¾«Ó¢¼Ò½ÌÍøÒÑÖªº¯Êýf(x)=
x2
x+m
µÄͼÏó¾­¹ýµã£¨4£¬8£©£®
£¨1£©Çó¸Ãº¯ÊýµÄ½âÎöʽ£»
£¨2£©ÊýÁÐ{an}ÖУ¬Èôa1=1£¬SnΪÊýÁÐ{an}µÄÇ°nÏîºÍ£¬ÇÒÂú×ãan=f£¨Sn£©£¨n¡Ý2£©£¬
Ö¤Ã÷ÊýÁÐ{
1
Sn
}
³ÉµÈ²îÊýÁУ¬²¢ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨3£©ÁíÓÐÒ»ÐÂÊýÁÐ{bn}£¬Èô½«ÊýÁÐ{bn}ÖеÄËùÓÐÏÿһÐбÈÉÏÒ»ÐжàÒ»ÏîµÄ¹æÔòÅųÉÈçÏÂÊý±í£º¼Ç±íÖеĵÚÒ»ÁÐÊýb1£¬b2£¬b4£¬b7£¬¡­£¬¹¹³ÉµÄÊýÁм´ÎªÊýÁÐ{an}£¬ÉϱíÖУ¬Èô´ÓµÚÈýÐÐÆð£¬Ã¿Ò»ÐÐÖеÄÊý°´´Ó×óµ½ÓÒµÄ˳Ðò¾ù¹¹³ÉµÈ±ÈÊýÁУ¬ÇÒ¹«±ÈΪͬһ¸öÕýÊý£®µ±b81=-
4
91
ʱ£¬ÇóÉϱíÖеÚk£¨k¡Ý3£©ÐÐËùÓÐÏîµÄºÍ£®
·ÖÎö£º£¨1£©°ÑµãµÄ×ø±ê´úÈëÇó³öm¼´¿ÉÇó¸Ãº¯ÊýµÄ½âÎöʽ£»
£¨2£©ÏÈÀûÓÃÌõ¼þÇó³öan=
Sn2
Sn-2
£®ÔÙ°Ñan»»µôÕûÀíºó¼´¿ÉÖ¤Ã÷ÊýÁÐ{
1
Sn
}
³ÉµÈ²îÊýÁУ¬È»ºóÀûÓÃÇó³öµÄSnÀ´ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨3£©ÏÈÇó³öb81ËùÔÚλÖã¬ÔÙÀûÓÃÿһÐÐÖеÄÊý°´´Ó×óµ½ÓÒµÄ˳Ðò¾ù¹¹³ÉµÈ±ÈÊýÁУ¬Çó³ö¹«±È£¬ÔÙ´úÈëÇóºÍ¹«Ê½¼´¿É£®
½â´ð£º½â£¨1£©Óɺ¯Êýf(x)=
x2
x+m
µÄͼÏó¾­¹ýµã£¨4£¬8£©µÃ£ºm=-2£¬
º¯ÊýµÄ½âÎöʽΪf(x)=
x2
x-2
£¨2·Ö£©
£¨2£©ÓÉÒÑÖª£¬µ±n¡Ý2ʱ£¬an=f£¨Sn£©£¬¼´an=
Sn2
Sn-2
£®
ÓÖSn=a1+a2++an£¬
ËùÒÔSn-Sn-1=
Sn2
Sn-2
£¬¼´2Sn+Sn•Sn-1=2Sn-1£¬£¨5·Ö£©
ËùÒÔ
1
Sn
-
1
Sn-1
=
1
2
£¬£¨7·Ö£©
ÓÖS1=a1=1£®
ËùÒÔÊýÁÐ{
1
Sn
}
ÊÇÊ×ÏîΪ1£¬¹«²îΪ
1
2
µÄµÈ²îÊýÁУ®
ÓÉÉÏ¿ÉÖª
1
Sn
=1+
1
2
(n-1)=
n+1
2
£¬
¼´Sn=
2
n+1
£®
ËùÒÔµ±n¡Ý2ʱ£¬an=Sn-Sn-1=
2
n+1
-
2
n
=-
2
n(n+1)
£®
Òò´Ëan=
1£¬n=1
-
2
n(n+1)
£¬n¡Ý2
£¨9·Ö£©
£¨3£©ÉèÉϱíÖдӵÚÈýÐÐÆð£¬Ã¿ÐеĹ«±È¶¼Îªq£¬ÇÒq£¾0£®
ÒòΪ1+2++12=
12¡Á13
2
=78
£¬
ËùÒÔ±íÖеÚ1ÐÐÖÁµÚ12Ðй²º¬ÓÐÊýÁÐ{bn}µÄÇ°78Ï
¹Êb81ÔÚ±íÖеÚ13ÐеÚÈýÁУ¬£¨11·Ö£©
Òò´Ëb81=a13q2=-
4
91
£®
ÓÖa13=-
2
13¡Á14
£¬
ËùÒÔq=2£¨13·Ö£©
¼Ç±íÖеÚk£¨k¡Ý3£©ÐÐËùÓÐÏîµÄºÍΪS£¬
ÔòS=
ak(1-qk)
1-q
=-
2
k(k+1)
(1-2k)
1-2
=
2
k(k+1)
(1-2k)(k¡Ý3)
£¨16·Ö£©
µãÆÀ£º±¾ÌâÊǶÔÊýÁкͺ¯ÊýµÄ×ۺϿ¼²é£®Éæ¼°µ½µÈ±ÈÊýÁеÄÇóºÍÎÊÌ⣬ÔڶԵȱÈÊýÁÐÇóºÍʱ£¬Ò»¶¨ÒªÏÈÅжϹ«±ÈµÄÈ¡Öµ£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªº¯Êýf(x)=x-2m2+m+3(m¡ÊZ)Ϊżº¯Êý£¬ÇÒf£¨3£©£¼f£¨5£©£®
£¨1£©ÇómµÄÖµ£¬²¢È·¶¨f£¨x£©µÄ½âÎöʽ£»
£¨2£©Èôg£¨x£©=loga[f£¨x£©-ax]£¨a£¾0ÇÒa¡Ù1£©£¬ÊÇ·ñ´æÔÚʵÊýa£¬Ê¹g£¨x£©ÔÚÇø¼ä[2£¬3]ÉϵÄ×î´óֵΪ2£¬Èô´æÔÚ£¬ÇëÇó³öaµÄÖµ£¬Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2011•ÉϺ£Ä£Ä⣩ÒÑÖªº¯Êýf(x)=(
x
a
-1)2+(
b
x
-1)2£¬x¡Ê(0£¬+¡Þ)
£¬ÆäÖÐ0£¼a£¼b£®
£¨1£©µ±a=1£¬b=2ʱ£¬Çóf£¨x£©µÄ×îСֵ£»
£¨2£©Èôf£¨a£©¡Ý2m-1¶ÔÈÎÒâ0£¼a£¼bºã³ÉÁ¢£¬ÇóʵÊýmµÄÈ¡Öµ·¶Î§£»
£¨3£©Éèk¡¢c£¾0£¬µ±a=k2£¬b=£¨k+c£©2ʱ£¬¼Çf£¨x£©=f1£¨x£©£»µ±a=£¨k+c£©2£¬b=£¨k+2c£©2ʱ£¬¼Çf£¨x£©=f2£¨x£©£®
ÇóÖ¤£ºf1(x)+f2(x)£¾
4c2
k(k+c)
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£ºÕã½­Ê¡¶«ÑôÖÐѧ¸ßÈý10Ô½׶ÎÐÔ¿¼ÊÔÊýѧÀí¿ÆÊÔÌâ ÌâÐÍ£º022

ÒÑÖªº¯Êýf(x)µÄͼÏñÔÚ[a£¬b]ÉÏÁ¬Ðø²»¶Ï£¬f1(x)£½min{f(t)|a¡Üt¡Üx}(x¡Ê[a£¬b])£¬f2(x)£½max{f(t)|a¡Üt¡Üx}(x¡Ê[a£¬b])£¬ÆäÖУ¬min{f(x)|x¡ÊD}±íʾº¯Êýf(x)ÔÚDÉϵÄ×îСֵ£¬max{f(x)|x¡ÊD}±íʾº¯Êýf(x)ÔÚDÉϵÄ×î´óÖµ£¬Èô´æÔÚ×îСÕýÕûÊýk£¬Ê¹µÃf2(x)£­f1(x)¡Ük(x£­a)¶ÔÈÎÒâµÄx¡Ê[a£¬b]³ÉÁ¢£¬Ôò³Æº¯Êýf(x)Ϊ[a£¬b]Éϵġ°k½×ÊÕËõº¯Êý¡±£®ÒÑÖªº¯Êýf(x)£½x2£¬x¡Ê[£­1£¬4]Ϊ[£­1£¬4]Éϵġ°k½×ÊÕËõº¯Êý¡±£¬ÔòkµÄÖµÊÇ_________£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£ºÉϺ£Ä£Äâ ÌâÐÍ£º½â´ðÌâ

ÒÑÖªº¯Êýf(x)=(
x
a
-1)2+(
b
x
-1)2£¬x¡Ê(0£¬+¡Þ)
£¬ÆäÖÐ0£¼a£¼b£®
£¨1£©µ±a=1£¬b=2ʱ£¬Çóf£¨x£©µÄ×îСֵ£»
£¨2£©Èôf£¨a£©¡Ý2m-1¶ÔÈÎÒâ0£¼a£¼bºã³ÉÁ¢£¬ÇóʵÊýmµÄÈ¡Öµ·¶Î§£»
£¨3£©Éèk¡¢c£¾0£¬µ±a=k2£¬b=£¨k+c£©2ʱ£¬¼Çf£¨x£©=f1£¨x£©£»µ±a=£¨k+c£©2£¬b=£¨k+2c£©2ʱ£¬¼Çf£¨x£©=f2£¨x£©£®
ÇóÖ¤£ºf1(x)+f2(x)£¾
4c2
k(k+c)
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º2009-2010ѧÄêºÓÄÏÊ¡Ðí²ýÊг¤¸ðÈý¸ß¸ßÈýµÚÆߴο¼ÊÔÊýѧÊÔ¾í£¨Àí¿Æ£©£¨½âÎö°æ£© ÌâÐÍ£ºÑ¡ÔñÌâ

ÒÑÖªº¯Êýf£¨x£©¡¢g£¨x£©£¬ÏÂÁÐ˵·¨ÕýÈ·µÄÊÇ£¨ £©
A£®f£¨x£©ÊÇÆ溯Êý£¬g£¨x£©ÊÇÆ溯Êý£¬Ôòf£¨x£©+g£¨x£©ÊÇÆ溯Êý
B£®f£¨x£©ÊÇżº¯Êý£¬g£¨x£©ÊÇżº¯Êý£¬Ôòf£¨x£©+g£¨x£©ÊÇżº¯Êý
C£®f£¨x£©ÊÇÆ溯Êý£¬g£¨x£©ÊÇżº¯Êý£¬Ôòf£¨x£©+g£¨x£©Ò»¶¨ÊÇÆ溯Êý»òżº¯Êý
D£®f£¨x£©ÊÇÆ溯Êý£¬g£¨x£©ÊÇżº¯Êý£¬Ôòf£¨x£©+g£¨x£©¿ÉÒÔÊÇÆ溯Êý»òżº¯Êý

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸