考研数学二-历年考研真题1987-2018

？．下列矩陀中“|IJr4llTOl1＿110llO100lOO,、r4-c`,、＿＿L,助?lT0l眺OlOOlO$|u丿ri|PlOrl—飞—lODl10BIOO,、丁S.设A.fl为n阶矩阵，记r(X)为矩阵X广入r七i初-r{..f).B.r(AJA)=r(A).C.r(..'.IB)..:m五仁(A儿l(B)}D1.;,,(.AB).,.r{.41B1)，则_、=-』:9-14小颗．妇小瑾矗分护只山分卢泣11,「志心－拐点处的切紩万在是12.尸Jt,在t==!晌酝处的�..,)'=sifflfl4ll没函坎:a:(工_\')由方程tn,z+,,;-l.,,,,�·“没A为3阶昭革，名，生心妇耽汉天的同量组若A«i-芯h十生+«p古位气=气42气，．位i,,._红�+,如贝JA忙三、解答履：l仁乃小僵，共9.t分．一室l:S.(本过涓分10分〉衣郓汾I古尔皿石亏士的值岱写出文字说明．l6.(本题涓分10分)(待定）l7.(本过污分10分）｛了＇一如D由单l(0�心五）与叶蚳城，计五二重荻分lt凸(.'i.c+2.)沁吟八•-co.stIS.t本过涓分10分｝已k�ln2一I,晌i(x-1.)(x一矿x+lkl'nx•l)已0城闷芷万＂竺个图形的面积之和是否存小m嘈20.(()(.O匐0}.点.t(OJ),设P是L上的动乱'S,酶的面积，若P运动到点1(3,4)时沿x轴正i口此时S关干时间t窃靴翠21(本n分）-Oo.叮斗－肋吐2,...).证明伈｝忱坟，并求史环·卫（本过涡分11分）设实二次型／伍，X;丙）'(立一(1)(2,)求／（气心为）的坟范如)�+伍+xJ)�+(�+叩）;•其中a.(本昆涓分lJ分）l.2a卧妇戏，鲍�+lo)可经l7-,a,(:l)(,:)求涓足A]'..B的可过庙屯polll10-，、＿＿B201718432.11cos,0(),0xxfxaxbx0x(A)12ab(B)12ab(C)0ab(D)2abA0011cos12limlim,()2xxxxfxaxaxa0x11.22babaA.2()fx(1)(1)1,(0)1fff''()0fx111101011010()()0()0()()()()()AfxdxBfxdxCfxdxfxdxDfxdxfxdxB()fx0110()()fxdxfxdxC,D.2()21fxx112112()2103fxdxxdxB.3nx()Alimsin0nnxlim0nnx()Blim()0nnnxxlim0nnx()C2lim()0nnnxxlim0nnx()Dlim(sin)0nnnxxlim0nnxDAnxlimsin0,limnnnnxxA21nxB,C.D.4A22(cos2sin2)xxAeeBxCxB22(cos2sin2)xxAxeeBxCxC22(cos2sin2)xxAexeBxCxD22(cos2sin2)xxAxeeBxCxA21,248022i222*2*212()(1cos2)cos2,(cos2sin2),xxxxxfxexeexyAeyxeBxCx***2212(cos2sin2),xxyyyAexeBxCxC.5(,)fxy(,)xy(,)(,)0,0fxyfxyxyA(0,0)(1,1)ffB(0,0)(1,1)ffC(0,1)(1,0)ffD(0,1)(1,0)ffC(,)(,)0,0,(,)fxyfxyfxyxyxy(0,1)(1,1)(1,0)fffD.610m1()vvt/ms2()vvt10,20,30ts051015202530()ts(/)vms1020A010tB01520tC025tD025tB00t001200(t),(t),ttvdtvdt0210(t)v(t)10tvdt025tC.7A123(,,)P1012PAP123(,,)AA12B232C23D122B11231232300011(,,)(,,)12222PAPAPPA,B8200210100021,020,020001001002ABC,A,ACBCB,ACBCC,ACBCD,ACBCB0EAA2,2,1,3(2)1rEAA100~020002A0EBB2,2,1.3(2)2rEBBC~ACBC.4914424.(9)21arcsinyxx_______2yx22limlim(1arcsin)1,limlimarcsin2,2xxxxyyxxxxxyx(10)()yyxsintxteyt220tdydx______18'220222coscos,11cossin(1)cos1181tttttttdydxdyttedtdtdxetdytetedyedxdxdxedt(11)20ln(1)(1)xdxx_______120002020ln(1)1ln(1)(1)1ln(1)11(1)11.(1)xdxxdxxxdxxxdxx(12)(,)fxy(,)(1)yydfxyyedxxyedy(0,0)0f(,)______fxyyxye,(1),(,)(),yyyyxyfyefxyefxyyedxxyecy()yyyyyfxexyecyxexye()0cy()cyC(0,0)0f(,).yfxyxye13110tan______yxdydxxlncos1.11110000tantantanlncos1xyxxdydxdxdyxdxxx.1441212311Aa112_____a-1112A4121111211323112222aa1a.152394...1510030limxtxxtedtx23030limxtxxtedtxxtu6000xxtxuxuxxtedtueduuedu003300220310022=limlim2limlim332xxxuxuxxxuxxxuedueueduxxueduxexx1610(,)fuv2(,cos)xyfex0xdydx220xdydx2'''111200(1,1),(1,1),xxdydyffdxdx0'''''12121002''2''''''2''111221221222''''111220(,cos)(0)(1,1)sin(1,1)1(1,1)0(1,1)(sin)(sin)sincos(1,1)(1,1)(1,1)xxxxxxxxxxyfexyfdyfefxfffdxdyfefexfexfxfefxdxdyfffdx'102''''111220(1,1)(1,1)(1,1)(1,1)xxdyfdxdyfffdx171021limln1nnkkknn14211122102000111111limln(1)ln(1)ln(1)(ln(1))2214nnkkkxxxdxxdxxxdxnnx1810()yx333320xyxy()yx(1)1y(1)0y2233'33'0xyyy1'0y1x1x2266'3''3''0xyyyyy21x1110xxoryy1,1xy2''(1)10y1,0xy2''(1)20y1x(1)1y1x(1)0y1910()fx[0,1]20()(1)0,lim0xfxfx()()0fx(0,1)()2''()()(())0fxfxfx(0,1)I()fx0()(1)0,lim0xfxfx10()lim0xfxx0,(0,)x()0fxx()0fx0(0,)0xf()fx()fx[0,1]()fx[,1]()0,(1)0ff(,1)()0f