7.png)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)E,F是椭圆C上异于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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3 . 已知椭圆
,过点
,
的直线倾斜角为
,原点到该直线的距离为
.
(Ⅰ)求椭圆的标准方程;
(Ⅱ)斜率大于零的直线过
与椭圆交于E,F两点,若
,求直线EF的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83770dfcae8b8e1288aa85d50a63d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)斜率大于零的直线过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ff329f3b12cf5678e99941e7188621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571b8177177b21d405d0cbc162bf9c2a.png)
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4 . 已知过抛物线
的焦点
,且斜率为
的直线与抛物线交于
两点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64c631ee509ed4dcb72332ded9c8adc.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db63cef6d8bbb08137d71c6f7b6e741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64c631ee509ed4dcb72332ded9c8adc.png)
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2018-11-05更新
|
2376次组卷
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7卷引用:【全国百强校】吉林省实验中学2018-2019学年高二上学期期中考试数学(文)试题
【全国百强校】吉林省实验中学2018-2019学年高二上学期期中考试数学(文)试题【全国市级联考】江西省南昌市2017-2018学年度高三第二轮复习测试文科数学(五)试题【全国市级联考】江西省南昌市2017-2018学年度高三第二轮复习测试卷理科数学(五)试题湖北省武汉市武昌区2020-2021学年高三上学期1月质量检测数学试题(已下线)专题21 椭圆、双曲线、抛物线的几何性质的应用(测)-2021年高三数学二轮复习讲练测(新高考版)(已下线)专题25 椭圆、双曲线、抛物线的几何性质的应用(测)-2021年高三数学二轮复习讲练测(文理通用)(已下线)专题9-1 圆锥小题压轴九类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)
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解题方法
5 . 已知函数
在区间
上是单调递增函数,则
的取值范围为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98546f2d694ce7b135686dadc58be1ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f9d4a382c45d579e11c4b3bf026a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2018-06-30更新
|
2903次组卷
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6卷引用:【全国百强校】吉林省长春市一五0中学2017-2018学年高二下学期期末考试理数试卷
名校
6 . 已知函数
与
在
(
,且
)上有
个交点
,
,……,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070c1940b9d5319ae14fa52d2dc4a7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1373f91c68c991044216646aba51cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7ba4ecabfe36e68210c4b23ce862e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df093be916b6cd6d234aac3055df422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54700061d9f312959c7159c268dede44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140060099161bff9f7de5287c78bc341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f1b623a0dc016eeb949e523ffbdda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bfa7813e94691709d47a3c71c914a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9744a2fa09343e1110d32bc47127f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070c1940b9d5319ae14fa52d2dc4a7f0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2018-01-11更新
|
1767次组卷
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3卷引用:吉林省梅河口市第五中学2019-2020学年高二5月月考数学(文)试题
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7 . 已知
有两个零点
,下列说法正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef96ff936eb415b1f8fe6b9166d8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
A.![]() | B.![]() |
C.![]() | D.有极小值![]() ![]() |
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解题方法
8 . 已知函数
,
.
(1)当
时,比较
与
的大小;
(2)设
,若函数
在
上的最小值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdb5f2195549cf8ef0ef396dad48517.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e205a7dc01a9e0bd2a8cb8bb1cc8ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322a00c551f56405c5ce86af4bf1c232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f687bffdf3c157729d5d98c113f909.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8423ce8cf2b05f36f65f59e2cf1a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc5aea4d6ce0d4ffd1df735b81ac5905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2017-12-06更新
|
571次组卷
|
6卷引用:吉林省梅河口市第五中学2018届高三上学期第三次月考数学(理)试题
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解题方法
9 . 已知函数
的图象的一条切线为
轴.
(1)求实数
的值;
(2)令
,若存在不相等的两个实数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfef97d0278145d87702673a8772f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cdc169e38ca517ec655ee3875182df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5f4aadc17b6d5c9760a75fab7fb760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b725fdc8de9800f2692f6fea8585b1e9.png)
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2017-06-03更新
|
962次组卷
|
5卷引用:吉林省实验中学2016-2017学年高二下学期第二次月考(5月)数学(理)试题
名校
10 . 函数
,
(
是自然对数的底数,
).
(Ⅰ)求证:
;
(Ⅱ)已知
表示不超过
的最大整数,如
,
,若对任意
,都存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87f5e72f33b3e95ddb3fa57648aa0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4007f8b43cce86c17127b8e0609986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ab8c30f5b674110d636d756c71a0ea.png)
(Ⅱ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fab6009ffb15a88bd843a1c2b8d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b075b070ede7d669757c8bb807c869ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a947b8558a4eb3349cee0cc55cd9f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aae852c3129efc16934aefc54201f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d0f219b20e94f38e8618b6e68a8913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2017-05-11更新
|
1126次组卷
|
2卷引用:吉林省东北师范大学附属中学2017届高三下学期第三次模拟考试数学(文)试题