名校
解题方法
1 . 定义在R上的函数
满足
,且
,
①
的值域为
; ②
的最小正周期是4;
③当
时,
; ④方程
恰有4个实数解.
上述正确命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac67215b94c77be50360a64b16cceeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5448a19cf9cf7970ffb209d5e9ffa267.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2f360028740b06001ab1c3739c1fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350cbd2f5a3f5e72d5f0db5bd63964ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bf4aa648b06d0a9f4782bcd0821d4c.png)
上述正确命题的序号是
您最近一年使用:0次
2024-06-08更新
|
146次组卷
|
2卷引用:天津市滨海新区大港油田实验中学2023-2024学年高二下学期第二次月考数学试卷
2 . 已知
,函数
,
.
(1)若函数
的减区间是
,求
的值;
(2)讨论
的单调性;
(3)若方程
在
上恰有两个不同的解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344a6479c49871869bdb66f1d84bbaac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c34722c135157f1e3385d2393250d7.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5548c101f84334ab651fd7139e324f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa3a50b913a556376d974e6f6244e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
名校
3 . 已知函数
,
.
(1)若曲线
在
处的切线斜率为
,求
的值;
(2)讨论函数
的单调性;
(3)已知
的导函数在区间
上存在零点,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebf826591b9937b4250bbdd35af5726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2763b57a7399653fbded5264f0cee150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58411b65a71e9a452259eaf6ccea5313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a91dd794bff1e721302074907b6ad.png)
您最近一年使用:0次
2024-04-16更新
|
600次组卷
|
8卷引用:天津市滨海新区塘沽第一中学2023-2024学年高二下学期第一次统练数学试题
天津市滨海新区塘沽第一中学2023-2024学年高二下学期第一次统练数学试题天津市西青区杨柳青第一中学2022-2023学年高二下学期第一次适应性测试数学试题天津市西青区杨柳青第一中学2023-2024学年高二下学期第一次质量检测数学试题云南省大理白族自治州民族中学2023-2024学年高二下学期4月月考数学试题宁夏回族自治区吴忠市青铜峡市第一中学2023-2024学年高二下学期4月月考数学试题天津北京师范大学静海附属学校 (天津市静海区北师大实验学校)2023-2024学年高二下学期第二次阶段检测(期中)数学试题安徽省六安市裕安区新安中学2023-2024学年高二下学期期中数学试题天津市第九十五中学益中学校2023-2024学年高二下学期第二次学习情况调查数学试卷
名校
解题方法
4 . 已知椭圆
的焦距为2,且过点
.
(1)求椭圆
的方程;
(2)设
为
的左焦点,点
为直线
上任意一点,过点
作
的垂线交
于两点
,
①证明:
平分线段
(其中
为坐标原点);
②当
取最小值时,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08426685aa6a3a15fb175251cb578f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
5 . 已知数列
为等差数列,数列
为等比数列,且
,
,
,
(
).
(1)求
,
的通项公式;
(2)已知
,求数列
的前
项和
;
(3)求证:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5aa46a7512675ab55f82d18ca3cc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d1279460f2d2eca25ef419cd17ec6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f287759fad50450b0bf4f69ee80ecdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f759116865a2bacd2515981e7af2b552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232c753e94442cf89732ce7e9ac0ee1f.png)
您最近一年使用:0次
2023-11-22更新
|
1032次组卷
|
4卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第二次月考(期中)数学试题
天津市滨海新区塘沽第一中学2024届高三上学期第二次月考(期中)数学试题天津市河东区第三十二中学2024届高三上学期第二次月考数学试题(已下线)黄金卷05(已下线)专题09 数列的通项公式、数列求和及综合应用(9大核心考点)(讲义)
名校
解题方法
6 . 如图,四棱锥
中,侧面
为等边三角形,线段
的中点为
且
底面
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/a0d8d5f0-b5da-4507-8068-fe8bef9781b1.png?resizew=179)
(1)证明:
平面
;
(2)求点
到平面
的距离;
(3)点
在棱
上,且直线
与底面
所成角的正弦值为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4299cca48ff6abfb252ef73b5e62317d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d958839b418bbefd0504ad7c76eaf37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/a0d8d5f0-b5da-4507-8068-fe8bef9781b1.png?resizew=179)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
名校
7 . 已知函数
在
处的切线
与直线
平行.
(1)求实数
的值;
(2)若关于
的方程
在
上给有两个不相等的实数根,求实数
的取值范围;
(3)记函数
,设
是函数
的两个极值点,若
,且
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74da4b06c434c46d5a8958ad77f2592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b818e1793be8d9213e903e5224987a0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ffd07a1413aa5c7e77ddebbdb98904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b448fe164c2c2931805e3b3847dcdd75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a7bc480ecb0606cec412d2f29f5c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dafa6cf5b9002d734b287e7983ee7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90cd5b0638b6be502c18ac033e1bd5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-11-22更新
|
379次组卷
|
2卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷4
名校
解题方法
8 . 已知函数
,
.
(1)证明:对任意
,
;
(2)若函数
在区间
上单调递减,求实数
的取值范围;
(3)
是
的导函数,若函数
,证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebba733dae06b063b5e279189d5d30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139637feb9604ec0331be72fb94fdc39.png)
(1)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b58279e5447d871c84a91be4210fd9.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be336b37bc4750e005f68fe765661885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8dcb81937d675e4d0bb7c73d7a9220a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
,且函数
.若对任意的
不等式
恒成立,则实数a的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43505b8cf61c94b5f2e37d6bf6e54c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fdb100025aa61c42bdf6e621e771cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6e2c9f63b1e6638a09d121d05176741.png)
您最近一年使用:0次
2023-09-16更新
|
211次组卷
|
2卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷5
名校
解题方法
10 . 已知函数
,
,若函数
的图象经过四个象限,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b756aa61f446111bc7e6fa387ae5b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a3a24fd504e8d44f3bdb7d715a92ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-09-16更新
|
511次组卷
|
3卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷1