高等数学基础 国家开放大学答案

1第1章第2章(x)(x)2g(x)x，()fx2g(x)xx，fx12(x)lnx3，g(x)3lnxf(x)x1g(x)，fx1(x)(,)f(x)f(x)fy轴y轴xxx)yxxy2aaxxx)yy2x1x2yxyy1,x0y1,x0x21limx)0x22sinxxx01lim0limxsin0xxxx0sinxx1xx1xsinln(xx(x)f(x)xfx00limf(x)f(x)f(x)x00xx0limf(x)f(x)limf(x)limf(x)0xxxxxx000x29x3f(x)x)．(xx2xf(x)f1⒊．)．x2xx1x),x0(x)0kfxx．,x0xkx1,x0y．sinx,x0xx0limf(x)Axx0f(x)Ae,x0xf(x)x,x0(2),f,ff．2x1lgyxRsin3xlim．sin2xx0x12．xx1tan3xlim．xx01x12．xx0lim(x1)．xx3xxx226x85x4．x4(2)2,x1xf(x)x,1x1x1x1,(x)f《高等数学基础》第二次作业第3章f(x)f(x)f(0)0limlim（xxx0x0(0)f(0)0f()fxf(x2h)f(x)f(x)在x（002hf(x)0h02f(x)002f(x)f(x)00fx)fx(x)elim（fxx02e1e1ee24(x)x(xx(x99)f(0)（f9999!9999!(x)(x)(x)(x)若f若f若f若fxx00xx00xx00xx001sin,x0x2(x)f(0)fx．0,x0dfx)dxf(e)e2xxx(x)x1,2)在ffπ(x)x(,1)在4xy2xyyxlnxyy：(xx3)ex⑴y⑵ycotxxlnx2x2⑶y⑷yxx2xx3xxxxsinxlnx2⑸y⑹y4xx2⑺⑻yy3xetanxlnxx：yyye2x⑴lncosx3⑵⑶yxxx⑷⑸yy3xxcose2xye2x⑹⑺ysinxcosnxny5sinx2⑻⑼ye2sinxyxe2x2x⑽⑾yxeeexxyy(x)y：cosxe2y⑴y⑵yyxx2y2xy⑶xy⑷ylnxey⑸2y1esiny⑹y2xeey⑺3yx52⑻yxydy：cotxcscx⑴ylnx⑵ysinxarcsin1x1x⑶y1x⑷y31xsine⑸y⑹y2xtane3xxlnx⑴y⑵y⑶yxxarctanx32⑷yx(x)f(x)设f《高等数学基础》第三次作业第4章fb)f(a)ba(x)(a,b)f()f），则存在．在(a,b)在(a,b)在(a,b)在[a,b](a,b)(x)x4x1f2(,2)(2,)(1,(2,)x4x5(6,6)Ay2(x)f(x)0f(x)f(x)(a,b)在ab(,)f(x)f(x)在fx0x0()0,()0fx()0,()0fxfxfx0000()0,()0fx()0,()0fxfxfx0000(x)(a,b)f(x)0,f(x)0f(x)f在(x)(a,b)在ab，且当xx时(,)f(x)0，当xx时⒈设f内可导，x000()0fx()x是fx的0(x)f(x)()fxfxx是0．00x)y2．(x)e2fx(x)[a,b]在f(x)0f(x)[a,b]在f．f(x)25x3x3．y(x1)(x5)2x2x3在区间[0,y2axbxcxda,b,c,d(2,44)y32x2x1y22x(2,0)LVxx0xx)．0ex1．x《高等数学基础》第四次作业第5章不定积分第6章定积分及其应用1fx(x)()（fx112xx2xx3dAfxxfxd()()d()d()fxfxfxxfxfxxfx()d()()d()dx(x)xf(xxf（sinxcxccossinxccosxcd⒋x2f(x)dx3（dx1313(x3)x2f(x3)f(x)f(x)f31(x)dxF(x)c()dfxxfF(x)c[a,b]（x12F(x)cF(2x)cF(x)cxyf(x)yg(x)和xaxb和所[g(x)f(x)]dx[f(x)g(x)]dxaaf(x)g(x)x[()()]dbfxgxxbaa(x)f．(x)G(x)与F(x)G(x)与F．dedx⒊⒋x(tanx)x(x)dxcos3xcf(x)f13(sin)d⒍5xx231xx1p1cos111xdxcosd()sinc⒈⒉⒊x2xxxexdx2edx2ecxxx11xd(lnx)ln(lnx)cxlnxlnx1111sin2dxxcos2xcos2xdxxcos2xsin2xc⒋x22243lnx112exdeln)d(3ln)ln)⒌xxxe1x21112121141414⒍x101012xxede2e2xxe2xe2e2x10201x1e22e⒎xxxdeexdx21224111lnx1112eedlneexe1⒏xxx2xx12e111(x)[a,a]在a()d0fxx．fa(x)[a,a]在f(x)dx2f(x)dxaaf．a0(x)dx[f(x)f(xxafaa01第2章2fx1(x)(,)f(x)f(x)fy轴yxxy2aaxx)yy2