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1 . 已知函数eqId8724b3c071814c3886a60dc28c1d006d,则方程eqId9169690df3db4f3387590aa38de3459feqIdf035b8f27d4645bb9f6a66f4a3f51918是自然对数的底数)的实根个数为__________.
单选题 | 较难(0.4) | 2021·江苏淮安市·高三三模
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2 . 已知eqId982da3835b7946d999cc8604a2ece266eqId8164502d09d44990ac4f2f73ea67e37a,且eqIdf945be3daeae467ea117764b2f11f207,则eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7的值不可能是(   )
A.eqIdcfaabc95835f48ebb3097ad9aba05665B.eqId025fdc497eb4428486d689f4b2a12b1aC.eqIdb5508d7ab094420f9e99849b54e1109dD.eqIdc8ec2cf854d8471590d2cc8e076c44af
3 . 若关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqId08742201c0324c739b40afcd9e2ad4c9有且仅有两个不同的实数根,则实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围为(   )
A.eqId83f52297917541b391b55113043e5caaB.eqId3811592ba4f2442d8077a1714da96750C.eqIdad62649dd44e40ccbb2e07512c2ac3a0D.eqIdcc888a9e24a44996ba1ad710bdf56ed6
多选题 | 困难(0.15) | 2021·全国高三其他模拟
4 . 已知函数eqId92dcc93c5c4a41d9bc62ea99507e58f3在区间eqIdf99c1987d6ab400597cf8718fb579672上的最大值为eqId5521c8d144c34d678f5afefac4189a04,最小值为eqIdd9f8c3256f5a41e48593dfd7d3104672,令eqIdda8a2b9587944b5a951e293b35be56b4,则下列结论中正确的是(   )
A.eqId1d2899c3fd904f1296ed45027291c980B.eqIdb8eb96b89b034fe785ca3587f8711ef6的最大值为eqId317ed84d205b4156847380f7e9f38b08
C.eqIdb8eb96b89b034fe785ca3587f8711ef6的最小值为1D.当eqId3d14a2baadd5406fa63d022b74c1604d时,eqId15aede3b9b2546ac94b4c697fed2d56e
更新:2021/06/08组卷:0
单选题 | 较难(0.4) | 2021·河南洛阳市·高二期末(理)
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5 . 函数eqId144eff5c0e4649138a21f2b1b6a06907图象上不同两点eqId54baf25c28b24ce286f39872a8be097beqIdbbeddb35bce14e1a81bad8ff3c4e9697处的切线的斜率分别是eqId68ea1376657d449097dc7f615363f8f8eqId9808815d0a8d4460854d653d308d1e91,规定eqId09a97d05710a472ebc25196052bd9afc叫做曲线eqId144eff5c0e4649138a21f2b1b6a06907在点eqId052844cae8574a8ab842c38a039baac0与点eqId8754ce8cf7f34f04abb9a0c041f57f5c之间的“弯曲度”,给出以下命题:①函数eqId5ab2ea0efd32408d9077d0abe6d36009图象上两点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c的横坐标分别为1,2,则eqId1d52e070c6fb43d1b2a3ba5243daa81a;②存在这样的函数,图象上任意两点之间的“弯曲度”为常数;③设点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c是抛物线eqId0c450d8f660147c4a94279f3c928b33a上不同的两点,则eqId2013b688d26a44aa856386d476741cd8;④设曲线eqIdc4c1f026ce544f5c9dc16099ce0033f9上不同两点eqId54baf25c28b24ce286f39872a8be097beqIdbbeddb35bce14e1a81bad8ff3c4e9697,且eqId0309b9fcff7b4f8faf64c6a0e0e84ff1,若eqIdf79ce765b2e04d9ebf1b7a633adc5aa4恒成立,则实数eqId69f56ef2c88b4b73a560da59f5247a82的取值范围是eqId2634038e67f543e0a725ee3f8941f5ea.以上正确命题的序号为(   )
A.①②B.②③C.③④D.②③④
解答题 | 较难(0.4) | 2021·浙江高一期末
6 . 已知函数eqId22abb75fee8147cc8d8789f98406b243,函数eqId03f22a9455ac447f9dfcd9e76c9f17a1,其中eqId1d786ecab17c472e88f7bc19a1fff36f
(1)若eqId4a68554497984e5eb09903dd40fb7818恒成立,求实数t的取值范围;
(2)若eqId11c13ae48af54736ba46e39afb199140
①求使得eqIded494405a42b4cf8a4db34a50f1a2543成立的x的取值范围;
②求eqId9c705d01261145f1a3b3d15d276106ff在区间eqId92c433f95ab74d2197341ff9234c7029上的最大值eqId6fcb96dc52ad4bbe9249e4d4a63bd35a
更新:2021/06/07组卷:0
7 . 已知函数eqId144eff5c0e4649138a21f2b1b6a06907的定义域是eqId1d40c107624b4197bad0d10756051733,满足eqId8504d8108c1a4a55acd3c15ae8b8cc0ceqId6a5b1bce77a94dd2b92626fa8034b231,若存在实数k,使函数eqId88cba2fe30f74581964396d68c8b8ff4在区间eqId4402e513815e4c9ab8f62e9cbe6d3852上恰好有2021个零点,则实数a的取值范围为____
解答题 | 较难(0.4) | 2021·浙江高一期末
8 . 已知函数eqId814ff50540cf47bb9562b8105a28253f,其中eqIdff0e455f0e0444c9b0ba479e95400f1c
(1)当函数eqIde4a0e3706b56447b90fe1b2781f91b14为偶函数时,求m的值;
(2)若eqIde6f0b8af9cc24958ad65ef74c5fbf445,函数eqId6b9524fec88046c2bc70de087759da87,是否存在实数k,使得eqIdd077167f12154199a0f30bcefb739eb5的最小值为0?若存在,求出k的值,若不存在,说明理由:
(3)设函数eqIdaefc60ecf061488a994fe016f6d4dae3,若对每一个不小于2的实数eqId735b8047beee4dee870fc72ae837a245,都有小于2的实数eqIdecaaaffea9af458c8e6dff16f15c1a73,使得eqId2a5fcc7390864320810bc43bd9ab97c3成立,求实数m的取值范围.
更新:2021/06/07组卷:0
多选题 | 较难(0.4) | 2021·全国高三月考
9 . 设函数eqIde4a0e3706b56447b90fe1b2781f91b14满足:①eqId415b682e214f4e00ae9492435b675b67;②eqIdc834ac6f769b41feaeb36224ef3024b0;③eqIde0ed851b36db4feaa424b92a3f732cba.当eqId2d569479cd1c43c1af15895792b64db6时,函数eqIde4a0e3706b56447b90fe1b2781f91b14与函数eqId711fe3d5f94e445abcb74f16a6b93936eqIdfc48ac844f00454ab0aa2de40b58a917交点的横坐标从左到右依次构成数列eqId054d5a7de5684002909fe944c86227c2,则下列结论正确的是(   )
A.函数eqIde4a0e3706b56447b90fe1b2781f91b14的值域为eqIde89570ce52e44e0a86e751f7cca036a1
B.函数eqIde4a0e3706b56447b90fe1b2781f91b14是偶函数
C.对任意的eqId4d2187284c5d4de29906363f7d21f60feqIda4293c1184d247c99064fd9bd1f291c9,数列eqId054d5a7de5684002909fe944c86227c2的前eqId92478644b29a4a0e8470a8c89d31b49f项和eqIddf0355fa229f4025af65817a1e6bb262
D.当eqId42194baaccd841ea9f59b21820051052eqId5790ef4f0dda4f619edf362da41e0bc0时,满足eqId731bfa908a8b498f82da1acb7b25fa97eqId92478644b29a4a0e8470a8c89d31b49f的最小值为17
10 . 定义域为实数集的偶函数eqId4837c94ef0ff4dcf9b1dda4df363275a满足eqId4de6a63790614cf7803cc973a6c25172恒成立,若当eqIdb6167f70a41546d0903ab04dc04d986d时,eqId5cd82768c190426d951738d97aa566e9,给出如下四个结论:
①函数eqId4837c94ef0ff4dcf9b1dda4df363275a的图象关于直线eqId1a796752c3044bc28a044feb53df36ff对称;
②对任意实数eqId70a27b6ddf6b478285353abb3b1f3741,关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqId5cee418ebb3e47f5b0c25d2a4284719f一定有解;
③若存在实数eqId70a27b6ddf6b478285353abb3b1f3741,使得关于eqIda9cd3f94eb8045438f75e9daccfa7200的方程eqId5cee418ebb3e47f5b0c25d2a4284719f有一个根为2,则此方程所有根之和为eqId16a2e4c11b554606869f586053b6c512
④若关于eqIda9cd3f94eb8045438f75e9daccfa7200的不等式eqId385748c8fb8a482799301676df970fef在区间eqId47bb553718a644a9aba68733ad08312a上恒成立,则eqId70a27b6ddf6b478285353abb3b1f3741有最大值.
其中所有正确结论的编号是__________
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