高阶微分中值定理的-中间点-的渐近性

JOURNALOFBEIJINGINSTITUTEOF19912CIVILENGINEERINGANDARCHITECTURENo.21991()Il.,:,,,12345,,n(6),r(x)=(1)Cf(x+k)=0f={!{,((X+,1+;2++,)d;ld;d;D00(1)t::1m=0,1,2,,n1,,c-m=(2)o(+1)!2.m=n+1:f(x)=1m0,(1),n1,f(x)=:199006282:83(1)Cx+ko0x0,t=(1)C=0{)\/Ok=0(1)C-2m:,f)(x)=!,(1)(1)C:x+=r.{!,dylyx0,t1,n!(i)C:0(i)C:Jk}1{n/!3,,,=,:,f)(x)=(,:+)r,(i),()Cx+k=(+)!(x+g,++)d,dles+,,,X,+2,++2tZt1+,,!X+,)x=0t=,nk{{72/n+l(1)C__(n+1)!2.1(1)CkO_(n+1)!2,,(2)19912:(7)1f(x)a,b,(a,)n,(a,b),,C(ba)n=(),1:2(1)f(x)a,,(2)f(x)an+1(),1,:,:_al1111::6baZ:F()=,C(),(ba)+,n,(2),a.f1(a):lim~C;((a)1,,C)-(ba)nr)()(+1)!(ba)=,,,C,()a)1(n+1)!:(,):,i,(J,-.k(a)na(n+1)!2..r(+,)()=f+)()n~(3)..”,”JI”J+bk(ba)n,_:,=*:__*k(a)_71,U.l,U-,,J,U-,,,1,11111.,,C(),(ba)+l2:((;(,(,n..an=lim(ba)=lim(),lim.(ba)lf)()f)(a)aaba1;(+l)r__,_j111inba(4)a,b,ba,lima,(3)(4),-baZn,,:(8)3f(x),g(x)a,,(a,b)n,g(x),g(x),g(x),(a,b),.21|1,C:f-,Cg-k(a)(ba)f()g()†3:4(1)f(x),g(x)a,b:;(2)g(x),g(x),g((x)a,b;(3)f(x),g(x)an+1(),f(a)g(a)f(a)g+(a),3,aaŽLlim:k(ba)F()n,C};,Cg-,n,(a)1(2),,t_;_k(ba)zim-(af)(a)g(a)a),Cg861991=lim6es(i)C)if2!=0(n+1)!(ba),c-k(ba)n(n+1)!(a)†=lim-,1(n+1){g)(a)C-k)g)(af)ag:(a)i,;_;:,=11m;-i~~eeZ1){1{{g)aLn1):gal\/(n)b(a)k(ba)a,les|j_ka))g}b}g(a(I\,/\,a,.-,ktba)l}o-la}/(n+1)!g)(a)(n+1)!2f1(a)g(a)f(a)g+(a)((a)g(a)f(a)g(+)(a)(5)(a)gnbk(ba)a,b,b,a,bk(ba)na,3,(2),:~)ng(a)(i)e(a)1=lim-,O,C-Cg-k(a)n.(_g()g(a)(ba)+1(i)Cg)b-=lim6gt(a)f)()f(a)g()=0k(a)g)()g(a)(ba)6.IJa=linl-.(a)a)gf(()(a))()g(a)gL2:,cg!(a)abaf(a)g(a)f((a)gn)(a)g()(a)2f(a)g(a)f(a)g(a)g(a)!:ag(a){aa(6),b(a,,a,*a,-(a)n(5)(6),Ž1im:=1,,,Bernardeobn,onthemeanvaluetheoremforitegrals,Amer,Math,Monthly,1982Vol.89,300301AltonsoG.AzPeitia,ontheLagrangerenainderoftheTaylorformula.Amer,Mth,Monthly1982,Vol.89,311312,1985,(2):5357,988,(1):8687,1989,(1):]231260G,G:,,:,1981,60.GabrielKlambauer315.,,1987,(1):]1]3,881991AsymPtotieProPertyoftheInterPoint,,inMeanValueTheoremsofDifferentialsofHigherOrderZhuang(DePartmentofDexiongBasieSeienees)AbstraetInthisPaPer,thea,ymPtotietheorem,ofdifferentialsofhighertheorem,oftheinterPointintended.ProPeryoftheainterPoint,)inmeanvalueorder15diseusged.andtherebythea,ymPtotiemeanvaluetheoremgofdifferentialsareexKeywords:agymPtotieProPerty,differentialsofhigherorder,dlfferenee