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1 . 已知向量eqId068aa187b98540d1978c4070d52fafedeqId01e04081988b46c89e7108fc13294d37eqId8d8ce131b31e41b1aa3b03c2d0ade896,其中eqIda4be99d332154d13a4a6ed1ff6444fe7eqId5f904d1376ac4de7a7d6cfea92ff6981均为正数,且eqId950ebe5d377147b5b015bc8a0e0ec94a,下列说法正确的是(   )
A.eqIdf087b35a5011425daaafbf14a5e61064eqId5f16eb46594d47b58ffc973b5cc2dd0d的夹角为钝角B.向量eqIdf087b35a5011425daaafbf14a5e61064eqId5f16eb46594d47b58ffc973b5cc2dd0d方向上的投影为eqId5222c2ea3b544c58bafb590c9238c493
C.eqId41a8eab873ba4c9dbd3e863f5f7c4e7fD.eqId7ee9cba96d234881be35f27c0dd43136的最大值为2
2 . 已知函数eqId5ffa17bde0b441ad8badf266b0a75a31.
(1)求eqId9b37d03e47a347fc8fab9f814ba5fac4eqId88d6a2e7f0eb421182eca0986d496135上的最小值,并求此时eqIda9cd3f94eb8045438f75e9daccfa7200的值;
(2)设eqId016fcd8f795245938c035b1cb817f498,用定义证明:函数eqId94ecc92a54a64619be8fcf2a983e1319在区间eqIdafd01e592c8a437aa1210738a0130efb上是严格减函数.
3 . 已知函数fx)=axa>0,a≠1)的图象经过点eqId536793918db741f0b87251bdcdf81d91.
(1)函数fx)=gx)+hx),其中gx)为奇函数,hx)为偶函数,求hx),gx)的解析式;
(2)x∈(0,1]时,2lnhx)-lngx)-t=0有解,求实数t的取值范围.
4 . 如图,在eqIdbedf755e0fdb4d078d6859360706b163地正西方向eqIdbea1b856f28f4ebb91431baf22bb9347eqId052844cae8574a8ab842c38a039baac0处和正东方向eqIde834159eb1c54a1eb6a448ce43aa658aeqId8754ce8cf7f34f04abb9a0c041f57f5c处各有一条正北方向的公路eqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4,现计划在eqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4路边各修建一个大型物流中心eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175.为缓解交通压力,决定从eqIdbedf755e0fdb4d078d6859360706b163地分别向eqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4修建公路eqId9608739a1d8547df8df8461d80f9f5f2eqId7b71ac6238b649bba16fd5463c7b0b56,其中eqIdf1325a0e6c22479f8b33f2aaedd18b9d为直角,设eqId08d4def543214e92b90e1bf8f8c62b9d.
说明: figure
(1)为减少对周边区域的影响,试确定eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175的位置,使eqIdf7576c864fef47b3b3211b9636da3b3feqId22c3d4d1daae49df9bb9bfd4d4b608d3的面积之和最小;
(2)为节省建设成本,试确定eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175的位置,使eqIdbedf755e0fdb4d078d6859360706b163eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175的距离之和最小.
填空题 | 较易(0.85) | 2021·全国高一课时练习
5 . 已知eqIdaa1312dcc8e24925b421f7767761a363,则eqId2d87544c3223433fab4215d111a4a8a4的最大值为________
更新:2021/09/14组卷:192
6 . 已知偶函数eqId712025229b074102b2e9249a39598ecb,有eqId0d3680f6c70744818eac9476fb46fd9beqId5652ee1fa741458fbc2791c22d44790a时,eqId27327932f23748bbb5fd931a028f1cc9成立,则eqId6106e9b4ee9f457f9e29741dc1563709对任意的eqIdb5706584ddc64530b68e964587fe3b9a恒成立的一个必要不充分条件是(   )
A.eqId466c7bde692249b189c23152906e6cebB.eqIdc9c2b2ede5284c8fade61d1b5e514159
C.eqId241952b270704e13aee614fbeb1748baD.eqIdaa15c870be914f788fcfae985df1dc99
8 . 若eqIdaa1312dcc8e24925b421f7767761a363,则eqIdcd316b53a3f34b3488b2a1f9d780c787有(   )
A.最小值eqIddd4bf187d3fd47f6bcc24e568e09643eB.最小值eqId401586f7a7f248b7904a4cfeaa2ed2f0
C.最大值eqId401586f7a7f248b7904a4cfeaa2ed2f0D.最大值eqId8898c1dc81824f3098bbeae74e8f11fd
解答题 | 一般(0.65) | 2021·广东高一期末
9 . 某厂生产某种产品的年固定成本为eqId807c2d382ea84cca852734fdaace0088万元,每生产eqIda9cd3f94eb8045438f75e9daccfa7200万件,需另投入成本为eqIdc5a07649fc3a47c9ab287025687e17b8.当年产量不足eqId149474e84ad84225841eced3061e9d26万件时,eqId8e83f9d3110249ba8e7ddb5d0081a144(万元);当年产量不小于eqId149474e84ad84225841eced3061e9d26万件时,eqIdf732a452d0ca445e946829f38e078ba4(万元).通过市场分析,若每件售价为eqId2ec8ba9fb61a48879d34627ec236b8d6元时,该厂年内生产的商品能全部售完.(利润eqId1f2c92dfd3d8438ca50bd7b1c0ed8a80销售收入eqIdf201fbc3bac04f3396a13987cd2540b3总成本)
(1)写出年利润eqId93395b3e07c644308e9416ab29fa76fe(万元)关于年产量eqIda9cd3f94eb8045438f75e9daccfa7200(万件)的函数解析式;
(2)年产量为多少万件时,该厂在这一商品的生产中所获利润最大?
单选题 | 一般(0.65) | 2022·全国高三专题练习
10 . 某企业投入eqId727650e20a234e51a97c72f164196d56万元购入一套设备,该设备每年的运转费用是eqIdc0d74ce4837b43509d665192a9ccaa88万元,此外每年都要花费一定的维护费,第一年的维护费为eqIdc052ddfbd4524f67a79e0e77c2e5656a万元,由于设备老化,以后每年的维护费都比上一年增加eqIdc052ddfbd4524f67a79e0e77c2e5656a万元.为使该设备年平均费用最低,该企业需要更新设备的年数为(   )
A.eqId401586f7a7f248b7904a4cfeaa2ed2f0B.eqId62503849440740cf8754af7e844ba72cC.eqId5557c7b84f794778b10717993bbb709eD.eqId0bad15ca833c426894079a104ff88a36
更新:2021/09/04组卷:131