关于积分中值定理中间值探讨.doc

关于积分中值定理中间值的探讨24???X6?3Vol124m?No16???k?(?6????????(???M??????)JournalofChangChunTeachersCollege(NaturalScience)2005??12?(Dec12005???????l?d?U???l?d???U?????????s??(???k?l???;????????,?)?????km?130000)[??m???]?X???????????????>????lnx?sf(x)-blnx]?k(x]?+x,)??,?????l?L???????????;??,???l?d?U???l?d???U???U??????m4[???=??]???l;?d?U???l;?d???U;?U??[?d???l????]O172m?m?m?[???=?N???2]Am?m?m?[?????s??]1008-178X(2005)06-0015202[?M?K???3]5[???o????]???s??(63),?I,???????9??,???k?l???;??????????????,?????l???????e??m41m??c?????l?d?U???l?>?????l?d?????A???X???l,?O???=[1m22]?d?????????l?L?????????????d???U???U??????m4?O???=[3m24m25]?d?????????l?L????????????,?e??????????x]?+x,???Lf(x)x2]?k?sf(x)ex]?k??,???d???U?????s????m4?X???e???????????>????lnx?sf(x)-blnx]?k??,???l?d?U???l?d???U???U??????m4?c?lm???????f(x)?O[a,b]?J????,?i?O[a,b]?J???O6?,??x8baf(x)dx=f(6?)(b-a)m4???c?l?O???????X?????????l?????d???????m,?r?????d???U6???????,?????O???=?d?????y???mm42m??G?????????l1m???6?????x8xalntdt=(x-a)ln6?(a>0),?ilimm?x]?+x,6?-ax-a=e-1???a:?:??x8xalntdt=tlnt|xa-x8xat??1tdt=xlnx-alna-(x-a)?w??m?1xx8xalntdt=lnx+a-alnax-1]?+x,(x]?+x,)???>m?ln6?=1x-ax8xalntdt=xx-a??1xx8xalntdt]?+x,(x]?+x,)???)m???x]?+x,??m?6?]?+x,??m?m?(x-a)ln6?=xlnx-x+(a-alna)?w??m?x(ln6?-lnx)=aln6?-x+(a-alna)??m?m?ln6?-lnx=aln6?x-1+a-alnax(1)???>m?aln6?x=ln6?6???a6?x,???dlimm?6?]?+x,ln6?6?=0,|a6?x|x?a?w??m?limm?6?]?+x,aln6?x=0m?m??p?Mlimm?x]?+x,a-alnax=0???>?:(1)?f???mm?limm?x]?+x,(ln6?-lnx)=-1???)m?limm?x]?+x,ln6?x=-1m?m???limm?x]?+x,6?x=e-1??5????200-09-2019-1limm?x]?+x,6?-ax-a=limm?x]?+x,6?-a6???6?x??xx-a=e-1???????l2m???f(x)?O[a,+x,)?J????,?elimm?x]?+x,[f(x)-blnx]=k(b>0)?e6??>?c?l?d?????l?d?U???l???d???U,?i?)limm?6?]?+x,6?-ax-a=e-1???a:??f(x)-blnx=5(x),?ilimm?x]?+x,5(x)=km?m?m?xBf(x)=blnx+5(x)m??e5(x)?O[a,+x,)?J?L?)?????:??x8xaf(t)dt=(x-a)f(6?)=(x-a)[bln6?+5(6?)],?em?x8xa[blnt+5(t)]dt=b(xlnx-x+a-alna)+x8xa5(t)dtm?m?xBbln6?+5(6?)=bx-a(xlnx-x+a-alna)+1x-ax8xa5(t)dt=bxx-a??(lnx-1+a-alnax+1x-ax8xa5(t)d