2015年电大专科《微积分初步》期末复习题资料参考小抄

电大微积分初步期末复习题资料参考小抄1、填空题（1）函数的定义域是2LN1XF答案且2X3（2）函数的定义域是24LXXF答案2,1,（3）函数，则74XXFXF答案32（4）若函数在处连续，则0,1SINXKXFK答案1K（5）函数，则XXF2F答案2（6）函数的间断点是13XY答案（7）XSINLM答案1（8）若，则2SI4L0KXX答案（9）曲线在点的切斜率是1F,答案21（10）曲线在点的切线方程是XFE,0答案Y（11）已知，则XF3F答案LN227（F1（12）已知，则XFLNF答案，121X（13）若，则XFE0F答案X20F（14）函数的单调增加区间是YX312答案,1（15）函数在区间内单调增加，则应满足2AXF,0A答案0（16）若的一个原函数为，则F2LNXF答案X2（17）若，则CXF2SIDXF答案COS（18）若_答案XSIN（19）2DE答案CX2（20）SIN答案X（21）若，则CXFFDXFD32答案321（22）若，则CXFXF12答案F122（23）_DCOSIN12XX答案3（24）E12LDXX答案0（25）XDE02答案126已知曲线在任意点处切线的斜率为，且曲线过，则该曲线的方程是XFYX15,4答案1227由定积分的几何意义知，XAD02答案42A28微分方程的特解为10,Y答案XYE29微分方程的通解为3Y答案XCYE30微分方程的阶数为XYSIN473答案42单项选择题（1）设函数，则该函数是（）2EXYA奇函数B偶函数C非奇非偶函数D既奇又偶函数答案B（2）下列函数中为奇函数是（）ABCDXSIN2EX1LN2X2X答案C（3）函数的定义域为（）5LN4XYABC且D且5X0X5X4答案D（4）设，则（）12XFXFABX2CD21X答案C（5）当（）时，函数在处连续K0,2XKEXFXA0B1CD3答案D（6）当（）时，函数，在处连续K0,12XKXFA0B1CD答案B（7）函数的间断点是（）232XFAB,1X3XCD无间断点答案A（8）若，则（）XXFCOSE0FA2B1C1D2答案C（9）设，则（）YXLGDYABCD2XLN10LN10XD1DX答案B（10）设是可微函数，则（）XFY2COSFABD2COSXD2INCDXFINFSC答案D（11）若，其中是常数，则（）3SIAXFXFABCD2COX6SINSINXCOS答案C（1）函数在区间是（）21XY,A单调增加B单调减少C先增后减D先减后增答案D（12）满足方程的点一定是函数的（）0XFXFYA极值点B最值点C驻点D间断点答案C（13）下列结论中（）不正确A在处连续，则一定在处可微XF00XB在处不连续，则一定在处不可导C可导函数的极值点一定发生在其驻点上D函数的极值点可能发生在不可导点上答案（14）下列函数在指定区间上单调增加的是（）,ABCDXSINXE2XX3答案B（15）下列等式成立的是（）ABDXFFDXFFCD答案C（16）以下等式成立的是（）AB1DLNXCOSDSINXXCD3LX答案D（17）（）XFDABCXCXFCDF211答案A（18）下列定积分中积分值为0的是（）ABXXD2E1XXD2E1CDCOS3SIN答案A（19）设是连续的奇函数，则定积分（）XFAXFDA0BCD0DAXFAXF0D0D2AXF答案A（20）下列无穷积分收敛的是（）AB0DINXS1DXCD102EX答案D21微分方程的通解为（）0YABCDCXXYY0Y答案C22下列微分方程中为可分离变量方程的是（）A；B；YXDYXDC；DSIN答案B3、计算题（1）423LIM2X解412LIM1LILI22XXXX（2）39LI23X解23461LI3LILIM323XXXX（3）4586LI24X解321LIM2LILI4424XXXX（4）设，求XY1EY解222XX1EX（5）设，求Y3COS4SINY解SINCO34S2XXY2（6）设，求XYE1Y解2X（7）设，求XYCOSLNY解I123XXTAN231（8）D10解CXXX1102D2（9）DSIN2解CXX1OSDSIN1I210E4LN0解ED422LN022LXXXX3152631E4LN011XDLN51E解271360LN510LN51L51L12E1EEXXD12XD0解1EDE0101XXX1320DSINX解1SINDCOCSI202020XX4、应用题（1）欲做一个底为正方形，容积为108立方米的长方体开口容器，怎样做法用料最省解设底边的边长为，高为，用材料为，由已知XHY22108,XHXXY431084222令，解得是唯一驻点，0432X6且，63XY说明是函数的极小值点，所以当，用料最省X6X31082H（2）用钢板焊接一个容积为4的正方形的水箱，已知钢板每平方米10元，焊接费40元，问水箱的尺寸如何3M选择，可使总费最低最低总费是多少解设水箱的底边长为，高为，表面积为，且有XHS24X所以,16422XS2令，得，0X因为本问题存在最小值，且函数的驻点唯一，所以，当时水箱的面积最小1,2HX此时的费用为（元）16042S请您删除一下内容，O_O谢谢2015年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄MANYPEOPLEHAVETHESAMEMIXEDFEELINGSWHENPLANNINGATRIPDURINGGOLDENWEEKWITHHEAPSOFTIME,THESEVENDAYCHINESE请您删除一下内容，O_O谢谢NATIONALDAYHOLIDAYCOULDBETHEBESTOCCASIONTOENJOYADESTINATIONHOWEVER,ITCANALSOBETHEEASIESTWAYTORUINHOWYOUFEELABOUTAPLACEANDYOUMAYBECOMEMOREFATIGUEDAFTERTHEHOLIDAY,DUETOBATTLINGTHELARGECROWDSDURINGPEAKSEASON,ADREAMABOUTAPLACECANTURNTONIGHTMAREWITHOUTCAREFULPLANNING,ESPECIALLYIFYOUTRAVELWITHCHILDRENANDOLDERPEOPLEASMOSTCHINESEPEOPLEWILLTAKETHEHOLIDAYTOVISITDOMESTICTOURISTDESTINATIONS,CROWDSANDBUSYTRAFFICAREINEVITABLEATMOSTPLACESALSOTOBEEXPECTEDAREINCREASINGTRANSPORTANDACCOMMODATIONPRICES,WITHTHEPOSSIBILITYTHATTHEREWILLBENOROOMSAVAILABLEITISALSOCOMMONTHATYOULLWAITINTHELINEFORONEHOURTOGETATICKET,ANDANOTHERTWOHOURSATTHESITE,TOONLYSEEATINYBITOFTHEPLACEDUETOTHECROWDSLASTYEAR,428MILLIONTOURISTSTRAVELEDINCHINAOVERTHEWEEKLONGHOLIDAYINOCTOBERTRAVELINGDURINGTHISPERIODISAMATTERTHATNEEDSTHOROUGHPREPARATIONIFYOUARESHORTONTIMETOPLANTHEUPCOMING“GOLDENWEEK“ITMAYNOTBEABADIDEATOAVOIDSOMEOFTHEMOSTCROWDEDPLACESFORNOWTHEREISALWAYSAPLACESOFASCINATINGTHATEVERYONEYEARNSFORARXANISAPLACELIKETHISTHEBEAUTYOFARXANISEVERLASTINGREGARDLESSOFTHECHANGINGOFFOURSEASONSBESTOWEDBYNATURE,ITSSPECTACULARSEASONALLANDSCAPEANDMOUNTAINSAREJUSTBEYONDWORDARXANISACRUCIALDESTINATIONFORTHERECOMMENDEDTRAVELLINGROUTE,“CHINAINNERMONGOLIAARXANHAILARMANZHOULI“ITISALSOTHEJOINTOFTHEFOURPRAIRIESACROSSTHESINOMONGOLIANBORDER,WHEREPEOPLEGRAVITATETOWARDSTHEEXOTICATMOSPHEREMIXEDWITHCHINESE,RUSSIAN,ANDMONGOLIAELEMENTSASAHISTORICSITEFORTHEYITIANBATTLE,ARXANSTILLEMBODIESTHESPIRITOFGENGHISKHANWALKINGINTOARXAN,YOUWILLBEAMAZEDBYAKALEIDOSCOPEOFGORGEOUSCOLORSALLTHEYEARROUNDTHESPRINGAZALEASBLOOMINGREDINTHESNOW,THESUMMERSEAWAVERINGBLUEINTHEBREEZE,THEAUTUMNLEAVESPAINTEDINYELLOWCOVERINGVOLCANICTRACES,ANDTHEWINTERWOODSSHININGWHITEONTHEVASTALPINESNOWSCAPEHINGGANLEAGUEARXANCITYISSITUATEDINTHEFAREASTERNAREAOFINNERMONGOLIAAUTONOMOUSREGIONITSFULLNAME“HARENARXAN“MEANS“HOTHOLYWATER“INTHEMONGOLIANLANGUAGEARXANISATOURISMCITYINTHENORTHERNFRONTIERWITHABLENDOFLARGEFOREST,GRANDPRAIRIES,VASTSNOWFIELD,HEAVENLAKECLUSTER,THERMIUM,ASWELLASVOLCANICCLUSTERITISARAREANDUNIQUEECOTOURISMBASEFILLEDWITHHEALTHYSUNSHINE,CLEANAIRANDUNSPOILEDGREENNESTLEDCLOSETOTHECOUNTRYSLARGESTVIRGINFOREST,ANDKNOWNFORITSSPRINGANDECOLOGICALENVIRONMENT,ARXANISMARVELEDATBYMANYTOURISTSASTHEPURESTLANDONEARTHYOUCANNOTMISSOUTTHEAUTUMNOFARXANITISDEFINITELYTHEBESTWITHBRIGHTLYCOLOREDSCENERYFULLOFEMOTIONSAUTUMNINTHENORTHERNPARTOFTHECOUNTRYCOMESEARLIERTHANTHESOUTHASEPTEMBERRAINFOLLOWEDBYTHEFOOTPRINTSOFAUTUMNBRINGSMORECOLORSTOTHEONCEEMERALDGREENMOUNTAINANDBLOOMINGGRASSLANDSHUTTERBUGSFLOCKTOSEEFORTHEMSELVESTHEMARVELOFSPLENDIDCOLORSAROUNDTHEMOUNTAINSANDWATERS,MANYOFWHOMHAVETRAVELALONGDISTANCEANDEVENCAMPHEREONLYTOCAPTUREAMOMENTOFTHENATUREWONDERTHESILVERBIRCHTURNSGOLDEN,W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