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题目列表(包括答案和解析)

1-10.CDBBA   CACBD

11.6ec8aac122bd4f6e 12. ①③④   13.-2或1  14. 6ec8aac122bd4f6e6ec8aac122bd4f6e  15.2  16. 6ec8aac122bd4f6e 17.6ec8aac122bd4f6e.

18.

解:(1)由已知6ec8aac122bd4f6e6ec8aac122bd4f6e          7分

(2)由6ec8aac122bd4f6e                                                                   10分

由余弦定理得6ec8aac122bd4f6e                          14分

 

19.(1)证明:∵PA⊥底面ABCD,BC6ec8aac122bd4f6e平面AC,∴PA⊥BC,                                  3分

∵∠ACB=90°,∴BC⊥AC,又PA∩AC=A,∴BC⊥平面PAC.                             5分

(2)解:过C作CE⊥AB于E,连接PE,

∵PA⊥底面ABCD,∴CE⊥面PAB,

∴直线PC与平面PAB所成的角为6ec8aac122bd4f6e,                                                     10分

∵AD=CD=1,∠ADC=60°,∴AC=1,PC=2,

6ec8aac122bd4f6e中求得CE=6ec8aac122bd4f6e,∴6ec8aac122bd4f6e.                                                  14分

 

6ec8aac122bd4f6e20.解:(1)由6ec8aac122bd4f6e①,得6ec8aac122bd4f6e②,

②-①得:6ec8aac122bd4f6e.                              4分

(2)由6ec8aac122bd4f6e求得6ec8aac122bd4f6e.          7分

6ec8aac122bd4f6e6ec8aac122bd4f6e   11分

6ec8aac122bd4f6e

6ec8aac122bd4f6e.                                                                 14分

 

21.解:

(1)由6ec8aac122bd4f6e得c=1                                                                                       1分

6ec8aac122bd4f6e,                                                         4分

6ec8aac122bd4f6e6ec8aac122bd4f6e

6ec8aac122bd4f6e                                                                                        5分

(2)6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e时取得极值.由6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e.                                                                                          8分

6ec8aac122bd4f6e6ec8aac122bd4f6e,∴当6ec8aac122bd4f6e时,6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e上递减.                                                                                       12分

6ec8aac122bd4f6e∴函数6ec8aac122bd4f6e的零点有且仅有1个     15分

 

22.解:(1) 设6ec8aac122bd4f6e,由已知6ec8aac122bd4f6e

6ec8aac122bd4f6e,                                        2分

设直线PB与圆M切于点A,6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e                                                 6分

(2) 6ec8aac122bd4f6e点 B(0,t),点6ec8aac122bd4f6e,                                                                7分

进一步可得两条切线方程为:

6ec8aac122bd4f6e,                                   9分

6ec8aac122bd4f6e6ec8aac122bd4f6e6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e,                                          13分

6ec8aac122bd4f6e,又6ec8aac122bd4f6e时,6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e面积的最小值为6ec8aac122bd4f6e                                                                            15分

 

 


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