2023年山东大学网络教育高升专入学考试样题答案

山东大学网络教育高升专入学考试样题答案【篇一：20２3年山东大学网络教育专升本高等数学模拟题(带答案）】ss=ｔｘt＞一、选择题:本大题5个小题,每小题6分,共3０分，在每小题给出的四个选项中,只有一项是符合题目规定的，把所选项前的字母填在题后的括号内。１．下列各组函数中,是相同的函数的是(ｂ).2ａ．f?x??lｎx和g?ｘ？?2lnxb．f?x？？|x|和g?x??ｃ.ｆ？ｘ??ｘ和g?x??d.f?x?？２｜ｘ|和g？x??1x2.若极限lｉｍf(x)?a存在,下列说法对的的是(ｄ）x？0f(ｘ）不存在a.左极限lｉm?x？0f(x)不存在b.右极限ｌim?x?0ｆ(x）和右极限lim？ｆ（ｘ)存在,但不相等ｃ.左极限lｉｍ?ｘ?0ｘ？0f(ｘ)?lｉmf(x)?limf(x)？ad.lｉm？?x?０x?0x?03.??1?１f?？？２dx的结果是（ｄ)．?x?x？１?？？ｃｂ.?fx?？?1?????cc．?x?？１?f??？cd.?f?x??1?？??c？ｘ？a．f??x2?ax?6?5,则a的值是（b）4．已知ｌiｍx?１1?xａ.7b.?7c.２d.35．线ｙ？2(ｘ?１)在(1,0)点处的切线方程是(d）ａ．y?？x?１b．y?？ｘ?1c.y？ｘ？1ｄ．y?x?1二、填空题：本大题共８个小题，每题5分,共40分。把答案填在题中横线上。6.函数y?__＿______(-3，3）____＿＿_________.?e?2x?1ｘ?０？7.设函数f?x???ｘ在x？0处连续，则a??ａx?０？?2．8．曲线y？2x2在点（1,2)处的切线方程为___ｙ-4x+2=0＿_____．９.函数y?1３x?x的单调减少区间为＿___【－1,1】３１0．若ｆ?（0)?1,则ｌｉｍx?0f(x)？f(?x)?x１１.求不定积分?ａrｃsｉn3x?x２?14arcsinxc4１2．设f(x)在?0,1?上有连续的导数且f(1)？２，则?1f(x)ｄx？3，?１xf(x）dx?-1１３．微分方程y???４y??4y?0的通解是(ｃ1?c２x）e？2x.三、计算题:本大题分为3个小题,共4０分。14.求lｉm解：ｌimsｉｎmｘ，其中ｍ,n为自然数.(１０分）x??sinｎxｍｓinmxmx=lｉm？x??sinnｘｘ？?ｎx15．求不定积分ｘlｎ(１?x)dx．(1５分)?？xln（1?x)dx1２ｌn（1?x)dｘ2？解:12x２?(xlｎ（1?ｘ)??ｄx）２1？x12?[x2ln（1?x)？1（x?１)?ln（1？ｘ）]?c2＝１6．求曲线？?x?t?在t？处的切线与法线方程.(15分）2？y?1?cｏｓty??sitn?t?？1k=解:？??当ｔ?时,x?,y?１所以切线方程为,y-x－1+？0222？法线方程为y+x-1-?０2四、综合题与证明题:本大题共２个小题，每题20分，共40分。217.设某公司在生产一种商品x件时的总收益为ｒ，总成本函数为（ｘ）？１00x?x2,问政府对每件商品征收货品税为多少时，在公司获得利润最大的c（ｘ）？200?５０x?x情况下,总税额最大？解:设每件商品征收货品税为a,公司获得利润l(ｘ)=r(ｘ)-c（x）-ａx＝100x?x2－（2０0？50x?x2）-ax=－2x2？(50?ａ)x?2００l?(x)??4x？50?a令l?(x)??4x？５0？a=0,则x=税收t=ax＝50-a,此时ｌ?（x)取得最大值4ａ（5０-a)41(50?2ａ)4令ｔ？?0,得：a=２５t??当a=2５时,总税额最大。２18.证明：当1?x?2时,4ｘlnx?x?2x?3.ｆ(x)?４xｌnx？(x2?2ｘ？3)f?(ｘ)?４lnx?2x？2证:令f?？（x)?2（2?ｘ)ｘ由于f??(1)?０,所以在x?1处,f（x)取得最小值,即f(x)ｆ（1)所以f(x)?0成立，即４xlnx?x2?2ｘ?３山东大学网络教育专升本数学模拟题2一、选择题：本大题５个小题，每小题6分,共30分,在每小题给出的四个选项中，只有一项是符合题目规定的，把所选项前的字母填在题后的括号内。1.函数f(ｘ)？19?x2的定义域是（ａ）a．（-3,3)b．[－3，３]ｃ．（？,）ｄ.（0，３）3,ａx3？b2.已知ｌiｍ?1,则（b)x？0ｘｔａn２xa．ａ?２,b？０b．a？1,b?0c.ａ？６,b?0ｄ.a?1,b？１3．假如?df(x）??dg(x)，则下述结论中不对的的是（a）.d?ｆ?(x）?ｄ?g?(x)？?a.ｆ(x)？g(ｘ)b．f(x)?g(x)c.ｄｆ(x)?ｄｇ(x)d.４．曲线y?x3?ｘ?２在点（1，0）处的切线方程是(b)a．y?2(x?1)ｂ.y?4(x?1)c．y?4x?1d.y?３(x?1)5.siｎｘcosxdx?（a）a．?二、填空题：本大题共８个小题，每题5分,共4０分。把答案填在题中横线上。?11１1cos２x？cｂ.cos２x?cc.?sin2x?ｃd.ｃos２ｘ？c4２421ｘ3?2x2?１６.ｌim__________．?2ｘ??4(x？1)(2x?1)7．已知曲线y?f？x?在x?2处的切线的倾斜角为?,则f?？２??8.设函数ｙ?ｙ(x)是由方程ex？eｙ？sin(xｙ)拟定，则y?56.x?０?12９.设f(ｘ)可导,y?f（ex),则ｙ？?_＿＿＿_ｅxf(ｅｘ)__＿___＿.10.已知x?0时，a(1?ｃｏｓx）与xsiｎx是等级无穷小，则ａ?11．不定积分?ｘcosxdx＝xsiｎx+cosx+c.）ｅ.12.设函数y？xe,则y???(2＋x3１3．ｙ???y？?y?０是___2_＿__阶微分方程.xｘ三、计算题：本大题分为3个小题,共40分。1４．求函数f(ｘ,y)?ｘ2?ｘｙ？y2？3ｘ?6y的极值(１0分）?ｘ？0?y?3??ｆx?（x,y）?2x？y?3?0解:??ｆy?（x,ｙ)?x？2y？6?０?？(x,y)？2，fｘy？?(x,y）?１,fyy?？(x,ｙ)？2,?＝30，所以在(０,３）处取得极小值ｆ（0，3）＝－9fｘｘ15．求不定积分解：令:t?？1dxx(１５分)x?t2，dｘ?２tdt,??2tｄt?2[ｔ?lｎ(1?t)］？c1?t2？xe?x，ｘ?0?１6．设函数f(x)??，计算1,？1？x?0?？１?cosｘ解:令t=x-２,则x＝t+2,dx=dt22?41f(ｘ?２）dx.（15分）？412111??te?tdt=tａｎ?(1?e?4)f(ｘ？2）dｘ？f(ｔ）dt？?=-1１+cost22?１０四、综合题与证明题:本大题共2个小题,每题２０分,共40分。1７．求曲线ｙ?14x?x3?1的凹凸区间和拐点.２解：解(１)y?？2x３?3ｘ2y？??6x2？6x(2）令y？?=0x=0,x=10)(3)x=0,x=1将定义域提成三个区间(-?,,（0,1），(1，+?)在以上三个区间内讨论y?？的符号变化及y的拐点情况，如表:【篇二：高起专英语试题】ｃlａss=txｔ＞i.语音知识（10分)在下面每组单词中,有一个单词的划线部分与其它单词的划线部分的读音不同。找出这个词，并把它前面的大写字母填入左边的括号里。(c（ｄ(ｂ（ｄｉi．词汇与语法知识（本题共20小题，每小题3分，满分60分)从a、b、c、d四个选项中，选出可以填入空白处的最佳答案。(a）６.ｈeｌeｎandｍarｙareｇooｄfriends._＿_____oｆｔengｏtoｓcｈooｌtogetｈer.ａ．theｙb．themc.ｔheｉrd.theｉrs(b)7.—whenｉshｅysbirｔhｄayparｔｙ，lynn?—the1８tｈ，____＿＿____abouttｈreeoｃlockｉntｈeafterｎｏoｎ．a.ｏnb.atｃ.tod.in(a）8.—caｎyourfaｔｈerdrｉｖe?—yｅs,aｎdheｕsuａｌly＿____＿______mｅｔoschool.a.driｖesｂ.drｏｖec.iｓdrｉvｉngｄ.hasdｒiven（c）９.—mａyiwatchtvfoｒawhile？—no,you＿_＿_＿_____.yｏuhaｖeｔoｆiniｓhｙourhｏｍewoｒkfｉrst.a.ｓhｏuｌｄｎtb.needntc.mustnｔd．wｏnt（c)10.—alicｅ,turndｏｗｎthetv,ｐlｅase.i____＿＿_＿___onthepｈone．—oh,sorrｙ.a.taｌkb.ｔalkｅdc.ａmtａlｋiｎｇd．havetaｌked(d)１１.—woｕlｄyoｕliｋｅtogotothecarｔoonｓhowｗitｈme?—ｉtsouｎｄｓｌｉｋefｕｎ,_＿________imtｏoｂuｓｙ.ａ.sｏb.forｃ.ord.but（d)12．—eｘcuｓeme．______ｉｓｉｔfroｍhｅreｔothｅbｕschａngｅcenter?—qｕiｔenear.iｔ’ｓoｎlyabｏｕthalfakilｏｍeter.ａ．ｈoｗｏftenｂ.ｈｏwsｏｏnｃ.howmuｃｈd.hｏｗfar(ｄ)13.—wｈyｄon’tyｏuleavesｃhoｏl？iｔsalreaｄyeighｔoclock.—becａuseｉ＿_________＿＿ｍyhomewｏrｋyeｔ.ａ.don’ｔｆinishｂ.waｓn’tfinｉshiｎgc．wontfiｎisｈd.haｖenｔfinｉｓhｅd(c)14.—the2023ｏlｙmpiｃgａmｅs_＿_＿＿___inbrazｉl.wouｌdyｏuliｋｅｔogｏtheｒe?—maybe,ifposｓible.ａ.areｈeldb.ｗeｒehelｄc.wｉllbeheldd.hａvｅbeｅｎｈeld(b)15．—cｏuldyｏｕpleasｅtｅllmｅ＿＿___＿___________?—suｒe.thereiｓaliｂrａryonbridgesｔreet.a.whereｃａｎｉborｒowsomeboｏkｓb.ｗheｒeiｃanbｏrrowsomebooｋsc.wheredｉdｉｂorrowｓomｅbｏoｋｓd.whereiborroweｄsomebｏｏks(ａ)16.whichofthefoｌloｗingｗorｄsmａtchesthesoｕnd/redi/?a.readｙｂ.readｃ.riｄeｄ.ｒed(c)17.ｗhichoｆthefolｌｏwｉｎgunderlinedpartｓｉsｄiffereｎｔinpｒoｎuｎciaｔｉonfromotheｒs?(a）18.infacｔ,mypａrentsarｅnotoｎlykinｄtｏme,buｔalsosｔrict___＿____me.a.withb.ｔoc.foｒd.at(ｃ)１9.theoldcoｍputｅrisｔheiｒsbutｔhｅnｅwcompuｔｅrｂelｏｎgstｏ______.a.weｂ.ourc．usd.ours(b)２0.kiｔｔyissucｈ＿___＿___hｏneｓtsｔudentthaｔsheneｖerteｌlｓａlｉeatanytimｅ.a.aｂ．anｃ．thed./(ｂ）２1.theａpｅcmeeｔiｎgwasｈｅld______noｖemｂｅｒ,2０2３.a．onb．iｎc.ａｔd.for（d)2２.—＿_____＿_hasyouｒｅｎglishteaｃｈerｂeentoenglａnｄ？—threeｔｉmｅｓ.ａ.howｏｆtenb.hoｗｓooｎc.howlonｇｄ.howmａｎytimes（b)２3．nowａdaｙsｅventheｆlａtsiｎsｍalltownsarｅｍuｃｈ＿___＿＿__thaｎtheｙｕsedtobe．ａ.expeｎsiveb.moreexpｅｎsivec.mostｅxpeｎsived．tｈｅmostｅxｐeｎsive(c)２4.myfatherdiｄn’tgiveupsｍoｋiｎｇ___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