(¸ß¶þÏÂÊýѧÆÚÄ©18·ÝºÏ¼¯)½­ËÕÊ¡ÑïÖÝÊи߶þÏÂѧÆÚÊýѧÆÚÄ©ÊÔ¾íºÏ¼¯ ÏÂÔر¾ÎÄ

¼´

f2k?2?lk?1 fk?1222222ËùÒÔfk2?1?fk?2?fk?1??fk?1?fk??fk?1?2fkfk?1?fk?1?fk?f2k?2?f2k?1?f2k?3

ËùÒÔ£¬µ±n?k?1ʱ£¬µÈʽҲ³ÉÁ¢£»¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­11·Ö ×ÛÉÏ£¬ÓÉ£¨1£©¡¢£¨2£©Öª£¬¶ÔÈÎÒân?N¾ùÓÐ21£®£¨±¾Ð¡ÌâÂú·Ö12·Ö£©

*f2n?lnºÍfn2?fn2?1?f2n?1£®¡­¡­¡­12·Ö fn??a??1?1?alnx?x???0????x?1??x?1?alnx??1?ax?alnx?a?1?x???'?½â£º(¢ñ) f?x??£¬¡­¡­1·Ö 22?x?1??x?1?Áîg?x??ax?alnx?a?1£¬

a?0ʱg?x???1Ϊ³£º¯Êý£¬²»¾ßÓе¥µ÷ÐÔ¡£ ¡­¡­¡­2·Ö

aa?x?1??0£¬g?x?ÔÚ?1,???Éϵ¥µ÷µÝÔö£» ¡­¡­¡­3·Ö a?0ʱg?x??a??xx'(¢ò)a?1ʱg?x??x?lnx?2£¬

e2eg?3??3?ln3?2?ln?0£¬g?4??4?ln4?2?ln?0 £¬ ¡­¡­¡­4·Ö

43

Éèg?b??0£¬Ôòb??3,4?¡£

ÒòΪ´Ëʱg?x?ÔÚ?1,???Éϵ¥µ÷µÝÔö¿ÉÖªµ±x??1,b?ʱ£¬g?x??0£»µ±x??b,???ʱ£¬g(x)?0£¬ ËùÒÔµ±x??1,b?ʱ£¬fµ±x?bʱ£¬f?x?min'?x??0£»µ±x??b,???ʱ£¬f'?x??0£¬

b?1?lnb??f?b??£¬ ¡­¡­6·Ö

b?1g?b??0£¬?b?lnb?2?0£¬¼´lnb?b?2£¬

ËùÒÔf?b??b£¬

b??3,4?£¬?f?b???3,4?£¬

?n?3£¬¹ÊÕýÕûÊýnµÄֵΪ1¡¢2»ò3¡£ ¡­¡­¡­8·Ö

x?1?lnx??3£¬ (¢ó)ÓÉ(¢ò)Öª£¬µ±a?1ʱ£¬f?x??3ºã³ÉÁ¢£¬¼´

x?11?lnx?3?x?1?3?x?1?2x?33?1??2??x?1?£¬ £¬lnx?xxxx£¬

Áîx?1?n?n?1?µÃln??1?n?n?1????2?331??1?2??2?3???¡­12·Ö

n?n?1??1n?n?1??nn?1?

Ôòln?1?1?2??ln3£¨n?1ÔÝʱ²»·ÅËõ£©

?11?ln?1?2?3??2?3???£¬ £®£®£®£®£®£®£®£®£® £®£®£®£¬

?23?1??1ln?1?nn?1?2?3??????. ??nn?1??

ÒÔÉÏn¸öʽ×ÓÏà¼ÓµÃ:

1??1ln?1?1?2??ln?1?2?3??...?ln?1?nn?1?ln3?2n?1?3???????? ???2n?1?73535?lne?2n???2n???2n?

2n?12n?12ËùÒÔln?1?1?2???1?2?3??...???1?n?n?1????2n?¼´?1?1?2???1?2?3??...???1?n?n?1????e2n?52??5£¬ 2¡£ ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­12·Ö

£¨22£©£¨±¾Ð¡ÌâÂú·Ö10·Ö£©Ñ¡ÐÞ4¡ª1£º¼¸ºÎÖ¤Ã÷Ñ¡½² ÒÑÖª£ºÈçͼ£¬PÊÇ¡ÑOµÄÖ±¾¶ABÑÓ³¤ÏßÉϵÄÒ»µã£¬¸îÏßOÓÚC¡¢DÁ½µã£¬ÏÒDFÓëÖ±¾¶AB´¹Ö±£¬HΪ´¹×㣬CFÓëµãE.

£¨¢ñ£©ÈôOB=4,AD=

,ÇóÏ߶ÎDFµÄ³¤.

PCD½»¡ÑAB½»ÓÚ

£¨¢ò£©ÇóÖ¤£ºPA¡¤PB£½PO¡¤PE£»

¡¾´ð°¸¡¿£¨¢ñ£©ÔÚÖ±½Ç¡÷ABDÖÐ,AD=AH?AB,¼´8=8AH,ËùÒÔAH=1,BH=7,ÓÖDH=AH?HB,¼´DH=7,ËùÒÔDF=£¨¢ò£©Ö¤Ã÷£ºÁ¬½ÓOD.

¡ßABÊÇ¡ÑOµÄÖ±¾¶£¬ÏÒDFÓëÖ±¾¶AB´¹Ö±£¬ HΪ´¹×㣬CÔÚ¡ÑOÉÏ£¬

¡à¡ÏDOA£½¡ÏDCF£¬¡à¡ÏPOD£½¡ÏPCE. ÓÖ¡ß¡ÏDPO£½¡ÏEPC£¬¡à¡÷PDO¡×¡÷PEC£¬ ¡à

2

2

2

.¡­¡­¡­5·Ö

PDPO¼´PD¡¤PC£½PO¡¤PE. ?PEPCÓɸîÏ߶¨ÀíµÃPA¡¤PB£½PD¡¤PC£¬¡àPA¡¤PB£½PO¡¤PE. ¡­¡­¡­¡­¡­10·Ö £¨23£©£¨±¾Ð¡ÌâÂú·Ö10·Ö£©Ñ¡ÐÞ4-4£º×ø±êϵÓë²ÎÊý·½³Ì ÔÚÖ±½Ç×ø±êϵxOyÖУ¬Ö±ÏßC1:Ϊ¼«ÖὨÁ¢¼«×ø±êϵ¡£ £¨¢ñ£©Çó

x=?2£¬Ô²C2£º?x?1???y?2??1,ÒÔ×ø±êÔ­µãΪ¼«µã£¬ xÖáµÄÕý°ëÖá

22C1£¬

C2µÄ¼«×ø±ê·½³Ì£»

£¨¢ò£©ÈôÖ±ÏßC3µÄ¼«×ø±ê·½³ÌΪ???4???R?£¬ÉèC2ÓëC3µÄ½»µãΪM,N ,Çó?C2MNµÄÃæ»ý

¡¾´ð°¸¡¿£¨¢ñ£©ÒòΪx??cos?,y??sin?£¬

¡àC1µÄ¼«×ø±ê·½³ÌΪ?cos???2£¬C2µÄ¼«×ø±ê·½³ÌΪ

?2?2?cos??4?sin??4?0.¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­5·Ö

£¨¢ò£©½«?=?42??32??4?0£¬

?2=2£¬´úÈë??2?cos??4?sin??4?0£¬µÃ½âµÃ?1=22£¬|MN|=?12£­?2=2£¬

ÒòΪC2µÄ°ë¾¶Îª1£¬Ôò?C2MNµÄÃæ»ý

11?2?1?sin45o=.¡­¡­¡­¡­¡­10·Ö 22£¨24£©£¨±¾Ð¡ÌâÂú·Ö10·Ö£©Ñ¡ÐÞ4¡ª5£º²»µÈʽѡ½² ÒÑÖªa,bΪʵÊý£¬ÇÒa?0,b?0£¬ £¨¢ñ£©ÇóÖ¤£º(a?b?)(a?1a211?)?9£» ba2£¨¢ò£©Çó(5?2a)2?4b2?(a?b)2µÄ×îСֵ¡£ ¡¾´ð°¸¡¿£¨¢ñ£©Ö¤Ã÷£ºÒòΪa?0,b?0£¬ËùÒÔ

¢Ù

ͬÀí¿ÉÖ¤

ÓÉ¢Ù£¬¢Ú½áºÏ²»µÈʽµÄÐÔÖʵÃ

¢Ú

¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­5·Ö

222222???(5?2a)?4b?(a?b)1?1?2£¨¢ò£©???????(5?2a)?1?2b?1?(a?b)?2?£¬

2ËùÒÔ(5?2a)?4b?(a?b)?22225£¬ 6µ±ÇÒ½öµ±

5?2a2ba?b255??,b?£¬ ʱȡµÈºÅ£¬½âµÃa?112121225525,b?ʱ£¬(5?2a)2?4b2?(a?b)2È¡×îСֵ¡£ 12126¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­10·Ö

ËùÒÔµ±a?

¸ß¶þÏÂѧÆÚÆÚÄ©ÊýѧÊÔ¾í

Ò»¡¢Ñ¡ÔñÌ⣺(±¾´óÌâ¹²10СÌ⣬ÿСÌâ4·Ö£¬¹²40·Ö£®ÔÚÿСÌâ¸ø³öµÄËĸöÑ¡ÏîÖУ¬Ö»ÓÐÒ»ÏîÊÇ·ûºÏÌâÄ¿Òª

ÇóµÄ)

1£®iÊÇÐéÊýµ¥Î»£¬Ôò¸´ÊýA£®1

21?iµÄÐ鲿ÊÇ( ) 1?iB£®?1

C£®i

D£®?i

2£®º¯Êýf(x)?xcosxµÄµ¼ÊýΪ( ) A£®f'(x)?2xcosx?xsinx C£®f'(x)?xcosx?xsinx 3£®Èô(3x?A£®3

0.422B£®f'(x)?2xcosx?xsinx D£®f'(x)?xcosx?2xsinx

221n)µÄÕ¹¿ªÊ½Öи÷ÏîϵÊýºÍΪ64£¬ÄÇônµÈÓÚ( ) xB£®6

C£®7

D£®8

4£®Èôa?3,b?log¦Ð3,c?log3sinA£®a?b?c

3£¬Ôò( ) ¦ÐC£®c?a?b

D£®b?c?a

B£®b?a?c

5£®¶¨ÒåÔÚRÉϵĺ¯Êýf(x)Âú×ãf(x)??A£®1

B£®2

?log3(9?x),x?0£¬Ôòf(3)µÄֵΪ( )

f(x?1),x?0?C£®£­2

D£®£­3

6£®ÉèÀëÉ¢ÐÍËæ»ú±äÁ¿?Âú×ãE??3£¬D??1£¬ÔòE?3(??1)?µÈÓÚ( ) A£®27

B£®24

C£®9

D£®6

7£®ÉèmΪ³£Êý£¬Å×ÎïÏßy?x2?2mx?m3?2m2£¬Ôòµ±m·Ö±ðÈ¡0,?3,?2ʱ£¬ÔÚƽÃæÖ±½Ç×ø±êϵÖÐͼÏñ×îÇ¡

µ±µÄÊÇ(ÕâÀïÊ¡ÂÔÁË×ø±êÖá)( )

A£®

B£®

C£®

D£®

8£®¡°º¯Êýf(x)?xx?a?bÊÇÆ溯Êý¡±ÊÇ¡°a?0ÇÒb?0¡±µÄ( )

A£®³ä·Ö²»±ØÒªÌõ¼þ

B£®±ØÒª²»³ä·ÖÌõ¼þ D£®³äÒªÌõ¼þ

C£®¼È²»³ä·ÖÒ²²»±ØÒªÌõ¼þ

9£®ÏÖÒª´Ó¼×¡¢ÒÒ¡¢±û¡¢¶¡¡¢ÎìÎåÈËÖÐÑ¡³öÈýÈ˵£Èΰ೤¡¢¸±°à³¤¡¢ÍÅÖ§ÊéÈýÖÖ²»Í¬µÄÖ°Îñ£¬ÇÒÉϽìÈÎÖ°µÄ¼×¡¢

ÒÒ¡¢±û¶¼²»ÔÙÁ¬ÈÎÔ­Ö°ÎñµÄ·½·¨ÖÖÊýΪ( ) £®£®£®£®£®£®£®A£®48

B£®30

C£®36

D£®32