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)ÔÚԵ㴦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