江苏省高校历届专科类数学竞赛试题汇总

第五届（2000年）专科类高等数学竞赛试题3d1(2)fx()fx．dxx1x)x0．．．x1．dxxx21(2)n6an1na．6nnn1[f(x)f(x)]sinxdx．a．a3e12x(x)fx(x1)0,1x1x0．．x．．1(x)x,g(x)xx0()fx是gx()f2xxk0f(x)lnxk)．3在e2．1．．0f(x)y2y4y0f(x)0f(x)0f(x)yx且00x（0x2y4z70,3x5y2z10xy11(z0(x2yz0．．．．x5yz0xy11(z0ln(1x)(axbx)dx28lima,b．x2x(lnx)2x0extt)dy26yy(x)．teyy102t0(x),g(x)[a,b](a,b)(a,b)x在6f()()()()0fxgxfxgx()(,)fx在abg(x)(x)asinxasin2xasinnxa,a,,a6f12n12n|f(x)|sinx||a2ana112nx(a,a)6ya22yx4x120F(x)(xt)ft)dt2fx．6xx220(21)8nx2n1.n01x1x(x)8f6xx1x5dx．x8(x)x0在g(x)8f13f(x)(xdxx(x8)f(x)．g231第六届（2002年）专科类高等数学竞赛试题5ln(1x)4．lim．1cos(1cosx)x0eexxlimx0c(c0)kc，．xk(x))在f．limf(x)0())fx在xlimf(x)0())fx在xlimf(x)1())fx在xdy2ln(1t),ytarctantx．dx2x(yx)1x()yyxyey．(arcsinxarccosxdx．．．1dx．x(1x)4111．xn．2nn1(x)[0,)在0ab8faf(xdxbf(xdx．ba00(x)kxsinx9f．k在1f(x)(,)0k1f(x)(,)在kx21．8e2x20442xyzxyz222:92xy2zk.k6kx1yz2118绕yy0,y2123222n29222．2123nn1(1)9knn(lnx)2kn2第七届（2004年）专科类高等数学竞赛试题5(x)x0,f(x)sinxcosx2x,f当22(x)f．0xsinxcosxcx与k2．当xc时，k为等价无穷小，则，．lim(sinx)2x2．．xnnnlimn．．n1n4nn2222(x)x2ln(1x)2(0)fnf．(n)e(1x)x．dx．(1xe)x2yzR1x．．n．(n1)2nn11(x)[a,b]在(a,b)内可导，f(a)af)f)1．()()ffxbba，222a(a,b)内至少有一点{(x,y)|yx4,yx,xy2,xy4}Dyx上D22xDyx4QPPyt于．22,Q||DyxP绕t(x)(,)在f(x)x0在x,xf有12f(xx)f(x)f(x)f(x)在(,)1212110)kk在x(1,0,1)Q(3,1,2)与x2yz12P|PM||MQ|M1xnn(32)nnn1第八届（2006年）专科类高等数学竞赛试题5222n1n2n2n．．n2n323231．(e2．xtx30x0lim(x3x2axb)0a，b．2x(x)(1xx)eff．2sinxdy2ln(1t),yarctantx．2dx2t11ln[(xa)(xb)]dx．xb．xa(xa)(xb)．,B,C,D4E,F|EFaa0，（AB与CD(PAPB)(PCPD)数P．8．A(4,0,0),B(0,2,0),C(0,0,2),O．OABC,bxcx02(x),,()x0，试问：abcfx在8fxx09(1,5):yxL．3LDL与0D的xx(x)在区间[0,)f(0)0,|f(x)f(x)18f|f(x)e1,x[0,)．xarctanx18dx．(1x)20y1(z0)222zx9x2z2A(1,0,5),B(1,0,1),C(1,0,0)为BCDDxA(0,5)DDn1n(9pn1npn1n9x2n2nn1第九届（2008年）专科类高等数学竞赛试题5ax2|x|bx|x|，blimarctan．ax．2x1nlim．．k(k2)nk1(x)x(x1)(x2)(x100)f(100)fa．x1，b()2fxxx0在xx2．dx．(1x)221(2,1,xy2z5．(1,1,1)xt,y2,z2t．．．nxnn1{x}xx6x(n){x}8为1n1nnn(x)[a,b]在(a0),f(xdx0(a,b)b8fa(xdxf)得f．a8分xOy(xb)ya(0ab)222xblimsin(tx)dxt8．20t0:x2yz20分）在平面内作一条直线，使该直线经过另一直线x2y2z:LL与3xy4z3(1)318n1nn1x22(x)f(x1)(12x)2第十届（2010年）专科类高等数学竞赛试题4xx)．．x3x0arctan(x)etanxy．y．2xyyy(x)x．yxcosx．y．y(n)．21xex．x2xarctan(x1x4)21．dx．02x2yz20,．xyz4x2y2z192221(1)n!n．．2n!nn1exaax2101(x)f(xdxxf(xdx，f在[0,1]0f(xdx0．a1．1x42lnxylnx与x(0,0)yxABCDEDCF1ABCD，为11111,E,F形BCCBAABCD111,E,FDA1a}a1,a2,a5,,aaan123n1nn11(n2,3,)xnxann1n第十一届（2012年）专科类高等数学竞赛试题443x416x5lim．．．x012n333lim．n4xsintdtxt3．lim．0xsinx23x0x)y(n)．y．arctanxdx2．x．1．x2．x1x1y3z(2,1,．122nk(n．k．n1n26331limn3．(ni)n22ni1fx1(x)x0在ff2f．x2x046(x)(,)在0