2015年电大高等数学期末考试复习试题资料

电大高等数学期末复习资料参考小抄1、求函数的定义域1）含有平方根的被开方数0，2）含分式的分母0含对数的真数0例1函数的定义域是1LN92XY2、函数的对应规律例设求2134,FXXF解由于中的表达式是X1，可将等式右端表示为X1的形式22122XFXF或令43112FTTTFTXT则3、判断两个函数是否相同定义域相同及对应规律相同例1、下列各函数对中，（B）中的两个函数相同A、B、2,YX21,XYC、D、2LN,L22SINCO,1XY4、判断函数的奇偶性若，则为偶函数；若，则为奇函数，FXFFFXFFX也可以根据一些已知的函数的奇偶性，再利用“奇函数奇函数、奇函数偶函数仍为奇函数；偶函数偶函数、偶函数偶函数、奇函数奇函数仍为偶函数”的性质来判断。奇函数的图像关于原点对称，偶函数的图像关于Y轴对称。例下列函数中，（A）是偶函数AB3SINFX31FXCDXACOS5、无穷小量极限为零的变量。性质无穷小量和有界变量的积仍是无穷小量例1）当时，下列变量为无穷小量的是（B）0A、COSXB、LN1XC、X1D、XE2）00LIMSNX6、函数在一点处极限存在的充要条件是左右极限存在且相等D0LIXA、1B、1C、1D、不存在7、极限的计算对于“”形01SIN20XL）利用重要极限约去零因子后再计算2301LN92XX且例1）2111000XLINXLINXLINXX2）3SILMSIL121XXSIN3LI1XX1SINLM3LI1XX48、导数的几何意义；处的切线的斜率在点表示曲线00FYF,00XFYXY处的切线方程在点（曲线例曲线在处的切线斜率是1XF2,解21F12,XY故切线方程为9、导数的计算复合函数求导原则由外向内，犹如剥笋，层层求导例1）设，求SINLXYY解2COI2例2）设，求DYSXYE解21INXDD10、判断函数的单调性的区间。系式的区间为单调递增函数单调递增，满足关0Y的区间。系式的区间为单调递减函数单调递减，满足关例函数的单调减少区间是12XY），故单调减少区间是（10211、应用题的解题步骤1）根据题意建立函数关系式，2）求出驻点（一阶导数0的点），3）根据题意直接回答例1）求曲线上的点，使其到点的距离最短XY20,2A解曲线上的点到点的距离公式为2,2YXD与在同一点取到最小值，为计算方便求的最小值点，将代入得22DXY2X2令2D令得可以验证是的最小值点，并由此解出，即曲线上的点01X1X2D2YXY2和点到点的距离最短2,12,0,A2）某制罐厂要生产一种体积为V的无盖圆柱形容器，问容器的底半径与高各为多少时用料最省解设容器的底半径为，高为，则其表面积为RHS2因为VHR22R所以RS22V由，得唯一驻点，此时，由实际问题可知，当底半径和高时可使0S3R3H3VR3H用料最省12、不定积分与原函数的关系设，则称函数是的原函数,FXFFXFCXFDF例1）若的一个原函数为，则（B）1A、B、C、D、LNX32X21X解321FF2）已知，则（答案C）SINXFDCFABCDSINXOSXCOSX解FXXFCOSI13、性质,FDXDFC例1）（B）XX32ABCDF32F1XF31XF例2）CDTANTANX14、不定积分的计算1）凑微分；2）分部积分1）常用凑微分,1,LN1,1,12XDXDXXDB2XDXCOSSICOS,E例1）若，则（B）CFFXFDABCDCXFCXF2CXF2CXF1解DFDF1例2）计算XE2解1D21XXCX1E例3计算LNSI解CXXDDXOSLNLI2）分部积分的常见类型XDDVXDXEENXNCOSCOSSINI的形式。凑成、把，再根据分部积分公式计算的形式凑成把VXDXNLUU例1）计算E解CEXDEXEXDXXXX例2）计算不定积分3COS解CXXDXXXXD3OS1SIN3SIN3I1SIN113COS例3）计算DDL1LLLNLNCXXXX1115、定积分的牛顿莱布尼兹公式设F（X）是FX的一个原函数，则XFDFBAABAF例若是的一个原函数，则下列等式成立的是（B）FXFABADXXAFDFXCDBFBBBA16、奇偶函数在对称区间上的积分若是奇函数，则有FX0AFXD若是偶函数，则有022AAAFXDFXD例112DX分析为奇函数，所以021X12XD例2）1D分析为偶函数故X112100|XX17、定积分的计算1）凑微分，2）分部积分；定积分的凑微分和不定积分的计算相同。例1）计算12XED解利用凑微分法，得21X11122|XXEDE例2）计算定积分21解利用凑微分法，得DX222111|XXEEE定积分的分部积分与不定积分的计算基本相同定积分的分部积分公式BABAVDUUDV例1）计算120XE解012101221201022XXXXXXEDEEDDD34E例2）计算21LNEXD解EXEDXXEE211LNLL2例3）计算20COSXD解210COS412SIN02SIN12SIN121202020XXDXXDX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AFTEREARNINGHISSPURSINTHEKITCHENSOFTHEWESTIN,THESHERATON,SENSONTHEBUND,ANDASPRINKLINGOFOTHERTOPNOTCHVENUES,SIMPSONLUFINALLYGOTTHECHANCETOBECOMEHISOWNBOSSINNOVEMBER2010SORTOFTHESHANGHAIBORNCHEFMIGHTNOTACTUALLYOWNCALIFORNIAPIZZAKITCHENCPKBUTHEISINSOLECHARGEOFBOTHKITCHENANDFRONTOFHOUSEATTHISSINANMANSIONSSTALWART“ITSCERTAINLYARESPONSIBILITYTOBETHEHEADCHEF,ANDTHENTOHAVETOMANAGETHERESTOFTHERESTAURANTASWELL,“THE31YEAROLDTELLSENJOYSHANGHAI“INHOTELS,FOREXAMPLE,THESEJOBSARESTRICTLYDEMARCATED,SOITSAGREATOPPORTUNITYTOLEARNHOWABUSINESSOPERATESACROSSTHEBOARD“ITWASATASKTHATMANAGEMENTBACKINSUNNYCALIFORNIAEVIDENTLYFELTHEWASREADYFOR,ANDAVOTEOFCONFIDENCEFROMACOMPANYTHAT,TODATE,HASOPENED250OUTLETSIN11COUNTRIESANDFORADDEDPRESSURE,THESHANGHAIBRANCHWASALSOCPKSCHINADEBUT“FORSUREITWASABIGSTEP,ANDUNLIKEALLTHEIROTHERASIAOPERATIONSTHATAREFRANCHISES,THEYDECIDEDTOMANAGEITDIRECTLYTOBEGINWITH,“SAYSSIMPSONTWOYEARSAGOAPRIVATEFRANCHISEETOOKOVERTHELEASE,BUTTHELINKSTOCPKHEADQUARTERSARESTILLSTRONG,WITHAMAINLANDBASEDBRANDAMBASSADORONHANDTOENSURETHEBUSINESSADHERESTOITSETHOSOFCREATING“INNOVATIVE,HEARTHBAKEDPIZZAS“,ASLICEOFPRBLURBTHATSIMPSONINSISTSLIVESUPTOTHEHYPE“THEYAREVERYINNOVATIVE,“HESAYS“THEPROBLEMWITHMOSTFASTFOODPLACESISTHATTHEYUSETHESAMESAUCEONEVERYPIZZAANDJUSTCHANGETHETOPPINGSEVERYONEOFOUR16PIZZASAUCESISAUNIQUERECIPETHATHASBEENFORMULATEDTOCOMPLEMENTTHETOPPINGSPERFECTLY“THELARGELYLOCALCUSTOMERBASEEVIDENTLYAGREESANDONSATURDAYANDSUNDAY,ATLEAST,THEPLACEISTEEMINGTHEKIDSEATFORFREEPOLICYATWEEKENDSISUNDOUBTEDLYABIGDRAW,ASWELLASISTHESPACIOUSSECONDFLOORLAYOUTOVERLOOKEDBYACANOPYOFGREENFROMFUXINGPARKOVERTHEROADTHECOMPANYISALSOFOCUSINGONINCREASINGBRANDRECOGNITIONANDINRECENTYEARSHASTAKENPARTINOUTSIDEEVENTSSUCHASTHEREGULARCALIFORNIAWEEKSTILL,THESTAAREHONESTENOUGHTOADMITTHATBUSINESSCOULDBEBETTERASGOOD,INFACT,ASINCPKSSECONDOUTLETINTHEPOPULARKERRYPARKSIDESHOPPINGMALLINPUDONG“SINANMANSIONSHASREALLYSTRUGGLEDTOGETTHENUMBEROFVISITORSTHATWEREENVISAGEDWHENITFIRSTOPENED,ANDITHASNTBEENEASYFORANYOFTHETENANTSHERE,“ADDSSIMPSON“WEREPLANNINGATHIRDOUTLETINTHECITYIN2015,ANDWEWILLPROBABLYCHOOSEASHOPPINGMALLAGAINBECAUSEOFTHEBETTERFOOTTRAFFIC“THETEAROOMSONCEFREQUENTEDBYCOCOCHANELANDMARCELPROUSTAREUPPINGSTICKSANDCOMINGTOSHANGHAI,XUJUNQIANVISITSTHEPARISIANOUTPOSTWITHSWEETTREATSONETHINGTHECENTURYOLDPARISIANTEAROOMANGELINAHASSHOWNISTHATLEGENDARYFASHIONDESIGNERCOCOCHANELNOTONLYHADSTYLEANDGLAMORBUTALSOBOASTEDGREATTASTEINFOOD,PASTRIESINPARTICULARONEOFTHEMOSTPOPULARTEAROOMSINPARIS,ANGELINAISFAMOUSFORHAVINGONCEBEENFREQUENTEDBYCELEBRITIESSUCHASCHANELANDWRITERMARCELPROUSTNOWANGELINAHASPACKEDUPITSFRENCHAMBIENCE,EFFICIENTSERVICE,ANDBEAUTIFUL,COMFORTINGDESSERTSANDFLOWNTHEMTOSHANGHAIATTHEFLAGSHIPDINEINANDTAKEOUTSPACEINSHANGHAI,EVERYTHINGMIMICSTHEORIGINALTEAROOMDESIGNEDFROMTHEBEGINNINGOFTHE20THCENTURY,INPARIS,THEHEIGHTOF“BELLEEPOQUE“THEPAINTINGSONTHEWALL,FOREXAMPLE,AREEXACTLYTHESAMEASTHEO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