电大经济数学基础年月期末复习资料

经典word整理文档，仅参考，双击此处可删除页眉页脚。本资料属于网络整理，如有侵权，请联系删除，谢谢！2018年177第一部分单项选择（1—5题）、填空（2—10题）.（每小题3分，共52题考10题）第1、6小题试卷知识点范围第一编微分学第1章函数（重点考试类型四个，共9题）xyf(x)D.f(x)x21,g(x)x1ln,()2lnf(x)sin2xf(x)(x),g(x)yxx2gxxxgx,()12x11f(x)sinxcosx122D1()fxf(x)f(x)0③lnf(x)0）f(x)0①②f(x)1(,4)ln(x,44,yA））4x220x2xx）选A4x0x4x2,5x0f(x)5,2x22x5,25x00x25x2即x32322xxf(x)。xx2320(01x2x1x24xxxxx1∴212fxf(x)求()1设f(x)(f(x）fx11xx2x2x11选C5.f(x)f111xff(x)xf(x)1xC(q)2qq50.C(q)C(50)C(50)802506()Cq3.65050q()求fx()fxf(xx22x6(x)x5f27x1txt1f(xft)x2x6t1t6t5()5fxx2222f(x)则f(x是偶函数对称y轴f(x)f(x)f(x)则f(x是奇函数对称坐标原点yxsinx22yx2xyxcosxyxx）yf(x)xxfsin8.Af(x)(x)sin(x)x(sinx)xsinxf(x)选Axx设f(x)y2()xfx10101010x9ffxx(x)y==()fx222第2、7小题试卷知识点范围第一编微分学第2章极限与导数微分（重点考试类型七个，共14题）1/10、x1xx0x1f(x)x0x1xxf(x)sinxxxxlim1limlim1110选A（sinxsinxxx0x0x0x01x1当x0xx2)x3xx11x00xx时∴选Dxxx0xx=1.xxsinxsinxlim101111lim1lim0∴（）x,是无穷小量；sinx是有界函数xxxxxxxxf(x)limf(x)0xx012、f(x)xx1()(,)fx在a2.1xax1x21lim(xxlimx1lim(x112fa∵在1∴flimf(x)2a2x1x1x1x1x1f(xx)f(x)若则lim）24x244x0f(xx)f(x)f(x)∵2选Alf(x)cosx42x0f(x)cos2(0)0.fx(0)cos2cos1则f(0)cos10f0yf(x)yy(x)(xx)y0001121211y.x12(3xx2(3112121113323yx1x11xx1y(0)012选A22221x）sincos)1xxyyyxx4y401211111x2yxx1y(4)xy(,)(4,2)242x24001yy(x)(xx)2(x4y40∴yyx4000()0正值，()单调递增；()0负值，()单调递增fxfxfxfx1,)-+）32XXx3,,在C33ln03303C33在0∴3yxxxxx(,)）x3xx25x2/10,D5x01110y5x105对D∴yx在x2323223203202yx3x2xx2令yx2xpEq(p)p()qpp32p32ppqpq(p)32pE(D)。p3232pppp121112()32022ppp1p选Dqppp2E()qppp()qp3232ppppppqpq(p)100e()ppEA.222ppppp1q(p)100e()100()50eepp选Apqp222()qp(50e2)Ep2q(p)2pp100e2第3、8小题试卷知识点范围第二编第1章不定积分、第2章定积分部分第3章积分应用（重点考试类型六个，共9题）121xsinx2cosx22cosx2cosx2cosx2211112xxxx2xxxyx：22222D222211xxxc：x2222选D22f(x)dxf(x)c2)df(x)f(x)c(f(x)dx)f(x)d(f(x)dx)f(x)dx若f(x)dx22xcf(x)2ln4x2x2x()fxdxf(x)dx22xc2ln4xfx()f(x)2ln4xx2x2x2()()()若fxdfx=fxdf(x)f(x)c()()()dfxfxcfxex1xdxdlnxxdxdx11d12db()2xx21f(x)dxF(x)cxf(1-x)dx=F1xc若222111f1x1xff1x1xdxf1x2xdxf1xdxdxd1x222222222222112fu)du1x2uf1xd1x=令22211(x)dxF(x)c∴∵ff(u)duFu)cf1xd1xF1xc22222(x)F)F(a)F(x)bbf是aa若F(x)f(x)是.bxx()()()fxFbFa()()()fxFxFaFxfbfa()()()()()fxFxbaaaa3/10xF(x是f(x)f(x)dxF(x)F(x)F(a)选Bxaa0f(x是奇函数af(x)dx2f(x)dx()a是偶函数fxa0220xxexex．xsinx．1dx．1d(cosx．2xxx322112222x2(x)22xxxxf(x)则f(x)f(x)f(x在是奇函数B2220选B1(xx2111xxdxcos111cosxxdxxx故cosxcosxxdxcos0dxx111111x1(21cos12xxdx111bbb()fx()fx、、()fxdxlimf(x)dxaaaba111dx.x32211111022x32x211111b1111lim((0=b：选C22bb22x3x22bb111）edxdxxx2xx1113111当a1时1当a1时选Bxa第4、9小题试卷知识点范围线性代数第2章矩阵（重点考试类型四个共10题）xaxa111stACmn设为A为B则C．mtns．．sn．tmC为nsC为sn选DAB；CBTTTnstB.A，BA，BA则Bnn②A，B则nmABAAT则AaaAijjiABBAA与B）A若A，B=BAA若B=CAOB=C若AOBOO，a选CCaijji123设=1A.25130aa2311A.aaa3223,B(AB)A2ABBABBA设An2224/10A()BAB222(AB)A2ABB即222A、BAA()ABBATTTTTBA为B1AB(A)A(AB)BA11111设A，B）若OAOBO或若OAO或BO()0(B)0(AB)0(AB)AB111BAABABAB111即111选D设AA1.B()I1ABAIBIAAAIAIB选C11B.TBATTTABT11ABTBA11ABTT11TBA选DTTT1204I）T=22431012110204130202T04）=T4222014342111202。1342(2)11132111111A31()2rA023023201134023000第5、10小题试卷知识点范围线性代数第3章线性方程组矩阵（重点考试类型五个，共11题）x2x4x1）123xx023x2311xxx1x71x111x22x0x22222x2x2x2x23333x2x4x1123xx0(2)2（2x20x2x2x2代入方程（3）由方程（3x将2332223x23x224(2)1x11x2选C得x112x23O则An))()秩A时..秩()秩(A秩(A).b则秩()秩(A时5/10bO）AXbr()r()n)则AX0r()n选Cxx0120=.xx0121111rAn()2()110rA1A201AXOA为50r(A)3.r(A)3。A是5r()min5(mn)AX0mnr()r(A)n0AmnrA()AXOn个nn111A（B.26011130130A12221032602(A)r(A)r()2r(A)1303选Br111xA1=）11x02111111r(A)1()()选DrArAr()22110001123x2xx(x,x为自由未知量）0A=0102134x2x23400004x2xx11021(x,x为自由未知量）112334201022xx34A01022400000000nrOr()rn.AXnn1(A)r=nr(A)nrr13214AXb011B）260112602241321413214011260112613214()()24rArAnA2(1)320112600112601126422000002241202241200000=nr(A)422选B第二部分微积分计算（11、12题每题10分共9题考2题）第11小题试卷知识点范围微积分第2章导数微分（重点考试类型三个，共5题）设2xx,求y2cos2sincos2sinsin22cosxx222yx2x2x2x222xxxxxx6/102sinxy设2x2sin2sinsin22lnsincosxxx2222yx2x2x22x2x2x2222xxxxxxx1x)求y,1x1011011lnxxx1ln1ln111ln1xxxxxxy21x1x1x2111011ln1lnx1ln0x11ln001x1xy010101x2102111x2yx，求xsincosxxecosxxyxxexxeexxxxxx()1221xsinxxe(x)x1x1)∴yex(22x2x2x设yxe2x，求112x121212lnln2xe2xye2xe2xexxxxx22x1ydxln12edx∴dy2xx2x第12小题试卷知识点范围第二编积分学第2章定积分、第2章定积分部分第3章积分应用（重点考试类型三个，共4题）1.x1lnxlnx)1dx1ln)1dln)21ln122原式c（cx2xxxln2)eex2.x0111152ln2ln22ln2ln211111ede12211211942解eeeeee022xxxxxxx22220000ex111111dx0xdx2e212e2xxdeeeeee=x222=eln1lnxxxxx222x2111111121111111exee2e1eee1=222222222222241cosxdx.x2020cosxdxxdsinxxsinxsinxdx011=x=cos0=20sin0sin0cosxcos222222222000第三部分线性代数计算（13、14题每题15分。共10题考2题）第13小题试卷知识点范围线性代数第2章矩阵（重点考试类型2个，共5题）151(AI)B.13617/10解答：15102525103701251012112510AIAI:I2112111236013712111075757512AI12222AI1B01320132323211113(I)1115120131200010131003120001202501IA105105010IA:I1050101201200010131000131006512000122104223411001065()533IA12301211322323∴0121100121101052321101310000111123111B012A02201153101111BAI:123532(1)0242014201012204224331=11011111252225024522012221212BA=，=XAB3523XAA1BA11A1XBA11210121012100131052A:I=232(2235010131013112521052∴A13∴XBA1==11233121221求X1100135ABIXAB1XABA111A1A:I=2223212210010212010054231122110032322∴21100101001211100105301213500100211001211013101542∴XAB1=542263215A5321721121103第14小题试卷知识点范围线性代数第3章线性方程组（重点考试类型二个，共5题）xx2xx0求齐次线性方程组.1234x3x2x01342xx5x3x0123410321121112(A)2n4rA10320111011122323221530110000x13x2x34（，xxxxx342348/10x3x2x012325300.xxx1233x8xx012313213210122231A2530101150时()3n当333238016005xx∴方程组有非零解，须50，5xxx13即（xxx123323xxx2124x2xxx3.12342x3xx5x512341101221101211012322(011001131A12113011012315501131x1x210111101011311011131x（x3332011030110x301102x00003000010000104xxx2124x2xx4x3.12342x3xx5x212341101221101211101221012132(32AA:b12143011301132011310113123152011320000x1x2xr()2r()13430，3（x,xx1x3x43234xx2，ab12x2xx01232xxaxb1231102110210142A12100112201132221a01ab001b6aa11014a10b60时即时r(A)2r()3r()r(A)112b6A0000非零a11014a10b60时时b6A0r(A)2r()2r(A)r(A)n31100001014a10a1(A)3r()3r(A)r(A)n3即时0112rA00非零非零第四部分微积分的应用（第15题本题20分）第15小题试卷知识点范围第二编积分学第3章积分应用（重点考试类型四个，共6题考1题）()43Cqq，.qC(q)2q2q182q318(q)C(q)dqC(4qdqC2qqC2qqC(q)qq）C22000qqq00