同济大学第六版高等数学上册课后答案全集

1-11.A=(--5)(5,+),B=[-10,3),AB,AB,ABA\(AB).AB=(-3)(5,+),AB=[-10,-5),AB=(--10)(5,+),A\(AB)=[-10,-5).2.AB,:(AB)C=ACBC.x(AB)C?x?AB?x?Ax?B?xACxBC?xACBC,(AB)C=ACBC.3.f:XY,A?X,B?X.(1)f(AB)=f(A)f(B);(2)f(AB)?f(A)f(B).yf(AB)??xAB,f(x)=y?(xAxB)yf(A)yf(B)?yf(A)f(B),f(AB)=f(A)f(B).(2)yf(AB)??xAB,f(x)=y?(xAxB)yf(A)yf(B)?yf(A)f(B),f(AB)?f(A)f(B).4.f:XY,g:YX,XIfg=,YIgf=,IXIYXY,xX,IXx=x;yY,IYy=y.:f,gf:g=f-1.yY,x=g(y)X,f(x)=f[g(y)]=Iyy=y,YX,fXY.x1x2,f(x1)f(x2),f(x1)=f(x2)?g[f(x1)]=g[f(x2)]?x1=x2.f,,f.g:YX,yY,g(y)=xX,f(x)=f[g(y)]=Iyy=y,,gf.5.f:XY,A?X.:(1)f-1(f(A))?A;(2)f,f-1(f(A))=A.(1)xA?f(x)=yf(A)?f-1(y)=xf-1(f(A)),f-1(f(A))?A.(2)(1)f-1(f(A))?A.,xf-1(f(A))?yf(A),f-1(y)=x?f(x)=y.yf(A)f,xA.f-1(f(A))?A.f-1(f(A))=A.6.:(1)23+=xy;3x+2032-x.),32[+-.(2)211xy-=;1-x20x1.(--1)(-1,1)(1,+).(3)211xxy--=;x01-x20D=[-1,0)(0,1].(4)241xy-=;4-x20|x|2.(-2,2).(5)xysin=;x0D=[0,+).(6)y=tan(x+1);21+x(k=0,1,2,???)12-+kx(k=0,1,2,???).(7)y=arcsin(x-3);|x-3|1D=[2,4].(8)xxy1arctan3+-=;3-x0x0D=(-0)(0,3).(9)y=ln(x+1);x+10D=(-1,+).(10)xey1=.x0D=(-0)(0,+).7.,f(x)g(x)(1)f(x)=lgx2,g(x)=2lgx;(2)f(x)=x,g(x)=2x;(3)334)(xxxf-=,31)(-=xxxg.(4)f(x)=1,g(x)=sec2x-tan2x.(1)..(2).,x0,g(x)=-x.(3)..(4)..8.?????=3||03|||sin|)(?xxxx,)6(?,)4(?,)4(?-,?(-2),y=?(x).21|6sin|)6(==?,22|4sin|)4(==?,22|)4sin(|)4(=-=-?,0)2(=-?.9.:(1)xxy-=1,(-1);(2)y=x+lnx,(0,+).(1)x1,x2(-1),1-x10,1-x20.x1x2,0)1)(1(112121221121---=---=-xxxxxxxxyy,xxy-=1(-1).(2)x1,x2(0,+),x1x2,0ln)()ln()ln(2121221121+-=+-+=-xxxxxxxxyy,y=x+lnx(0,+).10.f(x)(-l,l),f(x)(0,l),f(x)(-l,0).?x1,x2(-l,0)x1x2,-x1,-x2(0,l)-x1-x2.f(x)(0,l),f(-x2)f(-x1),-f(x2)-f(x1),f(x2)f(x1),?x1,x2(-l,0),f(x1)f(x2),f(x)(-l,0).11.(-l,l),:(1),;(2),,.(1)F(x)=f(x)+g(x).f(x)g(x),F(-x)=f(-x)+g(-x)=f(x)+g(x)=F(x),F(x),.f(x)g(x),F(-x)=f(-x)+g(-x)=-f(x)-g(x)=-F(x),F(x),.(2)F(x)=f(x)?g(x).f(x)g(x),F(-x)=f(-x)?g(-x)=f(x)?g(x)=F(x),F(x),.f(x)g(x),F(-x)=f(-x)?g(-x)=[-f(x)][-g(x)]=f(x)?g(x)=F(x),F(x),.f(x),g(x),F(-x)=f(-x)?g(-x)=f(x)[-g(x)]=-f(x)?g(x)=-F(x),F(x),.12.,,(1)y=x2(1-x2);(2)y=3x2-x3;(3)2211xxy+-=;(4)y=x(x-1)(x+1);(5)y=sinx-cosx+1;(6)2xxaay-+=.(1)f(-x)=(-x)2[1-(-x)2]=x2(1-x2)=f(x),f(x).(2)f(-x)=3(-x)2-(-x)3=3x2+x3f(x).(3)())(111)(1)(2222xfxxxxxf=+-=-+--=-,f(x).(4)f(-x)=(-x)(-x-1)(-x+1)=-x(x+1)(x-1)=-f(x),f(x).(5)f(-x)=sin(-x)-cos(-x)+1=-sinx-cosx+1f(x).(6))(22)()()(xfaaaaxfxxxx=+=+=-----,f(x).13.,:(1)y=cos(x-2);,l=2.(2)y=cos4x;,2=l.(3)y=1+sinx;,l=2.(4)y=xcosx;.(5)y=sin2x.,l=.14.:(1)31+=xy;31+=xyx=y3-1,31+=xyy=x3-1.(2)xxy+-=11;xxy+-=11yyx+-=11,xxy+-=11xxy+-=11.(3)dcxbaxy++=(ad-bc0);dcxbaxy++=acybdyx-+-=,dcxbaxy++=acxbdxy-+-=.(4)y=2sin3x;y=2sin3x2arcsin31yx=,y=2sin3x2arcsin31xy=.(5)y=1+ln(x+2);y=1+ln(x+2)x=ey-1-2,y=1+ln(x+2)y=ex-1-2.(6)122+=xxy.122+=xxyyyx-=1log2,122+=xxyxxy-=1log2.15.f(x)X,:f(x)XX..f(x)X,M,|f(x)|M,-Mf(x)M.f(x)X-MM..f(x)XK1K2,K1f(x)K2.M=max{|K1|,|K2|},-MK1f(x)K2M,|f(x)|M.f(x)X.16.,,x1x2:(1)y=u2,u=sinx,61=x,32=x;y=sin2x,41)21(6sin221===y,43)23(3sin222===y.(2)y=sinu,u=2x,81=x,42=x;y=sin2x,224sin)82sin(1==?=y,12sin)42sin(2==?=y.(3)uy=,u=1+x2,x1=1,x2=2;21xy+=,21121=+=y,52122=+=y.(4)y=eu,u=x2,x1=0,x2=1;2xey=,1201==ey,eey==212.(5)y=u2,u=ex,x1=1,x2=-1.y=e2x,y1=e2?1=e2,y2=e2?(-1)=e-2.17.f(x)D=[0,1],:(1)f(x2);0x21|x|1,f(x2)[-1,1].(2)f(sinx);0sinx12nx(2n+1)(n=0,1,2???),f(sinx)[2n,(2n+1)](n=0,1,2???).(3)f(x+a)(a0);0x+a1-ax1-a,f(x+a)[-a,1-a].(4)f(x+a)+f(x-a)(a0).0x+a10x-a1:210a,ax1-a;21a,.210a[a,1-a],21a.18.?????-==1||11||01||1)(xxxxf,g(x)=ex,f[g(x)]g[f(x)],.?????-==1||11||01||1)]([xxxeeexgf,?????-==010001)]([xxxxgf.?????===-1||1||e1||)]([101)(xexxeexfgxf,?????==-1||1||11||)]([1xexxexfg.19.,?=40(1-37).ABCDS0,L(L=AB+BC+CD)h,.1-3740sinhDCAB==,0)]40cot2([21ShBCBCh=?++hhSBC?-=40cot0,hhSL40sin40cos20-+=.hh0,040cot0?-hhS,40cot00Sh.20.90,60.,100,1,1,75.(1)px;(2)Px;(3)1000,(1)0x100,p=90.0.01(x0-100)=90-75,x0=1600.x1600,p=75.100x1600,p=90-(x-100)0.01=91-0.01x.?????-=160075160010001.091100090xxxxp.(2)?????-=-=160015160010001.031100030)60(2xxxxxxxxpP.(3)P=311000-0.0110002=21000().1-21.xn{xn},:(1)nnx21=;n,nnx21=0,021lim=nn.(2)nxnn1)1(-=;n,nxnn1)1(-=0,01)1(lim=-nnn.(3)212nxn+=;n,212nxn+=2,2)12(lim2=+nn.(4)11+-=nnxn;n,12111+-=+-=nnnxn0,111lim=+-nnn.(5)xn=n(-1)n.n,xn=n(-1)n.2.{xn}nnxn2cos=.nnxlim=?N,nN,xn,=0.001,N.0lim=nnx.nnnxn1|2cos||0|=-.?0,|xn-0|,n1,1n.]1[=N,?nN,|xn-0|.=0.001,]1[=N=1000.3.:(1)01lim2=nn;=-221|01|nn,12n,1n.?0,?]1[=N,nN,-|01|2n,01lim2=nn.(2)231213lim=++nnn;+=-++nnnn41)12(21|231213|,n41,41n.?0,?]41[=N,nN,-++|231213|nn,231213lim=++nnn.(3)1lim22=+nann;++=-+=-+nanannannannan22222222)(|1|,2an.?0,?][2aN=,?nN,-+|1|22nan,1lim22=+nann.(4)19999.0lim=???43421nn.|0.99???9-1|=-1101n,1101-n,1lg1+n.?0,?]1lg1[+=N,?nN,|0.99???9-1|,19999.0lim=???43421nn.4.aunn=lim,||||limaunn=.:{|xn|},{xn}.aunn=lim,?0,?NN,nN,-||aun,||un|-|a|||un-a|.||||limaunn=.{|xn|},{xn}.1|)1(|lim=-nn,nn)1(lim-.5.{xn},0lim=nny,:0lim=nnnyx.{xn},M,?nZ,|xn|M.0lim=nny,?0,?NN,nN,Myn||.nN,=?=-MMyMyxyxnnnnn|||||0|,0lim=nnnyx.6.{xn},x2k-1a(k),x2ka(k),:xna(n).x2k-1a(k),x2ka(k),?0,?K1,2k-12K1-1,|x2k-1-a|;?K2,2k2K2,