解题方法
1 . 已知双曲线的中心为坐标原点,其右焦点到渐近线的距离为
,离心率为
,
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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名校
2 . 已知函数
.
(1)讨论
的单调性;
(2)若
恰好有两个零点
,
,且
恒成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e107063f2300c028d91537c0cf70832a.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfab5631d1543bf2090b1c506698ee35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ed3f472299563e31282a44aa9fe202.png)
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2024-01-13更新
|
893次组卷
|
4卷引用:辽宁省抚顺市六校协作体2024届高三上学期期末数学试题
辽宁省抚顺市六校协作体2024届高三上学期期末数学试题江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(九)(已下线)模块2专题7 对数均值不等式 巧妙解决双变量练(已下线)专题10 导数12种常见考法归类(5)
解题方法
3 . 已知函数
.
(1)当
时,求函数
在
上的最大值.
(2)若函数
在定义域内有两个不相等的零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9738b5efda434f795949c1f95f824e53.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45da1d6c4fd59798ff6191eae2bc251.png)
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4 . 已知函数
的图象与函数
的图象有且仅有两个不同的交点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e05c465028a97e44f34b65e9258dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b907c64bce7b404b3bae277bb21d6a12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-05-29更新
|
1170次组卷
|
6卷引用:辽宁省抚顺德才高级中学2023届高三硬核提分(二)数学试题
名校
解题方法
5 . 已知函数
的图象在
处的切线方程为
.
(1)求
,
的值及
的单调区间.
(2)已知
,是否存在实数
,使得曲线
恒在直线
的上方?若存在,求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe57c09ce4f23c0ef11ad30da31d4c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ad3dcd5f916e1dfe8f2050d4dbebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-04-10更新
|
625次组卷
|
6卷引用:辽宁省抚顺德才高级中学2023届高三硬核提分(二)数学试题
解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6544d921bd97a49ff2053fb145f80ea.png)
(1)若
,证明:当
时,
.
(2)若
,
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6544d921bd97a49ff2053fb145f80ea.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1e9825879ab88b211a45a6faff224c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd395a9832f8180e714ebd48a1ae5835.png)
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2022-10-14更新
|
494次组卷
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3卷引用:辽宁省抚顺市重点高中2022-2023学年高三上学期12月考试数学试题
7 . 已知函数f(x)=lnx+a(x2+x),g(x)=x3+5x.
(1)讨论函数f(x)的单调性;
(2)当a=2时,证明:f(x)<g(x)﹣
.
(1)讨论函数f(x)的单调性;
(2)当a=2时,证明:f(x)<g(x)﹣
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
您最近一年使用:0次
8 . 已知函数f(x)=lnx﹣tx+t.
(1)讨论f(x)的单调性;
(2)当t=2时,方程f(x)=m﹣ax恰有两个不相等的实数根x1,x2,证明:
.
(1)讨论f(x)的单调性;
(2)当t=2时,方程f(x)=m﹣ax恰有两个不相等的实数根x1,x2,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186264a5a4c47b79108c6beb26093af0.png)
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2020-08-17更新
|
848次组卷
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6卷引用:辽宁省抚顺市六校(省重点)联合体2020届高三5月联考数学(理科)试题
辽宁省抚顺市六校(省重点)联合体2020届高三5月联考数学(理科)试题青海省海东市2020届高三第四次模拟考试数学(理)试题吉林省梅河口市第五中学2020届高三第五次模拟考试数学(理)试题(已下线)专题21 函数与导数综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)(已下线)专题21 函数与导数综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)(已下线)第08讲 双变量不等式:转化为单变量问题-突破2022年新高考数学导数压轴解答题精选精练
9 . 已知函数
,曲线
在点
,
(1)
处的切线方程为
.
(1)求函数
的解析式,并证明:
.
(2)已知
,且函数
与函数
的图象交于
,
,
,
两点,且线段
的中点为
,
,证明:
(1)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7471c6cd8a297e0a5005331037e24c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a63c52ed4d74feca1248b68657cdb4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28c0c0b1d8a4aba3693a95caf42d41b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec1718debe1c497bd0223cd6d5e668e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a54e0b4872cabdc0b07ea9380e4de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a350eb41c3b7e4face9c3299eff9d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8e72f73db207c3040f143d837d5995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24529eadaef974ec0625f8ca40682e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2c44bd75911eb48101f4d63fa2ca5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb554264d6838229cf2920a9bd99cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b0352e8a9e8d9b8c547c7a11cddf6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71351fd32b9c3832ea85a05000cd0319.png)
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2020-06-23更新
|
3200次组卷
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9卷引用:辽宁省抚顺市第一中学2020届高三第二次模拟考试数学(理科)试题
辽宁省抚顺市第一中学2020届高三第二次模拟考试数学(理科)试题湖南省益阳市桃江县第一中学2019届高三5月模拟考试理科数学试题2020届山东省临沂市临沭县高三上学期期末数学试题湖北省金字三角2019-2020学年高三下学期3月线上联考理科数学试题(已下线)专题05 函数与不等式相结合(第六篇)-备战2020年高考数学大题精做之解答题题型全覆盖湖北省金字三角2020届高三下学期高考模拟理科数学试题(已下线)第10讲 双变量不等式:中点型-突破2022年新高考数学导数压轴解答题精选精练(已下线)2022年高考考前20天终极冲刺攻略(一)【理科数学】(5月20日)(已下线)专题9:双变量问题
10 . 已知函数
,
.
(1)讨论函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab282db7397da172ca45ec7cd6026e98.png)
的单调性;
(2)证明:若
,则对于任意
,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2393c33de34b47a04178053cf381e7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab282db7397da172ca45ec7cd6026e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1a5f2533b8ea54b7022383f875666.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d217c7b12e12e5fb67472452518859ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd4ccfb66805e0631e5cb84b1d1e17d.png)
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