电大高等数学基础形成性考核手册答案7

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！高等数学基础形考作业1答案：第1章函数第2章极限与连续（一）单项选择题2ff(x)(x)g(x)x，f(x)x2，g(x)x1x1()x，gx2(x)lnxg(x)3lnxf(x)x1，3f(x)(,)f(x)f(x)轴xy轴yxyx2)yxcosxaaxxyyx)2yx1yx1,x0yx2y1,x0x2lim1limx)0x22xx0x0x01xxxxx0x1xxxx1xf(x)xf(x)x00limf(x)f(x)f(x)x00xx0f(x)f(x)f(x)f(x)0xxxxxx1/14（二）填空题x29x)．f(x)x3-x．f(x)f(xxx211)e⒊．x22xx1x),x0(x)x0kfxe．,x0xkx1,x0x0．ysinx,x0xx时的无穷小量fxAf(x)Axx()。00xx0（三）计算题e,0xxf(x)x,x0f(2),f,f．，22f00f11e，f2x1yx2x10x2x11yxx或02xx00x12x|xxRDAROhEBC2/14Rh222222Rh22hS2R2RhhRRh故222223x．2xx0sin3xsin3x3x2x31333xsin2x3xsin2xlimsin3xlimlim＝sin2x2122x0x0x02x2xx21lim．sin(xx1x21(xxxx111x2x1x1x1x1x13x．xx03x3x13x113133xxx3xx1x0x0x01x12lim．sinxx01x1(1x1xx2222x(1xx(1xxx0x02x02x0limsinx0111x0(1x1)2xlim(x1)．xx3x1111))]xxx1lim(x1)xlim(x3)xlimlime4e1x3xx31e3x1)xxxx)]33xxx3xx226x8lim．5x4x4x4x1x26x8x25x44x2x2422xlimlimlimx1413x4x4x43/14(2),x12xf(x)x,1x1x1x1,f(x)xx1）limfxlimx1xxlimfxlimx1110xxfx在x1limfxlimfxxx）limfxlimx212122xxlimfxlimx1xf11x在x1即limfxlimfxf1fxxx1fxx高等数学基础作业2答案：第3章导数与微分f(x)（一）单项选择题f(x)f(0)0xxx0x0(0)f(0)f()0fxf(x2h)f(x)f(x)x在0002hh02f(x)f(x)002f(x)f(x)00fx)fxf(x)exx0112eeee244/14f(x)x(xx2)L(x99)f(0)999999!99!若f若f(x)(x)若xxf(x)f(x)xx0000若xxxx0000（二）填空题1sin,x02x(x)f(0)．fx0,x0df(lnx)dxf(e)e22lnx5。xxxxxf(x)x12)在k1。2π(,1)y1。f(x)x在2x2y2xlnx)y2xx1yyxx。x（三）计算题y：⑴y(xxx3231xeyxxexx33(xexex:xx22⑵ycotxxlnx22csc22lnxxxxxxx2yxx2⑶yxlnx5/142xxxx2xlnxx2yxlnx22cosx2xy⑷x3cosx2xcosx2xxx(sin2ln2)2)xxxx3x3y2x4x3lnxx2⑸ysinx1(2))xx2xxxlnxxsinxlnxxsinx22xysinxx22⑹yxsinxlnx4sinxyx44xxcoslnxxxxx3xsinxx2⑺y3xsinxx3sinxx3x3(cos2)(sinln3xxxx22x2xxy232x3x⑻yetanxlnxxex1yexxexxtanxxxecosxx2：yyex⑴1211yeexexxx22xylncosx⑵1sinxysinxtanxcosxcos⑶yxxx6/14771yx8x88x⑷2yy2sinxsinx2sinxcosx2sin2xx2⑸yycosx2x2xcosx2ycosex2⑹yexeex22222xx⑺ysinxcosnxnnnxnxxnxnxnxsincoscossinsin()nn1yxysinx⑻5ln55cos5sinxsinxyxxyex⑼excosxcosxyyy(x)y：⑴ycosxe2yyxcossin22yxyxeyyyx2e2y⑵yyx1yyy..yyyxxsinylnx)x22xsinyx⑶y2yxxy2yx2sinyy2xy2ysiny2xycosyx22x2xcos.y2sinyy(2xcosy)y2y2y222⑷yxy7/14yy1yyyy1lnxey⑸2y1x1ey2yy(2yey)x⑹y21esinyxexsiny2ecos.ysineyxx2yecosyxeey⑺3yxex33eyeyyy2y2yxey⑻y52xy5xln55ln52ln2yyyxy12ln2ydydyydx）⑴ycotxcscx1xycscxxx(csccot)2xx22x⑵yx11xxxxxxx2xxysin2xyx⑶22sinxcosxdy2sinxcosxdxyyex⑹yseceedysecseceedxeexdxx22233xxxx8/14yx⑴111113232yxyxx22224y3x⑵3ln3ln33xxln333x2yyylnx⑶11yyxx2yxsinx⑷sincoscoscossin2cossinyxxxyxxxxxxx（四）证明题设f(x)f(x)f(x)f(x)()(()()()fxfxfxfx()fx高等数学基础形考作业3答案：第4章导数的应用（一）单项选择题fb)f(a)baf(x)），则存在(a,b)()f．在(a,b)在(a,b)在(a,b)在[a,b](a,b)f(x)x4x12D(,(1,(2,)(2,)(6,6)Ayx4x529/14f(x)f(x)0f(x)Cf(x)(a,b)在x(a,b)0f(x)Cf(x)x在0()0,()0fx()0,()0fxfxfx0000()0,()0fx()0,()0fxfxfx0000f(x)(a,b)f(x)0,f(x)0f(x)A在（二）填空题f(x)(a,b)在x(a,b)0xx时f(x)0xxf(x)0时x是000f(x)的(x)x是xf(x)f(x)f．000yx2)(,0)．(x)ex2(0,)ff(x)[a,b]在f(x)0f(x)[a,b]f(a)．在0,2f(x)25x3x3（三）计算题y(x1)(x5)25(2(yx2xxxxxx5(X15y+0—0+yf320f010/14yx22x3[0,220驻点）xyx））+—y22yx2x3x122f3f6f2f12最大值最小值f6f22x(2,y2设p(x,y是y2上的点2d为p到Ad(x2)y(x2)2xx12222(x2y2x1令d02(x2)2x(x2x22y2上点2)或-2(2。。L()，则体积VRhLhh2223：[(2)3]0令VhhLhLh][LhhL22223232RL当h,RL时其体积最大。333V，则体积VRh2RhR22VR2SR表面积11/14VRR3Vh3V：2令SVRR023VVRh33M62.562.5x2hhx2Sx4x22x2令Sx0xx53x2（四）证明题x0xx)．x上对函数fxln应用拉格朗日定理，有1ln1xln1x111x,故1xx)x0ex1x．设f(x)e(xx()x10fxe当时fx当,(0x）xff(x)e(xx高等数学基础形考作业4答案：第5章不定积分第6章定积分及其应用（一）单项选择题1f(x)f(x)x1lnxx212xx312/14Afxxfxfxd()()fx()d()df(x)dxf(x)df(x)dxf(x)dxf(x)xf(xxxcxccosxccosxcd23⒋xf(x)dxdxf(x)xf(x)323113(x)f(x3)f31(x)dxF(x)cff(x)dxxF(x)c2F(x)c1F(2x)c()Fxcx1dxexdxx1011dxdxx2x11（二）填空题f(x)f(xdx。F与(x)G(x)F(x)G(x)F(x)G(x)c。与dedx2。ex⒊⒋x(tanx)dxxc。(x)dxcos3xcf(x)9x)。f13xx3)d⒍5231xp1。x1p13/14（三）计算题cos1111xdxcosd()sinc⒈⒉⒊⒋⒌⒍x2xxxexx1dx2edx2ecxx1dxdx)x)cxxx11111xsin2dxxdc