ɽ¶«Ê¡2015Äê¸ß¿¼Ä£Äâ³å´Ì¾í²Î¿¼´ð°¸ ÎÄ¿ÆÊýѧ£¨¶þ£©
31---5B D D A C 6--10 C D D A B 11£®(0,1) 12£®70 13£®43 14£®16
?15£®¢Ù¢Ú¢Ü
f(x)?22sin16£®½â£º£¨¢ñ£©
?8xcos?8x?2(2cos2?8x?1)
?2sin?4x?2cos?4x?2sin(?x?)44£¬¡2·Ö
?T?ËùÒÔ£¬º¯Êýf(x)µÄ×îСÕýÖÜÆÚΪ
2??4?8£® ¡¡¡¡¡¡3·Ö
2k??ÓÉ
?2??4x??4?2k???2£¨k?Z£©µÃ8k?3?x?8k?1£¨k?Z£©£¬
?º¯Êýf(x)µÄµ¥µ÷µÝÔöÇø¼äÊÇ?8k?3,8k?1?£¨k?Z£©¡¡¡¡¡¡¡¡¡¡¡¡5·Ö
Qf(2)?2sin(?)?2cos?2244£¨¢ò£©£¬
f(4)?2sin(??)??2sin??244£¬?P(2,2), Q(4,?2)¡¡¡¡¡7·Ö ? |OP|?6, |PQ|?23, |OQ|?32 uuuruuurOP?OQ2?4?2?(?2)3ruuur?cos?POQ?uuu?3 |OP|?|OQ|6?32´Ó¶ø
??????sin?POQ?1?cos2?POQ?Éè?OPQµÄÍâ½ÓÔ²µÄ°ë¾¶ÎªR£¬
63£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡10·Ö
|PQ|?2Rsin?POQÓÉ
?R?|PQ|2332??2sin?POQ262?3
9S??R2??2¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡12·Ö ??OPQµÄÍâ½ÓÔ²µÄÃæ»ý
- 9 -
17£®½â£º£¨¢ñ£©Qº¯Êýy?f(x)?2ÔÚÇø¼ä(0,??)ÉÏÓÐÁ½¸ö²»Í¬µÄÁãµã£¬
2?f(x)?2?0£¬¼´ax?2x?4?0ÓÐÁ½¸ö²»Í¬µÄÕý¸ùx1ºÍx2
?a?0??x1?x2?2?0?a???xx?4?0?12a1???4?16a?0?0?a??411?P(A)?4?416 ¡¡¡¡¡¡¡6·Ö ¡4·Ö
£¨¢ò£©ÓÉÒÑÖª£ºa?0,x?0£¬ËùÒÔ
f(x)?2ax?4x£¬¼´f(x)?4a
?f(x)min?4a£¬
22Qf?x??bÔÚx??0,???ºã³ÉÁ¢ ?4a?b¡¡(?) ¡¡¡¡¡¡¡¡¡¡¡8·Ö
µ±a?1ʱ£¬b?1ÊʺÏ(?)£» µ±a?2,3,4,5ʱ£¬b?1,2¾ùÊʺÏ(?)£» µ±a?6ʱ£¬b?1,2,3¾ùÊʺÏ(?)£» Âú×ã(?)µÄ»ù±¾Ê¼þ¸öÊýΪ1?8?3?12£®¡10·Ö
¶ø»ù±¾Ê¼þ×ÜÊýΪ6?6?36£¬¡¡¡¡11·Ö
?P(B)?121?363£® ¡¡¡¡12·Ö
18£®Ö¤Ã÷£º£¨¢ñ£© Á¬½áBDºÍAC½»ÓÚO£¬Á¬½áOF£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡1·Ö
BAQABCDΪÕý·½ÐΣ¬?OΪBDÖе㣬?FΪDEÖе㣬
?OF//BE£¬ ¡¡¡4·Ö
OGCQBE?Æ½ÃæACF£¬OF?Æ½ÃæACF
?BE//Æ½ÃæACF£®¡¡¡¡¡¡¡¡¡¡¡5·Ö
£¨¢ò£© ×÷EG?ADÓÚG
EFD?AE?Æ½ÃæCDE£¬CD?Æ½ÃæCDE£¬?AE?CD£¬
QABCDΪÕý·½ÐΣ¬?CD?AD£¬QAEIAD?A,AD,AE?Æ½ÃæDAE£¬
?CD?Æ½ÃæDAE£¬¡¡¡¡¡7·Ö ?CD?EG£¬QADICD?D£¬
- 10 -
?EG?Æ½ÃæABCD¡¡¡8·Ö
?AE?Æ½ÃæCDE£¬DE?Æ½ÃæCDE£¬?AE?DE£¬QAE?DE?2£¬
?AD?22£¬EG?2 ¡10·Ö
1182V?SWABCD?EG??(22)2?2?333 ¡¡¡12·Ö ?ËÄÀâ×¶E?ABCDµÄÌå»ý
nn[3?(?1)]a?2a?2[(?1)?1]?0, n?2nQ19£®½â£º£¨¢ñ£©
?[3?(?1)2n?1]a2n?1?2a2n?1?2[(?1)2n?1?1]?0,
¼´
a2n?1?a2n?1?2¡¡¡¡4·Ö Qbn?a2n?1£¬?bn?1?bn?a2n?1?a2n?1?2
?{bn}ÊÇÒÔb1?a1?1ΪÊ×ÏÒÔ2Ϊ¹«²îµÄµÈ²îÊýÁÐ ¡¡5·Ö bn?1?(n?1)?2?2n?1¡¡¡¡6·Ö
nn[3?(?1)]a?2a?2[(?1)?1]?0, n?2n£¨¢ò£©¶ÔÓÚ
an?21?(3?1)an?2?2an?2(1?1)?0,¼´an2£¬
µ±nΪżÊýʱ£¬¿ÉµÃ
? a2, a4, a6, LÊÇÒÔ
µ±nÎªÆæÊýʱ£¬¿ÉµÃ
a2?112ΪÊ×ÏÒÔ2Ϊ¹«±ÈµÄµÈ±ÈÊýÁУ»¡¡¡¡¡¡¡¡¡8·Ö
(3?1)an?2?2an?2(?1?1)?0,¼´an?2?an?2£¬
? a1, a3, a5, LÊÇÒÔa1?1ΪÊ×ÏÒÔ2Ϊ¹«²îµÄµÈ²îÊýÁС¡¡¡¡¡¡¡¡¡10·Ö
11[(1?()n]12?[n?1?n(n?1)?2]?2121?2?T2n?(a1?a3?L?a2n?1)?(a2?a4?L?a2n)?n2?1?12n ¡12·Ö
20£®½â£º£¨¢ñ£©Qg(x)?ax?lnx£¬?g(1)?a£¬
g?(x)?a?1x
1?g?(1)???13Qg(x)ÔÚ(1,g(1))´¦µÄÇÐÏßÓëÖ±Ïßx?3y?5?0´¹Ö±£¬
- 11 -
1?(a?1)???1?a??23¡¡¡3·Ö
x?f(x)?e?a£®Áîf?(x)?0£¬µÃx?ln(?a)£® ¡4·Ö f(x)R£¨¢ò£©µÄ¶¨ÒåÓòΪ£¬ÇÒ
?Èôln(?a)?0£¬¼´?1?a?0ʱ£¬f(x)?0£¬f(x)ÔÚx?[0,2]ÉÏΪÔöº¯Êý£¬?f(x)min?f(0)?1£»¡¡¡¡5·Ö
2?Èôln(?a)?2£¬¼´a??eʱ£¬f(x)?0£¬f(x)ÔÚx?[0,2]ÉÏΪ¼õº¯Êý£¬
2f(x)?f(2)?e?2a£»¡¡6·Ö min?2?Èô0?ln(?a)?2£¬¼´?e?a??1ʱ£¬ÓÉÓÚx?[0,ln(?a))ʱ£¬f(x)?0£»x?(ln(?a),2]f(x)min?f(ln(?a))?aln(?a)?a ?ʱ£¬f(x)?0£¬ËùÒÔ
f(x)min×ÛÉÏ¿ÉÖª
1, ?1?a?0????e2?2a, a??e2?aln(?a)?a,?e2?a??1?¡¡¡8·Ö £¨¢ó£©g(x)µÄ¶¨ÒåÓòΪ(0,??)£¬
g?(x)?a?ÇÒ
1ax?1?xx£® Qa?0ʱ£¬?g?(x)?0£¬?g(x)ÔÚ(0,??)Éϵ¥µ÷µÝ
¼õ£®¡¡¡9·Ö
?Áîf(x)?0£¬µÃx?ln(?a)
??f(x)µ¥µ÷µÝÔö£¬¢ÙÈô?1?a?0ʱ£¬ln(?a)?0£¬ÔÚ(ln(?a),??)ÉÏf(x)?0£¬ÓÉÓÚg(x)ÔÚ(0,??)Éϵ¥µ÷µÝ¼õ£¬ËùÒÔ²»ÄÜ´æÔÚÇø¼äM£¬Ê¹µÃf(x)ºÍg(x)ÔÚÇø¼äMÉϾßÓÐÏàͬµÄµ¥µ÷ÐÔ£»¡¡¡¡¡10·Ö
?¢ÚÈôa??1ʱ£¬ln(?a)?0£¬ÔÚ(??,ln(?a))ÉÏf(x)?0£¬f(x)µ¥µ÷µÝ¼õ£»
?ÔÚ(ln(?a),??)ÉÏf(x)?0£¬f(x)µ¥µ÷µÝÔö£®ÓÉÓÚg(x)ÔÚ(0,??)Éϵ¥µ÷µÝ¼õ£¬?´æÔÚÇø
¼äM?(0,ln(?a)]£¬Ê¹µÃf(x)ºÍg(x)ÔÚÇø¼äMÉϾùΪ¼õº¯Êý£® ×ÛÉÏ£¬µ±?1?a?0ʱ£¬²»ÄÜ´æÔÚÇø¼äM£¬Ê¹µÃf(x)ºÍg(x)ÔÚÇø¼äMÉϾßÓÐÏàͬµÄµ¥µ÷ÐÔ£»µ±a??1ʱ£¬´æÔÚÇø¼äM?(0,ln(?a)]£¬Ê¹µÃf(x)ºÍg(x)ÔÚÇø¼äMÉϾùΪ¼õº¯Êý£®¡¡¡¡¡¡13·Ö
F1:(x?3)2?y2?81(x,y)PRP21½â£º£¨I£©ÉèÔ²ÐĵÄ×ø±êΪ£¬°ë¾¶ÎªÓÉÓÚ¶¯Ô²ÓëÔ²ÏàÇУ¬
- 12 -
Ïà¹ØÍÆ¼ö£º