
Ʒ/ѧŮ
ԭ/ѧ`롷
/Ǻ
廭/SDwing
/ׯӺ
ͼԴ/ĳX
¼/ù
У/ù
У++TXT/JoyJ from IVocaloid http://bbs.ivocaloid.com
ͼ/ĳXϡù
ͼ/ù
ת עȪͽ http://www.cnfmp.net/bbs
ΪͶ ɾϢ

߼
Ǻ (Hirosi Yuuki)
һȤǡдʽ롸д项ϲڻüʱ䲻ϵظĶͬһ顣Ҳϲ֣رϲ͹ԼֵķסҲᴵľѣrecorderϲӰɢǳϲáϲ֣ԡáûʲôȤǸޡСӣΪú˷ʱ䣬Ժȥһˣǳϲ༭ڿ֮ߺȾơ
վ http://www.hyuki.com/index.html

廭
Sdwing
SD
Ϊְҵϡҵǡڰ硹յļһĿǰ¸ֻ滭ӰֻϷ趨ԭϷʿš廭ձ鼮˯µ䡷ϵв廭Ȥǽ˸˫βҶָ̡
վ <> http://blog.yam.com/sdwing

ݼ飺
ϲѧó˽ϸкΪʱһµڿѧ죬һλͬѧȤĲŮ׶ȡ˺˳ڷѧͼѧʽ
һȥǵĹѧõٵǉҲȦӡȻһʼֻΪѧĳɼٵǉҲرѧҲ͸ѧᷢչԵĹϵѧ˵سǰ


TXTʽ˵
a<nη>-----------anηرģ2η<ƽ>ʾ3η<>ʾ
a<nεݽ׳>-----------anεݽ׳
<a>-----------a2θ
<nθa>-----------anθ
a<0>a<1>a<2>-----------±a0a1a2
a<b,c>-----------aϱb±c
رģ()<b,c>ָšڡϱ0±1
<k=mn,f(k)>-----------kֵm֮󲻶ϼ1ֱnkֵf(k)۳
<k=mn,f(k)>-----------kֵm֮󲻶ϼ1ֱnkֵf(k)ۼ͡
lim<xa,f(x)>-----------xaʱf(x)ļ
<,n,k>-----------nԪѡkԪصķ
<For All>-----------С
S<eΪףf(x)>-----------logeΪf(x)Ķ
ͼ

TXT׼ö߰ʽͼԭTXT
TXTĶעһпԱȽ϶ֵĶĶPSPĺ+xReaderСֺTTF塣һʾСôֱȿִܻλ󣬸ĶӰ졣⣬顰ʺϡĻˮƽĶ
УҪʽȫƪԼ50ҡԸ¼еƽ˷롣

ôֻJoyJ
1.ʵϣĳJ뷨鲢һС˵һʽȽرĿնˣѧȤϵͣĶȤۿۡѧRIPӦҲôҶԱһŵӡаް뱣־Ա׻
2.TXTѶ˷ָֹʽͼʵͷۣ൱ӣʡԣͷһμ400kϵķС˵ҡˣɧˡ
3.롶ѧŮ޹ϵ
4.RIPοĶ
֮Τߤˣ
By IVocaloid ֮ͼݳ JoyJ

Ƽ
ÿһѧ֮ǰѧҴӷֶƵֱ֤֤޲龫ǣѾ֮һʱ䣬ֻΪɻ֤һѧʽӡȻڹлĴۣ߼˼ĹǺҪޱȤֵģǺѧ˵ģҪʽʲôǷǳõһ¡һʽֹͣ˼˷ǳ࣬˼ʽ֮ǰȫȥȻѵʽͲ׶ǾȫҲӦҪ롺Ϊֹ֪ģ֮Ҳ֪ġ˵û취ʱͻֹͣ⡢ֹͣ˼Żҽ˵ѧûжôԺһӡΪûԲɡҲѧѧʱԸսĵٵٷǳΰ󡣡
Ϊеĸ߹ļ֣ΰĶ֣õڱУ߽ϲѧǵ߼˼·ͬߣӲͬǶ벻ͬһʶѧȤһ档һԴŮ׶ϿѧһҲԽɵٵٵȥ˽Ҫ߱Ļѧ֪ʶڶĶĶʱ߸Ҫջǣ߿һȤζ˼ڲ֪нѧã䣬õݵĿá
̽ʦ
2008.03.07

Ƽ
ں嫵֪ʶУѧһȴѧϰѧʡкܶĸҲиĶЩҪѧѧȴֲܵһζҪȥ˼⡢ȥ߼ܶΪЩԭ֮ȴʧȥ῿Լõ𰸵ɾͣһϧ顣
ʺϱѧȤĶҲʺϴѧѧĹߡеĽɫóѧˣö߸ĽⷨĲõ˼Ŀһ֣̽ͬʱҲϲѧȴֵĽɫĶ߾ͿվһĽǶѭ򽥽ѧϰ˻ѧУ̵ѧ﷦ζӴһ˸Ĺۣݲǹ̶ĳУǹ㷺ȤʽӣǿȽܸֻöᵽͬȤľʦύǿƬȥҪĲǴ𰸣Ǵʽϻոµľ鼰ᣬѧϰֵ
ͬ˵ѧԿԽʱ䣬ЩǧǰѧǸܵȤɾͣλִɿԸͬܣ÷ԼʣܵõµϾõĽűԲṼλøλѧС
һŮѧʦ
־


ҳ
뱾йص鱨ַá
http://www.hyuki.com/girl/
ҳ߸վһ֡



м򵥵СѧĲ֣Ҳѧѵĸ⡣
Ｐͼǳ˼;⣬Ҳʹѧʽ֡
޷ѧʽĺʱȰѧʽһԣרĵܾɣٵٻһͬǰġ
ѧŵĶǣܾ֮⣬ҲעеѧʽôĻᵽڹ±Ȥ


CONTENTS
Ƽ


1¡
11ӣ
12Լ
13ûȷ
2¡Ϊʽ
21Уſ
22
23
24ѧ
25ͽ
251Ķ
252ֵĶ
26ؼҵ·
27Լ
28׶ȵĽ
29ͼ
291ʽʽ
292ʽ͵ʽ
210ѧʽı˭
3¡صĻ
31ͼ
32ת
33صĻ
4¡쳲ɺ
41ͼ
411Ѱҹ
412ȱеĺ
413
414ɺ
42ץס쳲
421쳲
422쳲еɺ
423չʽ
424ʾ
425
43ع
5¡ƽ뼸ƽĹϵ
51ڡѧ֡
52
53ʽ
54һ
55νѧ
6¡׶ȵ
61΢
62
63΢
631һκx
632κx<2η>
633κx<3η>
634ָe<xη>
64ó
7¡ۻ
71ͼ
711׶
712ٵ
713ƹʽ
72ڻؼҵ·Ͻ廯
73ڡBeansʽ
74ԼнɺĻ
75ͼ
751׶ȵĽ
752ɺ
753Χ
754Ĺؿ
755
756뾶ΪԲ
8¡
81Ѱ
811ٵ
812׶
82Իеͼ
821ֺ
822Ȼĵطʼ
823
824ȫ
825Ǵڵ
83ֹݵֽ
84Ħ
85޴Ĺ
86ڽ
87磬
88֪Կףδ֪
89ֻĻ
891ۻ
892ȱȼ
893ӷֽΨһ
894޵֤
810̨
9¡̩չʽ뱴
91ͼ
911ſƬ
912ʽ
92ѧϰ
93Beans
931΢ֵĹ
932΢
933sin x̩չʽ
934ļ
94Լ
95
96ͼ
961ٵٵĳ
962ȥδ
963޵ս
10¡ֲ
101ͼ
1011ֲ
1012˼ʵ
102ȥ·
1021쳲
1022
103Beans
104Լ
1041Ϊѡ
105ֽ
1051ҵķ(ֲɺ)
1052׶ȵķ(ֲϽ)
1053ٵٵķ
106
107ѰҸϽ;
1071ɺ
1072һתǡɺ
1073ߵɭ̩֡չʽ
1074ߵɽ𡻵
1075;յ
1076ٵٵĻع
108ټ
β

οĶָ






ֻǼ䡣
޷䡣
С

޷ǡ
޷ڸʱһоѧŮǡ
ŵĽⷨĵĲŮ׶ȡ
ʵĻŮٵ١
ÿǶʱ⣬оͻḡֳѧʽչ˼άѧʽԽʱ䣬չŷá˹Լѧҵһ
ѧǳԽʱġ
ĶѧʽƷŴǰѧĸжʹǰͱ֤ҲνڵȷʵӵЩ߼ĿС
ѧԽʱ䡣
ҳصıءѧǸ˷ܵϷѵĽⷨΪĿ꣬ľѧļµս
ʱҿʼʹΪѧȴ޴Կƣ޷Լ񣬾޷ƶǵ˼
ֻǼ䡣
޷䡣
һеĿˣڸһ괺졭



1¡


һһ
һǶ
uӡd·ǡ


11ӣ

һ괺졣
ѧա
ӣʢÿ˶ܳոµһ⴫ͳУŬضѧѳɡ
Уݽյҽ磬۾סǷ
ѧYᣬصҵ;Уĵ뿪Уᣬһ̤M˲ŵӣΧ]κ˵·ϡ
15ꡣ151617ҵʱ18ˣᾭһ4ıһ

1535
162222244ı
1717
18233232


ڽͬѧӦҽܰɡóҽˣҪ˵ʲôԼأ
ϲѧȤʽλָ̡
˵ʻôĿɿڴɡ
ˣ͹ʱһΣȻͼȹʽɡ
ʱһø޴ӣҵǰ
һλŮվӣ
Ҳһ͵ܳ
Ҳ̧ͷӣ谵ɫӳ
һ紵ӣŮΧס
Ůҡ
һԼںڵĳ
촽ϴŽ۾
ķ
һһ

1123

ĸ֮Ů첢ָңƺڶ˵㣬㡣شһʲô
ҵҲָԼ
(Ҫһش)
ŮԵصͷʳָȻָҡ
ô£ΪʲôӣұҪֲֵϷأǡ
1123
ţԭˣҶˡ
1123֮5813Ȼ21ǡ
Ůĳңֹͣơ

һ⣬һĸ֡




Ǹֵ⡣˵
𣿲㲻Ҳˣ
¶ͬʱߵҵǰһָֻ֡൱ϸ
(Ҫ)
ڸ㲻״º֣˫˳ů֡
׶ȣָָ
׶ȵˡ


12Լ

ҹ
ϲҹ˳˯ҵʱ䡣ûκ˻ŵ磬ֻһˣ̯鱾̽硢ѧĴϡеĶ峺ĺˮ׳ľľ޷ˡ

׶ȡ

ֻǵһμ棬ȴ̸ֻĹˡһϲѧɣȫûκ˵£ͻȻͬѧʴҺϸһ֣Ƿǳ֣Щ΢ζǵŮ㡣

Ů

ҽ۾ϣűۻ׶ȵĶԻ



䡣
ϲѧΪ䶫Ҹϲ˼ѧҪ¾ɵļ䣬Ҫչµķ֡ԵĶֻǣ֡Ԫرûеڶַѧͬ񽫲Ϻ͵׼÷ϣʤĹؼǼ䣬˼
ôġ
ǣûô

㲻Ҳˣ
Ԥа취𣬻¶ı顣
׶ȡ
ڴӣķУѷ羰վҡҷĺڷָӼҰϸָԼ˫ů뵭ζ
֪ΪΣҵԺѾӲȥӰ


13ûȷ

׶ȣΪʲôʱҪأʵ
ʱ򣿡ֹͣ㲢̧ͷ
ͼң򿪵Ĵˬķ磬һƬ̣ͩԶϰ
¡
ѧУ½ҡͬѧʸ𽥵һصƽճϢ
ûвμκţҲνĻؼ硣ˣѧҲ̻ؼҡİΪܶʽͨǰͼҡ
ͺ͹ʱһûвμţǷѧͼ(гΪͼ)飬ǿɫֻԤϰ븴ϰΡ
ϲĻʽϳֹĹʽڱʼǱϡԭĶ廹ԭµʽΡʵƷ任Ȥ˼֤ʽϲЩڱʼǱͷ
ó˶ҲûпһѵңȤһ˶ԱʼǱʱȻдʽңǲôдԣһĹйһϷûбܡɵϷˣʷϵѧսϷֻһ֧ԶǦʡһʼǱҵԴܽеϷִ˲ƣ
ԼʹΪҲͬһͼҵȤ
ǣʵԭЩͬ
Ǿǵͼҵѧֻһ
׶ȡ
ͬ࣬ÿڷѧͼһΡ
ÿһ˼ʱὫԶǦʴҵгȻڱʼǱд֣˵һ£ⱾʼǱҵģ˵˻أ
ҲֳѧȻѣȤ̼ҡ
˵ʱָʲôʱ򣿡׶ҧ(ҵ)ԶǦʻš
ǵһμʱӣ¡
ǸûʲôɣֻǸպ뵽ˡôͻȻ
ûʲôͻȻ뵽ѡ
ϲ𣿡
Ӧòᡣ
ร֪ûȷ仰𣿡
ʲô˼
Ʃ1234Ϊʲô׶˵



ʱͼҵſͻȻ
׶ȡ˰ɣ
ϰ𣿡
׶ȰѱʻҲڵŮȥҪ߳ͼ֮ǰתͷ˵
һٸֻۡȤɡ
һ뿪ͼҡ
ټֻ
ô£





2¡Ϊʽ


ҵֻ
һβ`˩`


21Уſ

ϸ߶ֻѧ־IIIԾɺһûб仯֮ǰôΪġ

롢

µף߶󾭹һµϣУſڱһŮס
һɫţҺͿţŮи󣬾Уķߡ
߱Ұܶ࣬Ҳûпӡ󣬴ǸѧҼæŴȥ
ϴյŮСѧʱʱҸðϢΪ೤ŮҵԼҶڵ㣬ҪѧУϿร͵ֻǵ
֮ǰ׶˵֮ᷢʲô¡ȷûδغһģһ
ڴŲڿжҡҵġ


22

⡣1024м

ʱ䣬Ůóʱ׶ȱҧɿߵҵ⡣ûл࣬Һ׶ȶ꼶Ȼͬࡣ
㣿ҰŷŻؿڴ
10֮ǰش0123


ҵĻش׶ȵ˵ͷˣôһ⡣1024ȫĺǡ
׶ȣǸе£ġ˵֮վ
Ҳ˱ϻ⡢¶׶ȣٵ߳ҡ
ĺܱǸ1024ӵĺͰұݶ˼𰸡
	

23

ʹݣݶϻûʲôˣΪ̫õĹϵɡ
ŷװŰɫֽøֱʺдľ塣

ǽѧĵٵǉǸѧͶͬССһѧáΪѧ۹ѧ£дš
ȻҶѧȤеϿݾҺܳ˵֮ѧϣܽ⡣
ǳǸæµʱˣϣл̸ѧһڴͽ
ٵǉ

ҽŶĴΡ
ԭٵǉĦŵ===ٵǉͬССһѧáȫûӡ󣬲óѧѧȷʵܶ࣬
ȲЩŻõȻеʧˣҲá
ѧڴͽҼ氡


24ѧ

𣿡

һĿγ̣ǰͽҵ;У׶ͻȻʡ
2047̻ش1024ĺ;2047
Ϊ˼ʱԣɡ
š
Ҫȥͼ𣿡׶ȵ۾һ¡
ŲȥˣͻȻе¡
มĻͳؼҵɡ

׶ȳĻؼҵ
˵һn䡸͡ķΪΣ

Ҫʹn͵ʽ𣿡ʡ
ֻҪдĹ̾ͺˡ


25ͽ

Բ
սͽңͿٵһ˽ŵصţǰűʼǱǦʺС
ҡѧ̸һ̸ֲ֪ô졣˵ĻȽϷ㣬ԡ
ͽұУƹССͥܵҪͻѧʱʹáɽݹɣ½ǽ̨Ϊѧ㿴ʵá
Һ͵ٵһŵĳϣҴӿڴóϵš
Ѿˡǲ˼Ҳ̫ǵ㡣
ǰҡΡ
ûϵҲ㲻ǵҵġ
ңΪʲôʶҰڹʱӦòô۲ŶԡûμšѧֻͼӦòעĿ
ѧมҡǸ
ˡ˵̸̸йѧֵ飬˵ϸһ𣿡
õģллҴСѧʼ;ѧȤǽк󣬲Ͽλǿαá޷ȫ⡻֮ʦ˵ѧҪҪúѧϰԲҪ޷ȫ⡻⡣
ԭˡԾΪС޷ȫ⡻⣬ĳɼҲǺܺÆ
Ļ
ٵٱ߽ʳָָ׷촽ϱ˼ӵһͷ̷˫۵ĵٵǉ˵ĸоǻõССè֮ġ
ο֮һΧĿԣͲ̫⡣ģ⿼ʱͻῼúܲм
ϿأϿεʱö𣿡
Ͽΰʦ̵ʱˡ
ȴ޷ȫ⣿
ǰ޷ȫ⡣ܽ⣬ϿҲöʵȴûȫ⡣


251Ķ

ôʵøһ㣬֪𣿡
ţӦ֪
Ӧ֪˵˵Ķ壬ǻشʲôҪʽԼ˵Ϳˡ



ѧƺҲҪһҵԴˡڡ塻ӷֽ⡻ΨһԡܱѧôҲǺҪأ
ûܴѧǺҪġҪܱᣬѧŻʹܵܵԾʽ
ʽ
ôѧԡʽĻɡΪҪõڰ壬ǵȥ
ͽҵǰٵں棬Ÿ߼һҵıܵһ
ۣ
ԡԲ𡣡
ٵٱ¥ݰײҵı˿ҪʱվȽŲΣա






252ֵĶ

ôֵ֪𣿡ڰ岢վš



ٵǰ˸λ£һָŪʼǱԵһ߳˼
ڵȴķԡ
ҵĹ˷ˡ
ô˵
ұһùġҲܵضαĶʽҵѧһúɢɡ
̾һֳһʧӡ
˵㰡
ףٵٿҡ
ôĻڿʼͺˡȥѾȥˣǻڰڷֵδıͿˡ
ٵͻȻ۾Ȼվ
ǡǰڹȥҲûáδͺˡлл㣬ѧ
ţȵΪֹɣɫҲˣ´ٽ⡣
ģ
ţҷѧ󲿷ֶͼңʲôʵģҾͿˣٵ١
һ˲両ֹԣܸ˵¶΢Ц
õģ


26ؼҵ·

ѽˡ
߳Уſڵĵٵգܲտʼꡣ
ûɡ𣿡
ȻпԤϳ̫ϣԾˡûϵֻС꣬ܵľͺˡ
վǰͻʪˡ˳·ҵɡҲһ߰ɡ
˼ллѧ
ƺҵһθŮӹһɡ͵Ĵ֮УȻе㲻ϰߣĲس˳еֵһƬš
һʱ䣬о죬Ҳû뵽ȻиԼĿɰѧã͵ٵɣıͿ֪û
Ϊʲôѧ֪أ
֪ʲô
ǡǽ̸ЩѧйҲĲ֣Ϊʲôѧ֪ﲻأ
ŵˣһΪٵٻĵӦ
Ϊ̸⣬Ҳ;ֵĲ֣ҲʡѧʱΪĵطеš˺þá˺֮ܶ󣬲ŷ֡ԭˣ൱飬ۻЩ󣬻ὥѧȤ֡ǰתɡ
ת䡣ǡThe Bend in the Roadɡ·Ҳܵվ𣿡
ţת䡢סլȽϿ쵽վ
ȽϿ쵽𣿡
ǰϴҲȽϿม
ףٵٵٶͻȻ̫𣿹ȻҪϲ̫ס

˳վ
Ϊҵһ»Ҫȥ˵ټˡˣɡȽɡ
͵
ţ
ûûʲô顣ɡҾˣһỹģлл㡣
ٵٽַǰؾϹ


27Լ

ҹ
ڷٵٵĻȴг徢֮ӦûɳɣҪ֪ѧȤͺˡ
͵ٵ˵ʱҰڳǽ̵ߵ̬׶˵ʱкܴĲͬ׶ʼնһֱ˵һ̵ֱɡ
ó׶ȳĻؼҵȻͬͬѧؼҵ

׶ȵĻؼҵ
˵һn䡺Ӻ͡ķΪΣ






28׶ȵĽ

ȷȻܸӡ
׶ȿҵĴʱܸɴ½ۡ
а취дø𣿡
ԡ׶̻ش



ԭˣȻ̣Ҳˡ˵׶ȥͼ𣿡ʡ
ᣬҪȥӢӢϰˡ


29ͼ

ѧ㿴ҴӹеĿαѶȫˡҾͿԼϰˡ
ٵҵͼѧңЦ̯ʼǱ
มȻһϾˡ
Һϲรֱһ¿αһκҲŷ֣ѧкܴĲͬ㣬ʽǷ֣԰ɣѧ


291ʽʽ

ô˵ѧʽĻ⣬̸̸ʽʽٵнʽɣ




ԭ
ǰٵ١ξҳѧкֵĵʽɣ񷽳ʽʽʽӡ
õģһԿ
ѧкܶʽЩʽĳΪ˴Լ뷨дµģЩʽıһдЩѶϢĳˡ
ѶϢĳˡ


292γ͵ʽ

ĶʽʱעʽʽǺҪġ
ʽʲô˼
Ʃʽ



Сĸоˣⷽʽ͡ʽкܴĹϵɣ

210ѧʽı˭

ΪʲôѧУʦû취ѧһ̵ôϸأ
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32ת

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41ͼ

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׶ȴʱ߽ͼңֱ߽ǣͻȻ߿ٵٵӣ޴ͼ˶ǿٵٻæվ׶ȵֱ뿪ͼңҾվĿ͵ٵٳȥ

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42ץס쳲

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421쳲

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53ʽ

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61΢

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72ڻؼҵ·Ͻ廯

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812׶

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821ֺ




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84Ħ

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85޴Ĺ

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86ڽ

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87磬

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88֪Կףδ֪

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89ֻĻ

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912ʽ

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92ѧϰ

ڻؼҵ·ϣҺ͵ٵ۵סլСվǰһŵٵٵĽŲߡ



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ͼݻкܶܺõ飬ѧϰõĲο鵽ר鼮ѡѧУʦѧϰϺҪǴͷβѧУʦ̫ˣȤĻ

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ᣬһԼֵ䣬ȵϿβѧΪȶ¡ѧҪ˵ľɣ
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ڵٵ᰸ûκεֿ


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931΢ֵĹ

Ѿǵڼκ͵ٵһվǰĿBeansأʱѾϰ߲һˣΪʲôҪ˵ΪʲôĻΪŲĶʽº̯ʼǱ
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ȷʵǺܸӣϸʽԶƵʱĺۼĸ1!3!5!Щ׳˾ǲ΢ָ½Ľ룭ŵĽûxżηⶼ0101ĻԼֵĹʽǡ
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סƯдҲ𣿡;
Ȼû⣬ΪȤǷ⣬ԺֲܶͬдรҲx<2η>дxxԵʱдxxͲ̫ãôھͿԽƬϵ91ˡ
ףõģѾ˿Ƭˡɡ



ǡǸѧȻҲ̫˵Ǹsin xֻǸưɣֻǽĳsin xʾѣ̩չʽҲǽͬĺݼʽ֡͡sin x롺ݼ˵Ȼ൱һǺûиı䣬ԣݼʽ൱㡣˼Ҳ̫
᲻ᣬٵ٣ĺ˽ⱾʣҪоʱ̩ܽչʽʽչڱȽϷĶʽӳϽоղһ˼ĻǳãΪ޴Աرע㣬Ǹݼͻʮַ㣬˵쳲кͿʱõɺҲݼ
ܾúѧУϿʱȥעȽϸ΢ĵط˽ҪԶҪѧʲôʲôеһƬҡѧĻ෴ϸ΢ĵطͺ֮ԼһԹǶΪʲôʲôִȴס
šΪٵٵ

ٵٴҪ˵Ļ
ѧոȫ΢֡ݼ̩չʽչʽЩҲǵһһȴˣ̩չʽͨĶʽһоȻҪһܻСѵĺʽݼxk޺͵ķѾˡ
ٵٽȭͷǰ
Ҳǽѧ̹ҵ̩չʽѾȷʵˣҪоʱ̩͡չʽԿɡⶼѧĹ͡
ĿͻȻҵƿתϵͼֽٵٵϲ֪ΪȾһĨ̺졣
ԡԡȻҺܱǸ˷ѧıʱ䣬Һϲѧ˵ǳϲѧҡ
ٵٱ˵̧ͷȻ˵

һӶѧ̹ҵ̩չʽ


94Լ

ҹ
Լķ俴ŴӴľʦĿƬ趨ҵ¡




Ҳû취Ұ


95

֪ɣ
Ͻʱ׶ͻȻָ⡣
׶ҵͬͬѧѧ൱֣ѧУڵķΧԼϲ飬Լҳ⣬Ȼ⣬Ȼҵѧ㣬Ǹ׶ȱǲúԶҲҪԱУֻϣҲܿ硣
ѧáΰ£Ѿʼһһˣһվ鼮ǰţڵҴ󲿷ֶ޷ɡͬʱҲ뵽뵽֪ʶж㡣
ұò˽ԼѧأԼ£ֻšأƵطԼɣκ鿴ǴɣȻÿ춼ʽƺǱԶԶںͷ
ЩҲ޼£ٵһͣŬԼɡ
׶ȣǡnηʽn⡻𣿡
ţûϵnηʽn⣬ظͬ㡻
ó
ȻǸ˹ʦֵģ˾ȵʱŶʮ꣬òʿ֤òʿֻ֤Ǻܺġ
׶л໰ڿģʽˣ֮ǰƺͶһֱ죬һң̻صԼλ·ֳ໰ĲŮͰˡĸо
׶ȰڰǰʼϿΡ



ʱҵƺڽҡ

ร봫еϵɫŮĻ棡
Ϊ꼶ѧöζͬѧǣɷ˵ؽٵٵٺͼֽݸҡ
ѧ˼Ҵ㣬ġ
ȻʣѧҸ˵ӡл𡭡е⣬Сϵɫʲô˼ӽԺҾͽ熪

иĻܸม׶ԾɶźڰдʽͷҲص˵
ʲôʱôЭˣҲô֡
ۡڰôʽ׶ѧд𣿡
ˣٵ֪ɣ
ǰĶ໰ŮҪԵٵٿʼϿΡˡ
׶ٵԳٶ˵ʽԼnηʽнϵĹϵ



ԭˣǡnηʽнϵĹϵɡ
ʱ𣬾ŮҲ˵ҵԴʽûˡ仰ҡҡλε߻һ꼶Ľҡ
ܿɰŮأ硣
˵׶Ȳһ䯺ָ۾֮们䲢¶Ķ䣬ָָڿռлߣҵȻȻͣߵ˲䡣
˵ߣҲϲͣ촽ǻһֱȥŷḻĻ񡭡
ưɡ˵
ף
ϴ˵ľʦǦƣӦ˵ˡ׶Ȱѿҿ




Ѿ⿪׶ȣ
Ҫ˵⿪Ӧ˵ҼǵñĽõƬʱͻشˡ
⣿ǵá𰸣
ǰ(2)⡭˵֮ʦ¶Ц˵Ҫ𰸣ҪҴʽҳȤ⣬ҡ׶ʼ硣
šô𣿡
ǽʮͳѧȫ򵹵ĳ⣬ʦǳ֮ǰûκȷʦΪ⿪˱һٳ
һ£ôѵֻܽ⿪𣿡
ԡ
׶˵
ȻʮͳʱǸ⣬Ѿÿ춼ŵ
׶㻹Ŵ𰸰ɣ
ֻǿļѣѵôʦõƬ˼⣬뽫xΪzչķΧԿ
ม˵⡭԰ɣ(2)Ƿɢ𣿡
֪𣿡׶ȳԾؿң۾һ˲䷢â
ǲǣ˵ˣղҵʧԣһ룬ȲҪҡһæش
ڿƬдˡ⡹




96ͼ


961ٵٵĳ

ѧִ֡
һͼҡһķѧ뿪ʼļʱŮٵٱı˹
ôˣٵ٣
һֱٵ٣˿ʼ˼ԼӦҲҪʼˡ
Ǹ첻sin x̩չʽһؼ˼֮зˣsin xxı仯һֱ0รƩ硭
˵ŻĵٵóԼıʼǱ̯ҿ




Һһ˸˹ͷˡԲæʱ򻹴㡭
ϾĿõٵеɥֻڸ˵ʱɥʱҲֵúֱӣҲ˼æĿڣ
ǹĻ⣬뵽ʲôأ
ûʲô˵ġٵٹ۲ҵɫСĵ˵
Ȼ󡭡
ҡ
Եٵٵһ仰еޱ𾪡

Žsin xʽֽ⡣


ʲô




962ȥδ

ٵҲ˼𣿡
ۣ

ͻȻӱǶһȫûз׶Ⱦվں档
ŵĵٵٰѱʼǱǦʺжˤ£ʡƤͳߵĵ
ǵģ׶ȣٵٲ˼⣬sin xġʽֽ⡻
ѧǸʲôٵٱ߼ʱʡ
õٵٿƬ˵ƽ͵⣬ҵĿƬԦ<k=1,1/k<2η>>ֵ׶ȵĿƬԦ(2)ֵ⣬Ȼֵָ¡
ٵҵ˵󣬱ֳһɫҲǵȻģϾԼȫû˼⡣
ʱ׶ȼٵٵµıʼǱȻʼġ
ม
ǸȻٵѱʼǱûȴ׶ȵѹס֡
㰡׶ȵû뿪ʼǱ˵̵ٵǉsin x̩չʽ𣿡ţԭˣҲǴľʦսдšһӶǣǡ
ԡԲ𣡡ٵһûرʼǱ
š׶ȱ۾ָһڶָ״̬ʱΧ˶ᱣֳĬע׶˼ʱһǵ
׶۾
Ǿʹsin x̩չʽʼɡ
һ˵껰ҵıʺͱʼǱʼдʽ



sin xʽֽ⡻ǵٵǉ뷨ɣ
׶ͻȻβĶʷٵٵ˵ͷȻմ׶ûıʼǱǰǱдšһӶǣıʼǱԼ̩չʽĵٵ١



д׶ȷ·͵㽫Կʽĵٵ٣ͬʱ˵ٵǉҲ÷˰ɡ
ٵǺش𣺡ҪҪʲô
׶ԭضſ˫֣ϸ΢˵ȽϿx<2η>ϵ

ҿʽ
Ƚϵ
˲㡣
Ƚϵ
ס
ѵ
̫ˡ
ҿ׶ȡ
׶ٵٿȥ
ٵ١
ףôסף
һı飬ƺû֡




ٵٴ˳ȻͼңҪ󺰵顣
⿪ˣĽ⿪ˣ⿪ˣ
ٵٿ׶ȣȻٿҡ
׶ȵͷӽ˵
⿪ˣѾ⿪ˣʮѧҵ⡪ѾýˣһĽⷨ
׶Ƚʽ¸д




õģ͸һˡ׶ͷʳָ¶ЦݣЦݡ
ΪΪʲôʲʲôʱ̫̫ˣ
ٵȻ֮С




963޵ս

⿪ǵʦ¡ϵһ⿪ˣڹԪһ꣬ʦʮʱҲĵڶꡭ׶ϸ
ǷԽͰʱ䣬Ľⷨأʱǲֻʮꡭһǽĵڶꣿ
ǽ⿪𣿡ٵʡ
ǵģʦºü⿪ķһֽⷨ



ȻңΪѾ֪ʦⷨĹϵ
׶ȱ˵վ
Ȼú÷ʽĽ⽫sin xʽֽ⡻Ƿǳ˲Ȼлв̫ϽĲ֣Ҳжսľġ
׶ȽַŵȻŵĵٵͷϡ
ڶǵʦʦʾͬʱҲҪΪٵǉ֡
׶ȿʼ֣ҲվԵٵֻ֣˵Ȳɡ
׶ѧ㡭ѧ
ٵٽסߺգ۾գš
ͼңҪ
ЩѾҪˡ
ڡΪǵĻŮٵ֣

ĺͣ
11/2<nη>1/3<nη>1/3<nη>һ
ù̬׵չ֣
nΪżʱԽԲʦеİæʾ
ʵϣЩͶԦ<nη>ıһֱ
[25]



10¡ֲ


׵Ĵӵյ
С[8]


101ͼ


1011ֲ

һķѧ
ˡ׶ȱ˵߽ͼңƺõ˴ľʦ⡣
Һ͵ٵϵֽš





һֱû˵׶ӣ汬Ч
Ȼͣ¶Ի
ٵǉǸ䣬ȥߵλãҶҪС˵˼
׶һ£ٵٺҶͷͬ⡣
֪˻ж

Ǿڷѧͼؿʼù


1012˼ʵ




ǱУʱ䡣

ʦˣѾô˰
ʦǻᶨʱֵĹԱʦ޷ж߷ɫ۾һߵͼݵʱ䵽ˡ
֮ȵѾ֪101ĴP<9>30ˣ֪102Ĵ𰸡

101

P<9>30


102ȥ·


1021쳲

վ·ϡ
ٵٰڳһҪȭĶ
ʲôʡ
쳲ơ
ʲô
Ҳѹѧ֪Ϊơ

Ǵҷǳϲѧ˼ǰѧ˴кķʽڼʱʹมΪƣԼʹԲͨǸһЩʱҲԴԷ֪ɡ
ٵǉ¶һӡ
Կɡ
ٵٽ쵽ҵıǰ棬ڶĴΡ
֪𣿡
֪ʲô
Ҫϸָȵ֣1123ࡡ
ٵ±һΣָȷ1123ӡȻ
Ȼ󿴵쳲ƵʱҪȳȭĲӦΪ1123һ5ָȳ쳲У쳲ơ
ม׶ȣڸղŵP<9>
ѧҪҰ
ҿ׶ȣָҲڸűȻ
ף׶Ҳƣ㵽ʲôеطʡ
쳲ơٵǉ5ԺҪô죿358𣿼쳲ƼȥĻȫ˵ֶࡡ׶˵
5ͣˡǾһȰɣұȳ1123ĻҪӦ5มһһ
׶Ц֡
˾ò˼ֲСѧ
ٵȻָô۾ңû취ֻֻӦ
塣
áлл
ŮҲǾ


1022

ߵ˴·ԣΪõ·Сǰյٵ١ҡ׶ȵ˳ųһǰٵٲϵתͷ˵ƺеΣգҶ׶վҵܾò̫ڡ
101ֵ˶102Ե˶ˡ׶˵
ٵתͷ˵Ѿ101ˣ102ʵдP<15>ʱ֪ǳʲô˼ͻȻˣȻд50֣ȻûнԲᳬ1000֡
ٵ٣ǰ濴ǰ棬ҪСǰĵ߸ˡ
ûģѧ˵P<9>29ְɣٵٰѱʼǱǴ򿪡



 ס29֣30
Ҫôʡ
͸㿴һ١3֧1ԪӲ3˼
รԭˣдࡣ
ûТڣۣܡ׶ԽҵļűʼǱ⣬ĳңͬʱĹ㡣
ѽȷ˺üΡʹٵٵͷײƣҸողǲѹ

վˡ
Ҿˣ׶һµٵٵͷ뿪·ߺǸպ෴
׶ѧˡһ쳲ġٵ죬ϵضָͷ
ʱ׶Ⱦָ֣ڿл裬ûзٶȣҲûлͷ

103Beans

ڵٵҪҪȥȱȺǾ˳վǰġBeansҶλϡ
ٵٽţ̼뿧ȺֻڷҲ׽裬ƺƽе㲻̫һŻ˵Ļ
Ҳϣѧܱøһ㣬ȻûҪֻǲУ࣬뵥P<15>P<15>Ǹǳ
̾һ
ѧûҵλء
ף
ףٵٵԽԽ죬Ҹղ˵𣿰ղŵĲ㣡ԣҲǲ㣡ǵġ
ֻǰȥⲻ쳲ơ
һ
ٵٵͷ
ѧ꼶ʱҲҹж꼶ʱѧУʱзɣǹڶƵ⡣ڷѧ˵ˡѧǳԽʱġʷѧоƣǲִĵѧǳԽʱġҲҵ˵ʮоƵȲöʮһеԵ£ȻѾȥˣѧȴԽʱţִˡҴѧĻܵ飬ûĵΪѧǿԳԽʱġ
ô˵Һз⡣
ѧʱѧ󶼻ᵽͼȥɣУ֮ΪҪӽѧҲʼȥͼ䡭ҾͼĽ俴飬ѧһֱæż㣬ȫûע⵽ңҲΪ궬һͼĽ
̧ͷ¶˼Цݡ
ûע⵽һֱΪû˻ͼֻһˡ
ҡ֪ܺѧͬһеʱĺܸˣ¶дŸѧ̫ˣҷǳϲҡٵ١˵ٵٺʱľúʲôɹѧҲȥ̨ܸѧ׶ѧһѧҷǳ֡
ô˵ȥ̨û
ҲдͷɥʱȻܺѧۣԼһȴʲôҾʧˡ
šܶ飬ҿ׶ʱҲһĸо
ҵλáѧҵλ𣿶ѧԣҿֻһıѧöѣѧǷҵλأֻżԸ̽ѧҲԡ
ҵĳ򡭡Ϊ˵ٵٶڵ򡭡
ҿ˵
ţʲôʱСϲ͵ٵ˵Һֱǰڡѧ֡Ӧһκʱ򶼿ԽѧţԼûиı䡭ҲֻԼһ˾ʲôеʱͼȻȤڸ֣Ϊܺѧˡҵڵٵٵλһֱڣ˵ҺҪѡ
ͣٵָ֡лллҷǳˡƺ˵̫ˣԵΪֹ
ѵĵ·ڿռ֮С
ԭˣÿڻؼҵ·ϣٵٻߵɡ
ϣһ
޵ʱ


104Լ

Լҡ
ʾ2359֣2359
˶˯ˣڷѧҸʱ̡
˶սʲôʽûȤȤʽ仯ܸ˵غ˵Ҳֻõһ䡸ѡ
Ǻģ׶ٵٿԺһ⡢һһ֣֪ʶս̸ֽ֮ⷨΪĹͨԡϲʱ䣬͹ʱͼȹʱͬʱֻһڼ㡭ԲԣǸʱǸطٵٻҲڰɡ



  оֲɺɣҹ


1041Ϊѡ

ڷȦ˼ȻֵֺҪȥֻϵֱѡڱɡ֮ǰĽⷨҲ׶ȿСԵ˶˼˼ɡ

Ҵ򿪴ҹĿԶĹΪʲôһϲѧأѧʲôأ׶ô˵ģ

翵ж˵ѧıɡʦɵģ޴СĸԼоϣԲʵĦУλiȻĵeʦʼʹõ֣ʦڵʱ޷ɵĺϼһţڿ˹ϼһ

šδĳһµ

΢ɺ˼ԼǲнƵأ

ԲҼǲס
ԣҪҪ˼˼




뵽Ժиֳٵŷߵͣ½Ų
ף
ʲôҪĵط⡣
ٵڸǰ档
ҪҪ˼֮
ѡķϵ
ѡķϵ
õٵٵķ෽ʽѡţйϵһͷֲɺйأʽ޺͵޻ͺˣ֪ˡ
֪˻ж׶ȵҵ
Ҽæʼ㣬޻ԲܳΪxıչʽӦÿԵõʽɺP(x)

ҹԼУҰؿʼù



105ֽ

졣
ڷѧֽңӢӢҡ׶졣
ض˵ص͹
ӢӢһƽ̨ٵŸ±һ죬ͬǸж꼶Ȼͬѧ꣬ȴҺ׶Ȳͬ༶Ǹšǿ糤Ǹǳϲټ̵Ů
ţ͹׶΢Цؽֱڱһһֽգƺܺá
ٵǉû𣿲ǲӢӢ߶˵
ٵǉ
ûرҰɡһش
պʱ򣬱űʼǱĵٵٽֽҡ
ѧﰡһѧͼһȥء
(ⲻǺظں)ӢӢС˵
ŵ𣿡ٵǉǡ
ᣬٵ٣Ҳûʲô˵
ҪҸ˵𣿡
õĺõġˡ˵ٵãҪҪһѧɹ׶ȣҿдֲʽӰɡ
һP<n>ıչʽ𣿡׶ͻȻͣ½ŲϾʡ
ǣһP<n>ıչʽɺP(x)޻ʽһش
Ǿͺá׶ٶȻָЦݡ
ʹǰĺڰɡ
ߵֽǰ棬ƶʽڰ׼׶Ⱥ͵ٵҲҡ
ӢӢ˵ѽҪʼѧˡ󣬵ٵ־ͣ


1051ҵķ(ֲɺ)




ԭˣȤ׶˵
ǰ΢Цظ
׶ѧ㣬ԭˡʲô˼ѧǰʲô˼أȫҪ˳˵ٵٿʼԹ˵꣬ӢӢĸپϲ֡
ȥɡ׶˵
ٵ٣ղŵʽҪҶ˵




ͻưɡ׶֮̽˵
û
ţֻҪ֤102Ĳʽ÷ǵP<n>԰ɣ׶˵
šϡûұе㲻
˵ΪҲһP<n>ҲP<15>ܽ102׶ȵ˵
ף


1052׶ȵķ(ֲϽ)




׶ؽķ


1053ٵٵķ

ǡǸλٵپ֡
õģٵǉ𣿡׶ָ
⡭ҲҪ102Ľ⡣ٵ˵
รǾͻְɡ˵꣬׶ȵݳ۱ʡ
ˡҵķܿͻҽ֧15Ԫķȫд˳ֱĻP<15>ֵ176ԡ



׶Ѹȷϵٵоٵ֧
ûдǵٵǉֵ׵ʤءЦ׶ٵٵͷ
ٺ٣ûˡٵٿĵ˵
ֻƿԡ


106

ΪصҵңͻȻú㡣
Լλ£ſϡ
ִһP<n>ǸܱʣĿѾرòʽˣһһʱɺԽȫûа
治ġ
߽ңŲ׶ȣĽŲ𽥽ӽ
ôˣ׶ȵ
ûлشҲû̧ͷ
ۡ
ڰĽУ׶Ծûκζ
һĬ
Ƶ̧ͷ
ı鲢ƽһУǴ飬ͻȻ䣬׶ȵָˡ

1123

쳲ƣǰѧ˴кķʽڵҲûӦ
׶Ȱֱڱ󣬽Ա˵
ٵǉܿɰء
ûлش
ܲһɰ
ҡûлش
ҵ˵¸˵ġ硻
ûнΪߴ·ˡ˵
š׶˵ţڵϵκεطԼ׳ʱ֮УѧǲϵѰŸĽм䣬նؽҲǳе£Ҫ˵Ѱû𣿵ȻǣȥѰҾ޷֪Ƿܹҵʵȥô֪Ƿܹˣƣʱ򡢻·ʱ򣬼ˣȻС
ҡװɺܶӣɺԽⲢûаһԳ
ô׶˵ôҷֵɺP(x)ɡ˵껰¶΢Ц
׶һָٶȰڳ쳲ơ

1123

ſӦԼơ

5

Ȼſֻλϵңůָҵӡ

ƣʱϢɣߴ·ʱ߰ɡΪһȫǵó̡

˵껰ǰսҡ
ǵ۾ײ
Ƭͫס
˵ӲϿ
ء
ʦֵĻһɡҲ˵롣
͡׶˵


107ѰҸϽ;

˼졣
ѧ׶ͻȻ˵
ҵ쳲õϽˣɣˣѵٵǉҲ


1071ɺ

׶ŷ۱վڽ̨ǰ档
ٵٺұгڽҵǰϿΡ֮ûκˡ



1076ٵٵĻع

Һ͵ٵһ׶ọ́ȻЩطȷϣҪƷ;֮󡭡׷ʽ֮޷ĸо
ҿٵ٣ڳı鲻һ
ٵ٣ѵй𣿡Сʡ
ôᣬȫйٵٿʵЦš׶ѧƵĹУкܶҲĵطûйΪҲкܶطö
ٵٵͷ֮˵
ܾúԹˣǺó;Ȼкܶطû꣬ѾץŵĸоˣҳҸеȤʹЩҲҾú

-޺ͱ޺ͣʽ
-γɼʽϽĹ۲Ϊϸ
-Ϊ˽Ͷȡ
-ʹ͹ʽ
-ƿʱ̩չʽ
-鷳ʱı任
-ʦı
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ףոջһ̸ֱȴͻȻֻʣһˡܾúеį
ͬһѧһԵĵ·ôǵʱռȻޣս٣ҵؿڴһʹ
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찡
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[25]






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