名校
解题方法
1 . 已知
,
.
(1)判断函数
的奇偶性;
(2)令
,若函数
在
处有极值,且关于x的方程
有3个不同的实根,求实数m的取值范围;
(3)记
(e是自然对数的底数),若对任意
,
且
,均有
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22801c4ffc95c8c935ec52e9111a0973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43fb7af688c7d890a2221ab00eee4e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8463f441f99b82fa2f315b39baa25a4.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd95de578b27d676f4e9ac3db58af675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9355f07b98a27884fb028fef70e72df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191a9f1cd3402de148664b7fbe7a0c79.png)
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名校
解题方法
2 . 已知函数
.
(1)依次求
,
,
的值;
(2)对任意正整数n,记
,即
.猜想数列
的通项公式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fa4034048d54c492fe0d63802a6c2d.png)
(1)依次求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1556ea3eb80eaa649bc194ea9fb8756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f00a5dc1147eedb9375c06b44b94bc8.png)
(2)对任意正整数n,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fd35f1c211deee73932955593d76d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/facd124cd6698fea3fe5711d7548a685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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名校
3 . 给出函数
,
(1)若
,求不等式
的解集;
(2)若
,且
,求
的取值范围;
(3)若
,非零实数
,
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f18cf2aa76c59569a668ee8fb5ae420.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62acc97e485075f489e1d5e96e09958.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/867f0794e209c2aa6dc1ded523427ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3c5462af41f417a830b88fbad13bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e1d71a91451f7086d9237c0fea607e.png)
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4 . 已知
.用反证法证明:
,
,
,
中至少有一个数大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb06caf424378e9f84841321dfa001d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06fc7811f9525e8b8c833746d6af5c.png)
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名校
5 . 若定义域为D的函数
满足
是定义域为D的严格增函数,则称
是一个“T函数”.
(1)分别判断
,
是否为T函数,并说明理由;
(2)已知常数
,若定义在
上的函数
是T函数,判断
和
的大小关系,并证明;
(3)已知T函数
的定义域为R,不等式
的解集为
.证明:
在R上严格增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2378646933425e8a11d642b90432a152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842f20228995cb020d8963f332d12189.png)
(2)已知常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3215b7ec3903a56edd78345e2e473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9131181855dfd6c6a950eecc3865e4b0.png)
(3)已知T函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02a5802f50d0bac17f22f9a18f3d5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
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2023-10-13更新
|
418次组卷
|
3卷引用:上海市建平中学2024届高三上学期10月月考数学试题
名校
6 . 已知函数
.
(1)若经过点
的直线与函数
的图像相切于点
,求实数
的值;
(2)设
,若函数
在区间
为减函数时,求实数
的取值范围;
(3)对于函数
,若函数
有两个极值点为
、
,且不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c671eac6b138ff3226bff8ae0e79de6.png)
(1)若经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb50eb9d24b272091786deb65e860d88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c959ab293ef3ecbba70b635da3e2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3305ff38933d2880421f5bdaf6029d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c146f99862cda414d0f28c60b12072e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3305ff38933d2880421f5bdaf6029d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a93969738a9bb969f40cf587f1d5d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf5e27d7b100672cd54ee8eb0e530a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2023-10-11更新
|
282次组卷
|
3卷引用:上海市华东师范大学松江实验高级中学2024届高三上学期10月阶段检测数学试题
上海市华东师范大学松江实验高级中学2024届高三上学期10月阶段检测数学试题(已下线)第五章 导数及其应用 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)上海市松江二中2023-2024学年高二下学期5月考数学试卷
解题方法
7 . 如图,某生态农庄内有一三角形区域
,
,
百米,
百米.现要修一条直道
(宽度忽略不计),点
在道路
上(异于
,
两点).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/0dc8c034-6761-471f-9817-2d21b91c6f0a.png?resizew=168)
(1)若
,求
的长度;
(2)现计划在
区域内种植观赏植物,在
区域内种植经济作物.已知种植观赏植物的成本为每平方百米4万元,种植经济作物的成本为每平方百米2万元,新建道路
的成本为每百米2万元,求三项费用总和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6610676353016a9f7235d306b731c1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/0dc8c034-6761-471f-9817-2d21b91c6f0a.png?resizew=168)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a311738db3fc5431d14a0942542a62e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)现计划在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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8 . 证明:
是无理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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名校
9 . 已知
为实数,函数
.
(1)若函数
在
处的切线斜率为2,求
的值;
(2)讨论函数
在
上的零点个数;
(3)设
表示
的最大值,设
.当
时,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71f9fc7f49fbea75e6484333e605142.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f539a9f59662e4a7be3e758fd603d1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ac68482ffb69f09e33a5b641565801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c280315872e4eb09f59c00c26396efcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04bd9759565e4cd93839a2ce2b31b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . (1)设
,
,比较
与
的值的大小关系;
(2)已知
,
,
,其中
、
、
为实数,请用反证法证明:
、
、
中至少有一个为正数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b41d84627f6229005178c8b69d5d401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d18e9ca603e7d02cf1788acdf105f2.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651b911b5b89924a9f1715d847e9d419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a130665c0842c5594882a282eab790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0446cabe6eef4e5012d0bcf2be336f06.png)
![](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/071a7e733d466949ac935b4b8ee8d183.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/c5db41a1f31d6baee7c69990811edb9f.png)
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