Question

É趨ÒåÔÚÇø¼ä[x₁£¬ x₂]Éϵĺ¯Êýy=f(x)µÄͼÏóΪC£¬MÊÇCÉϵÄÈÎÒâÒ»µã£¬OΪ×ø±êÔ­µã£¬ÉèÏòÁ¿=£¬£¬=(x£¬y)£¬µ±ÊµÊý¦ËÂú×ãx=¦Ë x₁+(1£­¦Ë) x₂ʱ£¬¼ÇÏòÁ¿=¦Ë+(1£­¦Ë)£®¶¨Òå¡°º¯Êýy=f(x)ÔÚÇø¼ä[x₁£¬x₂]ÉÏ¿ÉÔÚ±ê×¼kÏÂÏßÐÔ½üËÆ¡±ÊÇÖ¸¡°kºã³ÉÁ¢¡±£¬ÆäÖÐkÊÇÒ»¸öÈ·¶¨µÄÕýÊý£®

£¨1£©É躯Êý f(x)=x²ÔÚÇø¼ä[0£¬1]ÉÏ¿ÉÔÚ±ê×¼kÏÂÏßÐÔ½üËÆ£¬ÇókµÄÈ¡Öµ·¶Î§£»

£¨2£©ÇóÖ¤£ºº¯ÊýÔÚÇø¼äÉÏ¿ÉÔÚ±ê×¼k=ÏÂÏßÐÔ½üËÆ£®

£¨²Î¿¼Êý¾Ý£ºe=2.718£¬ln(e£­1)=0.541£©

Answer 1

¡¾½â¡¿£¨1£©ÓÉ=¦Ë+(1£­¦Ë)µÃµ½=¦Ë£¬

ËùÒÔB£¬N£¬AÈýµã¹²Ïߣ¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡ ¡­¡­¡­¡­¡­¡­¡­¡­2·Ö

ÓÖÓÉx=¦Ë x₁+(1£­¦Ë) x₂ÓëÏòÁ¿=¦Ë+(1£­¦Ë)£¬µÃNÓëMµÄºá×ø±êÏàͬ£® ¡­¡­¡­¡­¡­4·Ö

¶ÔÓÚ [0£¬1]Éϵĺ¯Êýy=x²£¬A(0£¬0)£¬B(1£¬1)£¬

ÔòÓУ¬¹Ê£»

ËùÒÔkµÄÈ¡Öµ·¶Î§ÊÇ£®¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ ¡­¡­¡­¡­¡­¡­¡­¡­6·Ö

£¨2£©¶ÔÓÚÉϵĺ¯Êý£¬

A()£¬B()£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ ¡­¡­¡­¡­¡­¡­¡­¡­8·ÖÔòÖ±ÏßABµÄ·½³Ì£¬¡¡¡¡¡¡¡¡¡¡ ¡¡¡¡¡¡¡¡¡­¡­¡­¡­¡­¡­¡­¡­10·Ö

ÁÆäÖУ¬

ÓÚÊÇ£¬¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ ¡­¡­¡­¡­¡­¡­¡­¡­13·Ö

ÁбíÈçÏ£º

x	em	(em£¬em+1£­em)	em+1£­em	(em+1£­em£¬em+1)	em+1
		+	0	£­
	0	Ôö		¼õ	0

Ôò£¬ÇÒÔÚ´¦È¡µÃ×î´óÖµ£¬

ÓÖ0.123£¬´Ó¶øÃüÌâ³ÉÁ¢£® ¡¡¡¡¡¡ ¡­¡­¡­¡­¡­¡­¡­¡­16·Ö