1 . 已知函数
.
(1)若
,求
的取值范围;
(2)若
有两个不相等的实根
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfe72da09a3c70855e5481e5c8eaf80.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a1b101171cf52faf2e3e53d6725aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd25b0aac17082018e89b67803cd6a1.png)
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解题方法
2 . 已知向量
为互相垂直的两个单位向量,若向量
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a4a9537264201de1f4c0b5dd236077.png)
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
__________ 时,
取到最小值;此时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e00665a8c1971c54615a013740a0171.png)
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10814bc3db929e79874befe96cf4e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5719d3ef48c90aba13985cd42f9469f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a4a9537264201de1f4c0b5dd236077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3000ec4b24dc6547cd7aaafa7c4b4405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aafc1e049160afcf94f26f330012be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e00665a8c1971c54615a013740a0171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59adb100c1a95619a62c5fd5a07aade1.png)
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3 . 若某次乒乓球练习中,乒乓球发球后先后击中已方桌面
和对方桌面
,且
长为60英寸,球在
中点
处到达最高点,高度为
英寸,乒乓球网位于
上靠近
的三等分点
处,网高为6英寸,球恰好沿着网的上边界越过,其轨迹图象如下:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 已知
中,内角A,B,C所对的边分别为a,b,c,且
.
(1)求角
;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1444244e94e615d34822c487c9ddcb1.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4376dedfb7c9c5e56a15c138237049.png)
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5 . 已知定义域为
的函数
在区间
上单调递增,且
,若函数
是奇函数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98879a823e90f7249b95dde4223ba02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd084506fe160e072aa57164e25b83e.png)
A.4是![]() | B.![]() |
C.函数![]() | D.函数![]() ![]() |
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6 . 已知正实数
,
满足
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ae872ce8e0ca1d7c5ead7565d8d2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ee29ca15fba67a20f9963ed9b66ca7.png)
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7 . 如图,一根棒棒糖其顶部可近似看成一个直径为2cm的球,下面通过一个底面直径为0.2cm,高为6cm的圆柱体(裸露部分)加以支撑,则这根棒棒糖的体积约为( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14facc6aef16f3732c12631d858e8b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dde19dc4d3119bd2cbe4f04bc69f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c2a7421c540b94bff235b251b8b58.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知向量
,
.下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b981b38133d5d65060dd8ff4d65a66be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e383d576da2ca0c9e833d9d362929d.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若向量![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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10 . 如图,已知函数
在
单调递增,且经过点
,
,则
,
的值分别是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe3c339f6b1ab17fe76ebab9ae35eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b5e960105437b0cce733ef4f21b201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633ca6abf0a23f7986facd5941edfe2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921dc9e1e2bb357d8ea272c128a442d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/31/93be5e91-52b7-4a9f-b802-c7986c9efdcb.png?resizew=168)
A.1,![]() | B.1,![]() | C.3,![]() | D.3.![]() |
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