2019ѧÄê¸ßÖÐÊýѧµÚ¶þÕÂÍÆÀíÓëÖ¤Ã÷2.2Ö±½ÓÖ¤Ã÷Óë¼ä½ÓÖ¤Ã÷2.2.2·´Ö¤·¨¼ì²âÐÂÈ˽ÌA°æÑ¡ÐÞ1_2 ÏÂÔر¾ÎÄ

ÄÚÈÝ·¢²¼¸üÐÂʱ¼ä : 2024/12/23 20:40:16ÐÇÆÚÒ» ÏÂÃæÊÇÎÄÕµÄÈ«²¿ÄÚÈÝÇëÈÏÕæÔĶÁ¡£

2.2.2 ·´Ö¤·¨

A¼¶ »ù´¡¹®¹Ì

Ò»¡¢Ñ¡ÔñÌâ

1£®Ó÷´Ö¤·¨Ö¤Ã÷ÃüÌâ¡°Éèa£¬bΪʵÊý£¬Ôò·½³Ìx£«ax£«b£½0ÖÁÉÙÓÐÒ»¸öʵ¸ù¡±Ê±£¬Òª×öµÄ¼ÙÉèÊÇ( )

A£®·½³Ìx£«ax£«b£½0ûÓÐʵ¸ù B£®·½³Ìx£«ax£«b£½0ÖÁ¶àÓÐÒ»¸öʵ¸ù C£®·½³Ìx£«ax£«b£½0ÖÁ¶àÓÐÁ½¸öʵ¸ù D£®·½³Ìx£«ax£«b£½0Ç¡ºÃÓÐÁ½¸öʵ¸ù

½âÎö£º¡°·½³Ìx£«ax£«b£½0ÖÁÉÙÓÐÒ»¸öʵ¸ù¡±µÄ·´ÃæÊÇ¡°·½³Ìx£«ax£«b£½0ûÓÐʵ¸ù£®¡± ´ð°¸£ºA

2£®Ó÷´Ö¤·¨Ö¤Ã÷ÃüÌâ¡°ÈôÖ±ÏßAB£¬CDÊÇÒìÃæÖ±Ïߣ¬ÔòÖ±ÏßAC£¬BDÒ²ÊÇÒìÃæÖ±Ïß¡±µÄ¹ý³Ì¹éÄÉΪÒÔÏÂÈý¸ö²½Ö裺

¢ÙÔòA£¬B£¬C£¬DËĵ㹲Ã棬ËùÒÔAB£¬CD¹²Ã棬ÕâÓëAB£¬CDÊÇÒìÃæÖ±Ïßì¶Ü£»¢ÚËùÒÔ¼ÙÉè´íÎ󣬼´Ö±ÏßAC£¬BDÒ²ÊÇÒìÃæÖ±Ïߣ»¢Û¼ÙÉèÖ±ÏßAC£¬BDÊǹ²ÃæÖ±Ïߣ®

ÔòÕýÈ·µÄ˳ÐòΪ( ) A£®¢Ù¢Ú¢Û C£®¢Ù¢Û¢Ú

B£®¢Û¢Ù¢Ú D£®¢Ú¢Û¢Ù

2

2

2222

2

½âÎö£º½áºÏ·´Ö¤·¨µÄÖ¤Ã÷²½Öè¿ÉÖª£¬ÆäÕýÈ·²½ÖèΪ¢Û¢Ù¢Ú. ´ð°¸£ºB

3£®ÒÑÖªa£¬bÊÇÒìÃæÖ±Ïߣ¬Ö±ÏßcƽÐÐÓÚÖ±Ïßa£¬ÄÇôcÓëbµÄλÖùØϵΪ( ) A£®Ò»¶¨ÊÇÒìÃæÖ±Ïß C£®²»¿ÉÄÜÊÇƽÐÐÖ±Ïß ½âÎö£º¼ÙÉèc¡Îb£¬ ÓÉa¡Îc£¬´Ó¶øµÃa¡Îb£¬ ÕâÓëaÓëbÊÇÒìÃæÖ±Ïßì¶Ü£¬ ¹ÊÖ±ÏßcÓëb²»¿ÉÄÜÊÇƽÐÐÖ±Ïߣ® ´ð°¸£ºC

4£®·ñ¶¨½áÂÛ¡°×ÔÈ»Êýa£¬b£¬cÖÐÇ¡ÓÐÒ»¸öżÊý¡±Ê±£¬ÕýÈ·µÄ·´ÉèΪ( ) A£®a£¬b£¬c¶¼ÊÇÆæÊý

B£®Ò»¶¨ÊÇÏֱཻÏß D£®²»¿ÉÄÜÊÇÏֱཻÏß

- 1 -

B£®a£¬b£¬c¶¼ÊÇżÊý C£®a£¬b£¬cÖÐÖÁÉÙÓÐÁ½¸öżÊý D£®a£¬b£¬c¶¼ÊÇÆæÊý»òÖÁÉÙÓÐÁ½¸öżÊý

½âÎö£º×ÔÈ»Êýa£¬b£¬cÖÐÆæÊý¡¢Å¼ÊýµÄ¿ÉÄÜÇé¿öÓУºÈ«ÎªÆæÊý£¬Ç¡ÓÐÒ»¸öżÊý£¬Ç¡ÓÐÁ½¸öżÊý£¬È«ÎªÅ¼Êý£®³ýÈ¥½áÂÛ¼´Îª·´É裬ӦѡD.

´ð°¸£ºD

5£®ÉèʵÊýa¡¢b¡¢cÂú×ãa£«b£«c£½1£¬Ôòa£¬b£¬cÖÐÖÁÉÙÓÐÒ»¸öÊý²»Ð¡ÓÚ( ) A£®0 1C. 2

1B. 3D£®1

1

½âÎö£º¼ÙÉèa£¬b£¬c¶¼Ð¡ÓÚ£¬Ôòa£«b£«c<1£¬Óëa£«b£«c£½1ì¶Ü£¬Ñ¡ÏîBÕýÈ·£®

3´ð°¸£ºB ¶þ¡¢Ìî¿ÕÌâ

6£®ÒÑ֪ƽÃæ¦Á¡ÉƽÃæ¦Â£½Ö±Ïßa£¬Ö±Ïßb?¦Á£¬Ö±Ïßc?¦Â£¬b¡Éa£½A£¬c¡Îa£¬ÇóÖ¤£ºbÓëcÊÇÒìÃæÖ±Ïߣ¬ÈôÀûÓ÷´Ö¤·¨Ö¤Ã÷£¬ÔòÓ¦¼ÙÉè________£®

½âÎö£º¡ß¿Õ¼äÖÐÁ½Ö±ÏßµÄλÖùØϵÓÐ3ÖÖ£ºÒìÃ桢ƽÐС¢Ïཻ£¬ ¡àÓ¦¼ÙÉèbÓëcƽÐлòÏཻ£® ´ð°¸£ºbÓëcƽÐлòÏཻ

7£®Íê³É·´Ö¤·¨Ö¤ÌâµÄÈ«¹ý³Ì£®Éèa1£¬a2£¬¡­£¬a7ÊÇ1£¬2£¬¡­£¬7µÄÒ»¸öÅÅÁУ¬ÇóÖ¤£º³Ë»ýp£½(a1£­1)(a2£­2)¡­(a7£­7)ΪżÊý£®

Ö¤Ã÷£º¼ÙÉèpΪÆæÊý£¬Ôòa1£­1£¬a2£­2£¬¡­£¬a7£­7¾ùΪÆæÊý£®ÒòÆæÊý¸öÆæÊýÖ®ºÍΪÆæÊý£¬¹ÊÓÐÆæÊý£½________£½0.µ«0¡ÙÆæÊý£¬Õâһì¶Ü˵Ã÷pΪżÊý£®

½âÎö£ºÓɼÙÉèpΪÆæÊý¿ÉÖª(a1£­1)£¬(a2£­2)£¬¡­£¬(a7£­7)¾ùΪÆæÊý£¬ ¹Ê(a1£­1)£«(a2£­2)£«¡­£«(a7£­7)

£½(a1£«a2£«¡­a7)£­(1£«2£«¡­£«7)£½0ΪżÊý£® ´ð°¸£º(a1£­1)£«(a2£­2)£«¡­£«(a7£­7)

8£®Ó÷´Ö¤·¨Ö¤Ã÷ÃüÌâ¡°Èôa£«b£½0£¬Ôòa£¬bȫΪ0(a£¬bΪʵÊý)¡±£¬Æä¼ÙÉèΪ________£® ½âÎö£º¡°a¡¢bȫΪ0¡±¼´ÊÇ¡°a£½0ÇÒb£½0¡±£¬ Òò´ËÓ÷´Ö¤·¨Ö¤Ã÷ʱµÄ¼ÙÉèΪ¡°a£¬b²»È«Îª0¡±£® ´ð°¸£ºa£¬b²»È«Îª0 Èý¡¢½â´ðÌâ

9£®Éèx£¬y¶¼ÊÇÕýÊý£¬ÇÒx£«y>2£¬ÊÔÓ÷´Ö¤·¨Ö¤Ã÷£º

1£«x1£«y<2ºÍ<2ÖÐÖÁÉÙÓÐÒ»¸ö³ÉÁ¢£®

2

2

yx - 2 -

1£«x1£«y1£«x1£«yÖ¤Ã÷£º¼ÙÉè<2ºÍ<2¶¼²»³ÉÁ¢£¬¼´¡Ý2£¬¡Ý2.

yxyxÓÖÒòΪx£¬y¶¼ÊÇÕýÊý£¬ ËùÒÔ1£«x¡Ý2y£¬1£«y¡Ý2x.

Á½Ê½Ïà¼Ó£¬µÃ2£«x£«y¡Ý2x£«2y£¬Ôòx£«y¡Ü2£¬ ÕâÓëÌâÉèx£«y>2ì¶Ü£¬ ËùÒÔ¼ÙÉè²»³ÉÁ¢£® ¹Ê

1£«x1£«yy<2ºÍx<2ÖÐÖÁÉÙÓÐÒ»¸ö³ÉÁ¢£®

10£®ÉèµÈ±ÈÊýÁÐ{an}µÄ¹«±ÈΪq£¬SnΪËüµÄÇ°nÏîºÍ£® (1)ÇóÖ¤£ºÊýÁÐ{Sn}²»ÊǵȱÈÊýÁУ»

(2)µ±q¡Ù1ʱ£¬ÊýÁÐ{Sn}ÊǵȲîÊýÁÐÂð£¿ÎªÊ²Ã´£¿ Ö¤Ã÷£º(1)¼ÙÉè{Sn}ÊǵȱÈÊýÁУ¬ ÔòS2

2£½S1¡¤S3£¬

ËùÒÔa2

2

2

1(1£«q)£½a1¡¤a1(1£«q£«q)£® ÒòΪa2

2

1¡Ù0£¬ËùÒÔ(1£«q)£½1£«q£«q£¬ ËùÒÔq£½0£¬ÕâÓëµÈ±ÈÊýÁеĹ«±Èq¡Ù0ì¶Ü£® ¹ÊÊýÁÐ{Sn}²»ÊǵȱÈÊýÁУ®

(2)µ±q¡Ù1ʱ£¬¼ÙÉè{Sn}ÊǵȲîÊýÁУ¬

ÔòÓÐ2S2

2£½S1£«S3£¬¼´2a1(1£«q)£½a1£«a1(1£«q£«q)£® ÒòΪa1¡Ù0£¬ËùÒÔq(q£­1)£½0. ÓÖq¡Ù1£¬ËùÒÔq£½0. ÕâÓëq¡Ù0ì¶Ü£® ¹Ê{Sn}²»ÊǵȲîÊýÁУ®

B¼¶ ÄÜÁ¦ÌáÉý

1£®Éèa£¬b£¬c´óÓÚ0£¬Ôò3¸öÊý£ºa£«111

b£¬b£«c£¬c£«aµÄÖµ( A£®¶¼´óÓÚ2 B£®ÖÁÉÙÓÐÒ»¸ö²»´óÓÚ2 C£®¶¼Ð¡ÓÚ2

D£®ÖÁÉÙÓÐÒ»¸ö²»Ð¡ÓÚ2

½âÎö£º¼ÙÉèa£«111

b£¬b£«c£¬c£«a¶¼Ð¡ÓÚ2

Ôòa£«1b<2£¬b£«1<2£¬c£«1ca<2 ¡àa£«111

b£«b£«c£«c£«a<6£¬¢Ù

ÓÖa£¬b£¬c´óÓÚ0

)

- 3 -

111

ËùÒÔa£«¡Ý2£¬b£«¡Ý2£¬c£«¡Ý2.

abc111

¡àa£«£«b£«£«c£«¡Ý6.¢Ú

bca¹Ê¢ÙÓë¢Úʽì¶Ü£¬¼ÙÉè²»³ÉÁ¢

111

ËùÒÔa£«£¬b£«£¬c£«ÖÁÉÙÓÐÒ»¸ö²»Ð¡ÓÚ2.

bca´ð°¸£ºD

2£®¶ÔÓÚ¶¨ÒåÔÚʵÊý¼¯RÉϵĺ¯Êýf(x)£¬Èç¹û´æÔÚʵÊýx0£¬Ê¹f(x0)£½x0£¬ÄÇôx0½Ð×÷º¯Êý

f(x)µÄÒ»¸öºÃµã£®ÒÑÖªº¯Êýf(x)£½x2£«2ax£«1²»´æÔںõ㣬ÄÇôaµÄÈ¡Öµ·¶Î§ÊÇ( )

?13?A.?£­£¬? ?22?

C£®(£­1£¬1)

½âÎö£º¼ÙÉ躯Êýf(x)´æÔںõ㣬 Ôòx£«2ax£«1£½xÓÐʵÊý½â£¬ ¼´x£«(2a£­1)x£«1£½0ÓÐʵÊý½â£®

22

?31?B.?£­£¬? ?22?

D£®(£­¡Þ£¬£­1)¡È(1£¬£«¡Þ)

132

ËùÒÔ¦¤£½(2a£­1)£­4¡Ý0£¬½âµÃa¡Ü£­»òa¡Ý.

22

?13?ËùÒÔf(x)²»´æÔںõãʱ£¬aµÄÈ¡Öµ·¶Î§ÊÇ?£­£¬?. ?22?

´ð°¸£ºA

3£®ÒÑÖªÖ±Ïßax£­y£½1ÓëÇúÏßx£­2y£½1ÏཻÓÚP£¬QÁ½µã£¬ÊÇ·ñ´æÔÚʵÊýa£¬Ê¹µÃÒÔPQΪֱ¾¶µÄÔ²¾­¹ý×ø±êÔ­µãO£¿Èô´æÔÚ£¬Çó³öaµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

½â£º²»´æÔÚ£®ÀíÓÉÈçÏ£º¼ÙÉè´æÔÚʵÊýa£¬Ê¹µÃÒÔPQΪֱ¾¶µÄÔ²¾­¹ýÔ­µãO£¬ÔòOP¡ÍOQ. ÉèP(x1£¬y1)£¬Q(x2£¬y2)£® ÓÉ?

?ax£­y£½1£¬?

2

2

2

2

ÏûÈ¥y£¬ÕûÀíµÃ(1£­2a)x£«4ax£­3£½0. ??x£­2y£½1£¬

22

£­4a£­3ËùÒÔx1£«x2£½2£¬x1x2£½2. 1£­2a1£­2aÒòΪx1x2£«y1y2£½0£¬ËùÒÔx1x2£«(ax1£­1)(ax2£­1)£½0£¬ ËùÒÔ(1£«a)x1x2£­a(x1£«x2)£«1£½0£¬ £­3£­4a2

Ôò(1£«a)¡¤2£­a¡¤2£«1£½0£¬

1£­2a1£­2aËùÒÔa£½£­2£¬ÕâÊDz»¿ÉÄܵģ® ¹Ê²»´æÔÚÂú×ãÌâÉèÌõ¼þµÄʵÊýa.

2

2

- 4 -