¡¾¾«±à¡¿2020Äê¸ß¿¼ÊýѧһÂÖ¸´Ï°¶ÔµãÌá·ÖרÌâ2.3 º¯ÊýµÄÆæÅ¼ÐÔÓëÖÜÆÚÐÔ (ÎÄÀí¿ÆÍ¨ÓÃ)(ѧÉú°æ) ÏÂÔØ±¾ÎÄ

ÄÚÈÝ·¢²¼¸üÐÂʱ¼ä : 2025/7/9 21:42:27ÐÇÆÚÒ» ÏÂÃæÊÇÎÄÕµÄÈ«²¿ÄÚÈÝÇëÈÏÕæÔĶÁ¡£

µÚ¶þƪ º¯Êý¼°ÆäÐÔÖÊ ×¨Ìâ2.03 º¯ÊýµÄÆæÅ¼ÐÔÓëÖÜÆÚÐÔ

¡¾¿¼ÊÔÒªÇó¡¿

1.½áºÏ¾ßÌ庯Êý£¬ÁË½âÆæÅ¼ÐԵĸÅÄîºÍ¼¸ºÎÒâÒ壻 2.½áºÏÈý½Çº¯Êý£¬Á˽âÖÜÆÚÐԵĸÅÄîºÍ¼¸ºÎÒâÒå. ¡¾ÖªÊ¶ÊáÀí¡¿ 1.º¯ÊýµÄÆæÅ¼ÐÔ

ÆæÅ¼ÐÔ Å¼º¯Êý ¶¨Òå Èç¹û¶ÔÓÚº¯Êýf(x)µÄ¶¨ÒåÓòÄÚÈÎÒâÒ»¸öx£¬¶¼ÓÐf(£­x)£½f(x)£¬ÄÇôº¯Êýf(x)ÊÇżº¯Êý Èç¹û¶ÔÓÚº¯Êýf(x)µÄ¶¨ÒåÓòÄÚÈÎÒâÒ»¸öx£¬¶¼ÓÐf(£­x)£½£­f(x)£¬ÄÇôº¯Êýf(x)ÊÇÆæº¯Êý ͼÏóÌØµã ¹ØÓÚyÖá¶Ô³Æ Ææº¯Êý 2.º¯ÊýµÄÖÜÆÚÐÔ ¹ØÓÚÔ­µã¶Ô³Æ (1)ÖÜÆÚº¯Êý£º¶ÔÓÚº¯Êýy£½f(x)£¬Èç¹û´æÔÚÒ»¸ö·ÇÁã³£ÊýT£¬Ê¹µÃµ±xÈ¡¶¨ÒåÓòÄÚµÄÈκÎֵʱ£¬¶¼ÓÐf(x£«T)£½f(x)£¬ÄÇô¾Í³Æº¯Êýy£½f(x)ΪÖÜÆÚº¯Êý£¬³ÆTΪÕâ¸öº¯ÊýµÄÖÜÆÚ.

(2)×îСÕýÖÜÆÚ£ºÈç¹ûÔÚÖÜÆÚº¯Êýf(x)µÄËùÓÐÖÜÆÚÖдæÔÚÒ»¸ö×îСµÄÕýÊý£¬ÄÇôÕâ¸ö×îСÕýÊý¾Í½Ð×öf(x)µÄ×îСÕýÖÜÆÚ. ¡¾Î¢µãÌáÐÑ¡¿

1.(1)Èç¹ûÒ»¸öÆæº¯Êýf(x)ÔÚÔ­µã´¦Óж¨Ò壬¼´f(0)ÓÐÒâÒ壬ÄÇôһ¶¨ÓÐf(0)£½0. (2)Èç¹ûº¯Êýf(x)ÊÇżº¯Êý£¬ÄÇôf(x)£½f(|x|).

2.Ææº¯ÊýÔÚÁ½¸ö¶Ô³ÆµÄÇø¼äÉϾßÓÐÏàͬµÄµ¥µ÷ÐÔ£»Å¼º¯ÊýÔÚÁ½¸ö¶Ô³ÆµÄÇø¼äÉϾßÓÐÏà·´µÄµ¥µ÷ÐÔ. 3.º¯ÊýÖÜÆÚÐÔ³£ÓýáÂÛ

¶Ôf(x)¶¨ÒåÓòÄÚÈÎÒ»×Ô±äÁ¿µÄÖµx£º (1)Èôf(x£«a)£½£­f(x)£¬ÔòT£½2a(a>0). (2)Èôf(x£«a)£½

1

£¬ÔòT£½2a(a>0). f£¨x£©

1

(3)Èôf(x£«a)£½£­£¬ÔòT£½2a(a>0).

f£¨x£©4.¶Ô³ÆÐÔµÄÈý¸ö³£ÓýáÂÛ

(1)Èôº¯Êýy£½f(x£«a)ÊÇżº¯Êý£¬Ôòº¯Êýy£½f(x)µÄͼÏó¹ØÓÚÖ±Ïßx£½a¶Ô³Æ.

(2)Èô¶ÔÓÚRÉϵÄÈÎÒâx¶¼ÓÐf(2a£­x)£½f(x)»òf(£­x)£½f(2a£«x)£¬Ôòy£½f(x)µÄͼÏó¹ØÓÚÖ±Ïßx£½a¶Ô³Æ. (3)Èôº¯Êýy£½f(x£«b)ÊÇÆæº¯Êý£¬Ôòº¯Êýy£½f(x)¹ØÓÚµã(b£¬0)ÖÐÐĶԳÆ. ¡¾ÒÉÎó±æÎö¡¿

1.ÅжÏÏÂÁнáÂÛÕýÎó(ÔÚÀ¨ºÅÄÚ´ò¡°¡Ì¡±»ò¡°¡Á¡±)

1

(1)º¯Êýy£½x2ÔÚx¡Ê(0£¬£«¡Þ)ʱÊÇżº¯Êý.( ) (2)Èôº¯Êýf(x)ÎªÆæº¯Êý£¬ÔòÒ»¶¨ÓÐf(0)£½0.( )

(3)ÈôTÊǺ¯ÊýµÄÒ»¸öÖÜÆÚ£¬ÔònT(n¡ÊZ£¬n¡Ù0)Ò²ÊǺ¯ÊýµÄÖÜÆÚ.( )

(4)Èôº¯Êýy£½f(x£«b)ÊÇÆæº¯Êý£¬Ôòº¯Êýy£½f(x)µÄͼÏó¹ØÓÚµã(b£¬0)ÖÐÐĶԳÆ.( )

¡¾½Ì²ÄÑÜ»¯¡¿

2.(±ØÐÞ1P35Àý5¸Ä±à)ÏÂÁк¯ÊýÖÐΪżº¯ÊýµÄÊÇ( ) A.y£½x2sin x C.y£½|ln x|

3.(±ØÐÞ4P46A10¸Ä±à)Éèf(x)ÊǶ¨ÒåÔÚRÉϵÄÖÜÆÚΪ2µÄº¯Êý£¬µ±x¡Ê[£­1£¬1)ʱ£¬f(x)£½

2??£­4x£«2£¬£­1¡Üx<0£¬3??Ôòf??2?£½________. ?x£¬0¡Üx<1£¬?

B.y£½x2cos x D.y£½2x

£­

¡¾ÕæÌâÌåÑé¡¿

4.(2019¡¤¼ÃÄϵ÷ÑÐ)ÏÂÁк¯Êý¼ÈÊÇżº¯ÊýÓÖÔÚÇø¼ä(0£¬£«¡Þ)Éϵ¥µ÷µÝÔöµÄÊÇ( )

1

A.y£½x3 C.y£½|x|

B.y£½x4 D.y£½|tan x|

5.(2017¡¤È«¹ú¢ò¾í)ÒÑÖªº¯Êýf(x)ÊǶ¨ÒåÔÚRÉÏµÄÆæº¯Êý£¬µ±x¡Ê(£­¡Þ£¬0)ʱ£¬f(x)£½2x3£«x2£¬Ôòf(2)£½________.

2

6.(2019¡¤ÉϺ£³çÃ÷Çø¶þÄ£)Éèf(x)ÊǶ¨ÒåÔÚRÉÏÒÔ2ΪÖÜÆÚµÄżº¯Êý£¬µ±x¡Ê[0£¬1]ʱ£¬f(x)£½log2(x£«1)£¬Ôòµ±x¡Ê[1£¬2]ʱ£¬f(x)£½________.

¡¾¿¼µã¾Û½¹¡¿

¿¼µãÒ» ÅжϺ¯ÊýµÄÆæÅ¼ÐÔ ¡¾Àý1¡¿ ÅжÏÏÂÁк¯ÊýµÄÆæÅ¼ÐÔ£º (1)f(x)£½3£­x2£«x2£­3£» lg (1£­x2)(2)f(x)£½£»

|x£­2|£­2

2??x£«x£¬x<0£¬

(3)f(x)£½?2

?£­x£«x£¬x>0.?

¡¾¹æÂÉ·½·¨¡¿ ÅжϺ¯ÊýµÄÆæÅ¼ÐÔ£¬ÆäÖаüÀ¨Á½¸ö±Ø±¸Ìõ¼þ£º

(1)¶¨ÒåÓò¹ØÓÚÔ­µã¶Ô³Æ£¬ÕâÊǺ¯Êý¾ßÓÐÆæÅ¼ÐԵıØÒª²»³ä·ÖÌõ¼þ£¬ËùÒÔÊ×ÏÈ¿¼ÂǶ¨ÒåÓò£»

(2)ÅжÏf(x)Óëf(£­x)ÊÇ·ñ¾ßÓеÈÁ¿¹ØÏµ£¬ÔÚÅÐ¶ÏÆæÅ¼ÐÔµÄÔËËãÖУ¬¿ÉÒÔת»¯ÎªÅÐ¶ÏÆæÅ¼ÐԵĵȼ۵ÈÁ¿¹ØÏµÊ½(f(x)£«f(£­x)£½0(Ææº¯Êý)»òf(x)£­f(£­x)£½0(żº¯Êý))ÊÇ·ñ³ÉÁ¢.

¡¾ÑµÁ·1¡¿ (1)ÏÂÁк¯ÊýÖУ¬¼È²»ÊÇÆæº¯Êý£¬Ò²²»ÊÇżº¯ÊýµÄÊÇ( ) A.y£½x£«sin 2x 1

C.y£½2x£«x

2

B.y£½x2£­cos x D.y£½x2£«sin x

xx

(2)ÒÑÖªf(x)£½x£¬g(x)£½£¬ÔòÏÂÁнáÂÛÕýÈ·µÄÊÇ( )

22£­1A.f(x)£«g(x)ÊÇżº¯Êý B.f(x)£«g(x)ÊÇÆæº¯Êý C.f(x)g(x)ÊÇÆæº¯Êý D.f(x)g(x)ÊÇżº¯Êý

¿¼µã¶þ º¯ÊýµÄÖÜÆÚÐÔ¼°ÆäÓ¦ÓÃ

¡¾Àý2¡¿ (1)(Ò»Ìâ¶à½â)(2018¡¤È«¹ú¢ò¾í)ÒÑÖªf(x)ÊǶ¨ÒåÓòΪ(£­¡Þ£¬£«¡Þ)µÄÆæº¯Êý£¬Âú×ãf(1£­x)£½f(1£«x).Èôf(1)£½2£¬Ôòf(1)£«f(2)£«f(3)£«¡­£«f(50)£½( )

3