¡¾´ð°¸¡¿
·ÖÎö£º£¨I£©ÉèÁ½º¯ÊýͼÏóµÄ¹«¹²µãµÄ×ø±êP£¨x
£¬y
£©£¬°ÑPµÄ×ø±ê´úÈëµ½f£¨x£©ºÍg£¨x£©ÖÐÀûÓõĺ¯ÊýÖµÏàµÈµÃµ½Ò»¸ö¹Øϵʽ¼Ç×÷¢Ù£¬ÓÖÒòΪÔÚP´¦Óй²Í¬µÄÇÐÏߣ¬ËùÒÔ·Ö±ðÇó³öf£¨x£©ºÍg£¨x£©µÄµ¼º¯Êý£¬°ÑPµÄºá×ø±ê·Ö±ð´úÈëµ½Á½µ¼º¯ÊýÖÐÀûÓõ¼º¯ÊýÖµÏàµÈµÃµ½ÓÖÒ»¸ö¹Øϵʽ£¬ÓɹØϵʽ½â³öm£¬¼Ç×÷¢Ú£¬½«¢Ú´úÈë¢Ù£¬°ÑÓұ߱äΪ0ºó£¬Éè×ó±ßµÄ¹ØϵʽΪh£¨x£©£¬Çó³öh£¨x£©µÄµ¼º¯Êý£¬ÀûÓÃx´óÓÚ0µÃµ½µ¼º¯Êý´óÓÚ0£¬ËùÒÔh£¨x£©×î¶àÖ»ÓÐ1¸öÁãµã£¬¹Û²ì¿ÉµÃºá×ø±êΪ1ΪÁãµã£¬¼´¿ÉÇó³ömµÄÖµ£¬½ø¶øÇó³ö´ËʱPµÄ×ø±ê£»
£¨II£©ÓɵÚÒ»ÎÊÇóµÃµÄmµÄÖµºÍPµÄ×ø±ê£¬Çó³öº¯Êýg£¨x£©µÄ¶Ô³ÆÖᣬf£¨x£©Êǹ̶¨²»±äµÄ£¬ËùÒÔ½«g£¨x£©µÄ¶Ô³ÆÖáÏòÓÒÒƶ¯£¬Á½ÌõÇúÏßÓв»Í¬µÄ½»µã£¬¼´µ±x=
´óÓÚ
Áгö¹ØÓÚmµÄ²»µÈʽ£¬Çó³ö²»µÈʽµÄ½â¼¯¼´¿ÉµÃµ½´ËʱmµÄ·¶Î§£¬¶øµ±mСÓÚ-1ʱ£¬Å×ÎïÏß¿ª¿ÚÏòÏ£¬Ö»ÓÐÒ»¸ö½»µã£¬²»ºÏÌâÒ⣻
£¨III£©²ÉÓ÷´Ö¤·¨Ö¤Ã÷£¬·½·¨ÊÇ£º¼ÙÉè´æÔÚÕâÑùµÄm£¬¿ÉÉèM£¨x
1£¬y
1£©£¬N£¨x
2£¬y
2£©£¬ÇÒx
1£¾x
2£¬ÀûÓÃÖеã×ø±ê¹«Ê½Çó³öMÓëNµÄÖеã×ø±ê£¬È»ºó°ÑÖеãµÄºá×ø±ê·Ö±ð´úÈëµ½f£¨x£©ºÍg£¨x£©µÄµ¼º¯ÊýÖм´¿ÉÇó³öÁ½ÇÐÏß·½³ÌµÄбÂÊ£¬ÒòΪÁ½ÇÐÏßƽÐУ¬ËùÒÔÀûÓÃбÂÊÏàµÈµÃµ½Ò»¸ö¹Øϵʽ¼Ç×÷¢Û£¬ÇÒ°ÑÁ½µãµÄºá×ø±ê·Ö±ð´úÈëµ½f£¨x£©ºÍg£¨x£©ÖУ¬²¢Èú¯ÊýÖµÏàµÈ£¬¸ø¢ÛµÄÁ½±ßͬ³ËÒÔx
1-x
2£¬µÃ¹Øϵʽ¢Ü£¬°Ñ¢Ü»¯¼òºó£¬Éè¦ÌµÈÓÚ
´óÓÚ1£¬µÃµ½¹ØÓڦ̵ĵÈʽ£¬ÒÆÏîºóÉèh£¨¦Ì£©µÈÓÚµÈʽµÄ×ó±ß£¬Çó³öh£¨¦Ì£©µÄµ¼º¯Êý£¬Åжϳöµ¼º¯Êý´óÓÚ0£¬µÃµ½h£¨¦Ì£©ÔÚ[1£¬+¡Þ]Éϵ¥µ÷µÝÔö£¬¹Êh£¨¦Ì£©£¾h£¨1£©=0£¬Óë¸Õ²Å»¯¼òµÄµÈʽ¢Üì¶Ü£¬ËùÒÔ¼ÙÉè´íÎó£¬ËùÒÔ²»´æÔÚÕâÑùµÄm£¬Ê¹l
1¡Îl
2£®
½â´ð£º½â£º£¨I£©É躯Êýy=f£¨x£©Óëy=g£¨x£©Í¼ÏóµÄ¹«¹²µãΪP£¨x
£¬y
£©£¬
ÔòÓÐlnx
=£¨m+1£©x
2-x
¢Ù£¬
ÓÖÔÚµãP´¦Óй²Í¬µÄÇÐÏߣ¬
¡à
£¬¢Ú
¢Ú´úÈë¢Ù£¬µÃ
£®
Éè
£®
ËùÒÔ£¬º¯Êýh£¨x£©×î¶àÖ»ÓÐ1¸öÁãµã£¬
¹Û²ìµÃx
=1ÊÇÁãµã£¬¹Êm=0£®
´Ëʱ£¬µãP£¨1£¬0£©£»
£¨II£©¸ù¾Ý£¨I£©Öª£¬µ±m=0ʱ£¬Á½ÌõÇúÏßÇÐÓÚµãP£¨1£¬0£©£¬
´Ëʱ£¬±ä»¯µÄy=g£¨x£©µÄͼÏóµÄ¶Ô³ÆÖáÊÇx=
£¬
¶øy=f£¨x£©Êǹ̶¨²»±äµÄ£¬Èç¹û¼ÌÐøÈöԳÆÖáÏòÓÒÒƶ¯£¬
¼´
£¬½âµÃ-1£¼m£¼0£®Á½ÌõÇúÏßÓÐÁ½¸ö²»Í¬µÄ½»µã£¬
µ±m£¼-1ʱ£¬¿ª¿ÚÏòÏ£¬Ö»ÓÐÒ»¸ö½»µã£¬ÏÔÈ»²»ºÏÌâÒ⣬
ËùÒÔ£¬ÓÐ-1£¼m£¼0£»
£¨III£©¼ÙÉè´æÔÚÕâÑùµÄm£¬²»·ÁÉèM£¨x
1£¬y
1£©£¬N£¨x
2£¬y
2£©£¬ÇÒx
1£¾x
2£¬
ÔòMNÖеãµÄ×ø±êΪ
£®
ÒÔSΪÇÐÏßµÄÇÐÏßl
1µÄбÂÊ
£¬
ÒÔTΪÇеãµÄÇÐÏßl
2µÄбÂÊ
£®
Èç¹û´æÔÚm£¬Ê¹µÃk
s=k
T£¬
¼´
£®¢Û
¶øÇÒÓÐlnx
1=£¨m+1£©x
12-x
1ºÍlnx
2=£¨m+1£©x
22-x
2£®
Èç¹û½«¢ÛµÄÁ½±ßͬ³ËÒÔx
1-x
2£¬µÃ
¢Ü
£¬
¼´
£¬
Ò²¾ÍÊÇ
£®
Éè¦Ì=
£¬ÔòÓÐ
£®
Áî
£¨¦Ì£¾1£©£¬Ôò
£®
¡ß¦Ì£¾1£¬¡àh'£¨¦Ì£©£¾0£®
Òò´Ë£¬h£¨¦Ì£©ÔÚ[1£¬+¡Þ]Éϵ¥µ÷µÝÔö£¬¹Êh£¨¦Ì£©£¾h£¨1£©=0£®
¡à
¢Ý
¡à¢ÜÓë¢Ýì¶Ü£®
ËùÒÔ£¬²»´æÔÚʵÊýmʹµÃl
1¡Îl
2£®
µãÆÀ£º´ËÌâÒªÇóѧÉú»áÀûÓõ¼ÊýÇóÇúÏßÉϹýijµãÇÐÏß·½³ÌµÄбÂÊ£¬»áÌÖÂÛ¸ùµÄ´æÔÚÐÔ²¢»áÅжϸùµÄ¸öÊý£¬ÕÆÎÕ·´Ö¤·¨µÄÖ¤Ã÷·½·¨£¬ÊÇÒ»µÀ±È½ÏÄѵÄÌ⣮