1、 1 2016 2017 ( 14 5 70 .) 1 A=x|x=2k+1 k Z B=x|0b0) 3 2 F E AF 2 3 3 O (1) E (2) A l E P Q OPQ l 19 n a n n T 12 nn T aa a . 1 n a 2016 1 2 q n T n n T 2 * nN n a 0 n a 1 22 1 1 1 1 ( ) ( ) nn n n n n T T aa aa n a . 5 20 1 x 2 x ) ( 2 1 x x ) 0 ( ) ( 2 2 3 a x a bx ax x f . 1 2 , 1 2 1 x x ) (x f 2
2、 12 | | | | 2 xx b 3 ) ( ) ( ) ( 1 x x a x f x g 12 ( , ) x x x a x 2 2 1 ( ) (3 2) 12 g x a a . 6 ( 14 5 70 .) 1 1,3 2 5 3 26 54 5 4 6 11 157 (2, ) 8 5 33 , 9 5 10 10 511 100 10112 12 13 1 314 1 3 2 3 6 90 15 16 17 14 18 19 20 16 15 (1) 2 , 2, ( ) sin(2 ) 4 f x x 62 ( ) sin( ) 6 3 4 4 f 4 (2) , 22
3、x 53 2, 4 4 4 x 6 x 2 3 8 8 8 3 8 2 2 4 x 5 4 2 0 2 3 4 y 2 20 1 0 1 2 2 8 7 12 y f x , 22 3 , , , 2 8 8 2 14 16 1 AC BD O PO ABCD BD AC 2 PB PD O BD BD PO 4 AC PO O BD APC PC APC BD PC 7 2 ABCD / BC AD 9 , AD PAD BC PAD / BC PAD 11 BC PBC PBC PAD l / BC l 14 17 (1) , 2 2 (1 0 75 )(5 ) (1 0 75 )(7 )
4、 12 22 kb kb 2 2 (1 0 75 )(5 ) 0 (1 0 75 )(7 ) 1 kb kb b=5,k (2) p=q ,2 (1 t)(x 5) 2 2 x P B C A D 8 (1 ) t 2 2 ( 5) 1 ( 5) x x x t x 1+ 1 25 10 x x 25 () f x x x 12 1 2 1 2 1 2 12 25 0 4; ( ) ( ) ( ) 0 xx x x f x f x x x xx 25 () f x x x (0,4 0 x=4 ,f(x) 41 4 . x=4 t 5 x=4 4 18 :(1) F(c,0) 2 c 2 3
5、3 c 3. c a 3 2 a 2 b 2 a 2 c 2 1. E x 2 4 y 2 (2) l x l y kx 2 P(x1 y1) Q(x2 y2) y kx 2 x 2 4 y 2 1 (1 4k 2 )x 2 16kx 12 16(4k 2 3)0 k 2 3 4 x1,2 8k 4k 2 3 4k 2 1 . |PQ| k 2 1|x1 x2| 4 k 2 1 4k 2 3 4k 2 1 O PQ d 2 k 2 1 OPQ S OPQ 1 2 d|PQ| 4 4k 2 3 4k 2 1 4k 2 3 t t0 S OPQ 4t t 2 4 4 t 4 t . t 4 t t
6、 2 k 7 2 0 OPQ l y 7 2 x 2 y 7 2 x 9 19 1 1 1 2016( ) 2 n n a ( 1) 0 1 ( 1) 2 11 2016 ( ) 2016 ( ) 22 nn n n n n T | nn ba | nn RT 1 1 2016( ) 2 n n b ( 1) 2 1 2016 ( ) 2 nn n n R 1 1 2016 ( ) 2 n n n R R * 10, n n N 1 1 n n R R * 11, n n N 1 1 n n R R * ,0 n n N R * 10, n n N 1nn RR * 11, n n N 1nn
7、 RR n R 11 R 11 55 11 1 2016 ( ) 0 2 T 9 10 12 0, 0, 0 T T T max 9 12 ( ) max , n T T T . 3 10 12 12 11 10 11 9 1 ( ) (2016 ( ) ) 1 2 T a a a a T 12 n n T 2 2 n 3 22 2 1 2 3 1 2 1 3 ( )( ) a a a aa aa 2 1 3 a aa 2 2 1 3 a aa 1 22 1 1 1 1 ( ) ( ) nn n n n n T T aa aa 2 n 1 22 1 1 1 1 ( ) ( ) nn n n n
8、 n T T aa aa 21 2 11 1 1 1 () n n nn n n aa aa a 2 1 2 1 1 1 +1 nn n n n a a a a 22 1 1 +2 nn n n n a a a a 1 2 1 1 2 1 n n n n n n n n a a a a 1 2 1 1 22 1 ( ) ( ) 1 nn n n n n nn a a a a aa 2 n 1 11 2 () n nn n n aa c a 11 1, 1 nn c c c * 1, n c n N 2 11 n n n a a a 2, n * nN n a 10 20 1 ) 0 ( ) (
9、 2 2 3 a x a bx ax x f ) 0 ( 2 3 ) ( 2 2 a a bx ax x f 0 ) 2 ( 0 ) 1 ( f f ) 0 ( 0 4 12 0 2 3 2 2 a a b a a b a . 9 6 b a x x x x f 36 9 6 ) ( 2 3 2 ) 0 ( 2 3 ) ( 2 2 a a bx ax x f , 12 , xx ( ) 0 fx 12 | | | | 2 xx 2 1 2 1 2 1 2 ( ) 2 2| | 4 x x x x x x 8 | 3 | 2 ) 3 ( 2 ) 3 2 ( 2 a a a b 4 22 3 (3
10、 ) b a a 2 0 b 06 a 2 ( ) 3 (3 ) p a a a 2 ( ) 9 18 p a a a ( ) 0 pa 4 0 a 2 ( ) 0 pa 4 a 2. () pa (0,2) (2,3) 2 a () pa 12 () pa (0,3 12 b 23 3 2 1 , x x 0 ) ( x f ) )( ( 3 ) ( 2 1 x x x x a x f . 3 2 1 a x x a x 2 3 1 1 x | 1 ) ( 3 ) 3 1 ( | | ) 3 1 ( ) )( 3 1 ( 3 | | ) ( | a x x a x a a x x a x g
11、 2 1 x x x 1 . 3 xa ) 1 3 3 )( 3 1 ( | ) ( | a x x a x g | ( )| gx ) 3 1 3 )( 3 1 ( 3 a x x a a a a a x a 3 1 4 3 ) 2 ( 3 2 3 2 3 2 31 43 a aa 12 ) 2 3 ( 2 a a | ( )| gx 2 (3 2) 12 a a 11 2016 2017 21 10 A(a b)( a b) M cos sin sin cos B( b a) (1) M (2) C x 2 y 2 1 N 0 1 2 1 0 C 22 10 C P 2 4 sin 3 3
12、 2 C 23 10 3 4 1 2 1 4 (1) (2) 24 10 S ABCD SA ABCD 90 DAB ABC SA AB BC a 3 AD a ( 0) a E BS 1 DE SC 2 E BS B S CD E 12 A D B C S E13 21 10 (1)M a b b a acos bsin asin bcos b a acos bsin b asin bcos a cos 0 sin 1. M 0 1 1 0 M 1 M 1 0 0 1 M 1 0 1 1 0 (2) N x 1 2 y y x x y y 2x x 2 y 2 1 4x 2 y 2 22 1
13、0 sin 3 3 2 0 1 C (1,0). 3 C P 2 4 C PC 2 2 1 2 2cos 4 1 C C 2cos 23 10 (1) A B 14 C P(A) 3 4 P(B) 1 2 P(C) 1 4 . P P(A B ) P(A)P( B ) 3 4 1 1 2 3 8 (2) 1,2,3. P( 1) 1 3 4 1 4 P( 2) 3 4 1 1 2 3 8 P( 3) 3 4 1 2 3 8 1 2 3 P 1 43 83 8 E( ) 1 4 3 8 3 8 17 8 24 10 1 SA ABCD 90 DAB AB AD AS A AB AD AS x y
14、 z 1 (0,0, ) Sa ( , ,0) C a a (0,3 ,0) Da( 0) a SA AB a SA AB ( ,0, ) E x a x 0 xa ( , 3 , ) DE x a a x ( , , ) SC a a a 2 DE SC 0 DE SC 2 2 2 3 2 4 0 ax a a ax ax a 2 xa 0 xa DE SC 4 2 E BS B 21 ( ,0, ) 33 E a a 15 SCD 1 1 1 1 ( , , ) n x y z CDE 2 2 2 2 ( , , ) n x y z ( ,2 ,0) CD a a (0,3 , ) SD a a 1 1 0 0 n CD n SD 11 11 20 30 ax ay ay az 11 11 2 3 xy zy 1 (2,1,3) n 6 ( ,2 ,0) CD a a 21 ( , 3 , ) 33 DE a a a 2 2 0 0 n CD n DE 22 2 2 2 20 21 30 33 ax ay ax ay az 22 22 2 5 xy zy 2 (2,1,5) n 8 S CD E 12 12 12 4 1 15 2 105 cos |cos , | 21 | | | | 14 30 nn nn nn S-CD-E 2 105 21 10
