µÚÒ»·¶ÎÄÍø - רҵÎÄÕ·¶ÀýÎĵµ×ÊÁÏ·ÖÏíÆ½Ì¨

ɽ¶«Ê¡¸ßÈýÊýѧ³å´ÌÄ£Äâ(¶þ)ÊÔÌâ Àí

À´Ô´£ºÓû§·ÖÏí ʱ¼ä£º2025/11/20 5:51:16 ±¾ÎÄÓÉloading ·ÖÏí ÏÂÔØÕâÆªÎĵµÊÖ»ú°æ
˵Ã÷£ºÎÄÕÂÄÚÈݽö¹©Ô¤ÀÀ£¬²¿·ÖÄÚÈÝ¿ÉÄܲ»È«£¬ÐèÒªÍêÕûÎĵµ»òÕßÐèÒª¸´ÖÆÄÚÈÝ£¬ÇëÏÂÔØwordºóʹÓá£ÏÂÔØwordÓÐÎÊÌâÇëÌí¼Ó΢ÐźÅ:xxxxxxx»òQQ£ºxxxxxx ´¦Àí£¨¾¡¿ÉÄܸøÄúÌṩÍêÕûÎĵµ£©£¬¸ÐлÄúµÄÖ§³ÖÓëÁ½⡣

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 -

ËÑË÷¸ü¶à¹ØÓÚ£º ɽ¶«Ê¡¸ßÈýÊýѧ³å´ÌÄ£Äâ(¶þ)ÊÔÌâ Àí µÄÎĵµ
ɽ¶«Ê¡¸ßÈýÊýѧ³å´ÌÄ£Äâ(¶þ)ÊÔÌâ Àí.doc ½«±¾ÎĵÄWordÎĵµÏÂÔØµ½µçÄÔ£¬·½±ã¸´ÖÆ¡¢±à¼­¡¢ÊղغʹòÓ¡
±¾ÎÄÁ´½Ó£ºhttps://www.diyifanwen.net/c2t91y0tqw08njyy26yqz6tzp834d3b018oa_3.html£¨×ªÔØÇë×¢Ã÷ÎÄÕÂÀ´Ô´£©
ÈÈÃÅÍÆ¼ö
Copyright © 2012-2023 µÚÒ»·¶ÎÄÍø °æÈ¨ËùÓÐ ÃâÔðÉùÃ÷ | ÁªÏµÎÒÃÇ
ÉùÃ÷ :±¾ÍøÕ¾×ðÖØ²¢±£»¤ÖªÊ¶²úȨ£¬¸ù¾Ý¡¶ÐÅÏ¢ÍøÂç´«²¥È¨±£»¤ÌõÀý¡·£¬Èç¹ûÎÒÃÇ×ªÔØµÄ×÷Æ·ÇÖ·¸ÁËÄúµÄȨÀû,ÇëÔÚÒ»¸öÔÂÄÚ֪ͨÎÒÃÇ£¬ÎÒÃǻἰʱɾ³ý¡£
¿Í·þQQ£ºxxxxxx ÓÊÏ䣺xxxxxx@qq.com
ÓåICP±¸2023013149ºÅ
Top