文档介绍：12005年河南省普通高等学校选拔优秀专科生进入本科阶段学习考试高等数学试卷题号一二三四五六总分核分人分数一、单项选择题(每小题2分,共计60分)在每小题的四个备选答案中选出一个正确答案,并将其代码写在题干后面的括号内。不选、错选或多选者,???5)1ln(的定义域为为(C)??????x解:Cxxx???????????,图形关于y轴对称的是(D)??????????解:图形关于y轴对称,就是考察函数是否为偶函数,显然函数222xxy???为偶函数,?x时,与1?xe等价的无穷小量是(B):??xex~12~1xex?,.???????????121limnnn(B):2)1(2lim2)1(22121lim21lim21limennnnnnnnnnnnn??????????????????????????????????????????,??????????0,0,11)(xaxxxxf在0?x处连续,则常数?a(C).-?解:21)11(1lim)11(lim11lim)(lim0000??????????????xxxxxxxfxxxx,)(xf在点1?x处可导,且21)1()21(lim0????hfhfh,则??)1(f(D)??解:41)1(21)1(22)1()21(lim2)1()21(lim020??????????????????ffhfhfhfhfhh,??确定的隐函数)(yx的导数dydx为(A)A.)1()1(xyyx??B.)1()1(yxxy??C.)1()1(??yxxyD.)1()1(??xyyx解:对方程yxexy??两边微分得)(dydxeydxxdyyx????,即dyxedxeyyxyx)()(?????,dyxxydxxyy)()(???,所以dydx)1()1(xyyx???,)(xf具有任意阶导数,且2)]([)(xfxf??,则?)()(xfn(B))]([?)]([!?)]()[1(??)]([)!1(??nxfn解:423)]([3)()(32)()]([2)()(2)(xfxfxfxfxfxfxfxf!?????????????,????)()(xfn1)]([!?nxfn,(A)A.]1,1[,1)(2???xxfB.]1,1[,)(???xxexfC.]1,1[,11)(2???xxfD.]1,1[|,|)(??xxf解:由罗尔中值定理条件:连续、可导及端点的函数值相等来确定,只有]1,1[,1)(2???xxf满足,),(),12)(1()(?????????xxxxf,则在)1,21(内,)(xf单调(B),曲线)(xfy?,曲线)(xfy?,曲线)(xfy?,曲线)(xfy?为凸的解:在)1,21(内,显然有0)12)(1()(?????xxxf,而014)(?????xxf,故函数)(xf在)1,21(内单调减少,且曲线)(xfy?为凹的,??(C),又有水平渐近线,、垂直渐近线解:0lim;11lim0???????????xyyyxx,?????tbytaxsincos,则二阶导数?22dxyd(B)??4解:dxdttatbtatbdxydtatbxydxdytxtt?????????????????????????sincossincossincos22tabtatab322sinsin1sin?????,???Cedxexfxx11)(,则?)(xf(B)??:两边对x求导22111)()1()(xxfxeexfxx??????,???CxFdxxf)()(,则??dxxxf)(sincos(A)?)(??)(?)(??)(cos解:?????CxFxdxfdxxxf)(sin)(