1 . 设
,
,正实数数列
满足
,且当
时
.求证: ⑴当
时,
; ⑵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1465145d6bc8543d5c544dd99613970d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27008dcb6262187804a14cab9302a876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c10652cbb829968425b5d43b3e19eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a347b7b06cf3541256a952adfe637750.png)
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2 . 如图,
、
是双曲线
的两个焦点,一条直线与双曲线的右支相切,且分别交两条渐近线于A、B.又设O为坐标原点,求证: (1)
; ⑵
、
、A、B四点在同一个圆上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565bc68d208cd5e0c90a32851faf3814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a05d4d803a85dc1059912895954551b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/2019/1/28/2128340345315328/2129028866695168/STEM/cd48519e-7460-4653-91b5-2403e14064a5.png)
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3 . 设
、
、
是方程
的三个根,
且
.
⑴求
的整数部分;
⑵求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21db4e349477acece26642653c1876a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f5ae6592d62f1efb53e37647407722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c799b0a577c0c25274bc0554ea2753ea.png)
⑴求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
⑵求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe9c48c9f8e12cfb0ac44e7f4e919e1.png)
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4 . 半径分别为6、6、6、7的四个球两两外切.它们都内切于一个大球,则大球的半径是________
您最近一年使用:0次
2005高三·天津·竞赛
5 . 设集合
,其中
、
、
、
均为整数}.则集合
中所有元素的和等于( )种.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884e780fb67034b407c5ea3f551325d0.png)
![](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/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.1 | B.4 | C.7 | D.8 |
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2012高三·天津·竞赛
6 . 在正四面体
中,
、
分别是
、
的中点.则直线
和
所成角的余弦值是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2012高三·天津·竞赛
7 . 设椭圆与
轴交于
、
两点,对于椭圆上不同于
、
的任意一点
,直线
与
的斜率之积均为
.则椭圆的离心率为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2012高三·天津·竞赛
8 . 在
中,若
、
为锐角,且
,则对
的形状描述最准确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce39a643cf52415b72d697eba53de3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
A.直角三角形 | B.等腰三角形 |
C.等腰直角三角形 | D.以上均不对 |
您最近一年使用:0次
2012高三·天津·竞赛
9 . 已知
.则
的值是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eefb0cdf5002ba0f3058d2db2103879.png)
A.正数 | B.零 | C.负数 | D.以上皆有可能 |
您最近一年使用:0次