2019考研数一真题及解析

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2019ὃẆᦪ⚪ஹ⌱⚪8⚪⚪4ᑖᐳ32ᑖ.ᑡ⚪Ḅ⌱⚗ᨵ⌱⚗ᔠ⚪⌕"Ḅ.L$%—>0)*X—tanx0/2▤45ᑣ%=A.I.B.2.C.3.D.4.2.>?ᦪ/(X)=[r<0~'ᑣx=0/(x)Ḅxlnx,x>0,A.DEF᩽HF.B.RDEF᩽HF.C.DEFI᩽HF.D.RDEFI᩽HF.3.>S%,UᓫWXYḄᨵZᦪᑡ,ᑣᑡ[ᦪᦈ]Ḅ00001A.y^.u஻=1nC.ᓾab.rt=lx4.>?ᦪQ(x,y)=d᝞fghij☢(y>0)ᑁḄmnᨵᔣᐝqrstu஺wᨵyP(x,y)dx+Q(x,y)dy=0,yz?ᦪP(x,y)D{|21X2A-y—3'*B.-----.yyy11iC.-----.D.x---.yy5.>A3▤g▣E3▤ᓫ▣.*42+4=2E=4,ᑣXAxḄ|A.y+:+ᕒ.D.-x-y1-yl-6.᝞ᡠᨵ3j☢ujḄd

1ax+ay+az=4a=1,2,3)iXj2j3ᡂḄuឋdḄ£ᦪ▣¤X▣ᑖ¥¦|A,K,ᑣA.r(A)=20(A)=3.B./-(A)=2,r(A)=2.C.r(A)=1/(A)=2.D.r(A)=l,r(A)=l.7.>|©ª«¬ᑣP(A)=P(5)Ḅᐙᑖ®⌕ᩩ¬A.P(AU5)=P(A)+P(5).B.P(AB)=P(A)P(B).C.P(AB)=P(BA).D.P(AB)=P(AB).8.>©ª²³x0y´µw¶·¸᝱ᑖº%(஻,஻)ᑣp(x—r|?ᦪ/'(஻)DEz=/(siny-sinx)+Ëᑣ--------+---------------.cosxdxcosydy10.Ìᑖd2yy'—y2-2=0ÍÎᩩ¬y(0)=1ḄᱯÐy=;(1)"11.Ò[ᦪE^-x"ᙠ(0,+00)ᑁḄ¤?ᦪS(x)஻=0(2஻)Ö

212.>N|t☢/+y2+4z2=4(ZN0)ḄhÙᑣ“^4-x2-4z2dxdy=Lz13.>4=(,,a,%)|3▤▣.*Ûuឋ4ᐵ஺3=,+2஺2ᑣu2ឋdAx=0ḄÜÐ|:x14.>©ª²³XḄᭆ᳛àá|/(x)=5,U<%<2F(x)|XḄᑖº?ᦪ0,ᐸãᕒ|XḄᦪäåᑣæç(X)>è1U=.éஹÐê⚪Æ15~23⚪ᐳ94ᑖ.Ðêëᑏᦻîïðஹñðòᡈôõö÷.15.(ø⚪Íᑖ10ᑖ)x2>?ᦪy(x)Ìᑖdy+ù=”ÍÎᩩ¬y(0)=0ḄᱯÐ.(1)"y(x)û(2)"tuy=y(x)Ḅüýþÿ
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42019ºὃẆᦪ½%¾⚪%ஹ⌱À⚪1~8Â⚪ÃÂ⚪4ᑖᐳ32ᑖ.sᑡÃ⚪ÅzḄÆn⌱⚗#Èᨵ%n⌱⚗aÊᔠ⚪Ì⌕+Ḅ.1.ÎX-0¢Ïx-tanx;x”aÑ▤ÓÔÂÕ”=A.1,B.2.C.3.D.4.ூὃáâãCtanx=+஺(×3),ᡠÙ=+஺(Ú3ூá᪆௃æÎX-0¢ᡠÙç=3஺1x<02.ᦪ/(x)=<è%’ᑣx=0a/(%)Ḅxlnx,x>0,A."᩽).B.¥"᩽).C."Þ᩽).D.¥"Þ᩽).ூὃáâ௃æBூá᪆௃æ(1)/(0+0)=limxlnx=lim-=0,/(0-0)=limx|x|=0,/(O)=0,XT0+%->0+1XT(rXᡠÙᦪᙠx=0ᜐëì*ফf(O)=limîᔳ=%“ᡠÙᦪᙠx=0ᜐ¥"*XT0+XবÎx<0¢/(x)=-x2,//(x)=-2x>0,ᦪᓫP⌴ò*Î0"=1ூὃáâ௃æD

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7|7☢É7☢ØÙÎDÅ37☢Ǫ4).|7☢É7☢Vᐸ`7☢Úᔠ஺|7☢Ǫ(5)(5).¡Ï=2,¡A=1½¡Áு¡A,ᦑYM37☢º.£¡A=l,¤ᨵ|7☢£¿37☢7.Ü£¡A=2,37☢`Ö×ᨵ|7☢Ç.*HÈᨵ.37☢737☢Ǫ(6).37☢7ᐸ`ᨵ|7☢Úᔠνᨵ|7☢Ǫ(7).(6),¡ᓺ=1=¡Ð½£¡Y=¡Ð=1<11=3ᨵYÓÔ}M.37☢ᨵYÓÔ}Àᵫ¡ᓺ=1]¤ᨵ|7☢¿¡Y=1.Õ37☢`Ö×ᨵ1}7☢Ç.᝞4ᨵ2}ᡈ3}7☢ÞÇ஺ᑣÆ7.ÎV37☢ᨵYÓÔ}Àßà*cᨵ}º¥7☢஺ᓽ3}7☢Úᔠª7.âãä\ᑣP(A)=å(B)ḄᐙᑖÆ⌕ᩩ\*A.P(AUB)=P(A)+P(8).B.å(A8)=å(A)P(B).C.P(AB)=P(BA).D.P(AB)=P(AB).

8ூKὃMN+cèM᪆+%P(Aὡ)=P(A)—P(A5)=P(BA)=P(6)—P(AB)=>P(A)=P(B)ᦑ⌱CA⌱⚗*êᡈὅìºí஺B⌱⚗*îï஺D⌱⚗⌨ºñᩭᐵ஺8.âãóôxVyîïEõö᝱ᑖøN(஻,/),ᑣp{x-y|

916.1ᑖ,22»'-/2=078ᩩ:y(0)=1Ḅᱯy=,ூὃ௃y=,3/-2ூ᪆௃ᑖ@ABCJ4F=ேᩈa=>In(M+2)=%+G=>M+2=cey+2,)RᐭTUCC=3,ᦑy=J3e'-2(-D"17.XYᦪZ^-^x"ᙠ(0,+oo)ᑁḄ^ᦪS(x)=஻=0(2")!ூὃcS(x)=cos«ூ᪆௃ᵫ=£h-(6)2=cos4D(2஻)!«=o(2n)!18.Nkl☢/+y2+4z2=4(Z20)Ḅ)oᑣ0^-^-Az^dxdy=Lz32ூὃ௃—3ூ᪆௃ᵫ⚪pqJJஹ4-—4?2dxdy=y|Ady=my|dxdyᐸx஺:V+y2=4ᵫ|}~ᑖCឋJJjy\dxdy=4ᨴsinddd^rdr^y19.4=(%a,%)k3▤▣.a,%ឋᐵ=-஺1+24ᑣ2]ឋ,24=0Ḅktqஹூὃ[x=k-2,ksRJ>ூ᪆௃kr(A)22,2ᨵᦑ/•(A)«2nr(A)=2,ᵫ஺3=-+2”2[1](1)q/+q-2a2=0ᓽ(a1a,a?)-2=0,ᡠ2k,2ḄẠ2

10’1ஹᡠkX=G-2,keRJ,20.ABXḄᭆ᳛£¤k/(x)=,2,0<%<2F(%)kXḄᑖ¥ᦪ,0,ᐸ¦ᕒkXḄᦪ¨©ªᑣP«(X)>£X-1)=_____:2ூὃ௃±3Xூ᪆௃XḄᭆ᳛£¤k/(X)={5'0,?32EX-dx=-^%2(1%=—•—=—=—022°23τ630x<02xF(x)=<—02P{b(X)ZEX_l}=p{b(X)»}=P{XN2}=p[j=x2222=3ᨵ®ஹ⚪15~23⚪ᐳ94ᑖ.¯ᑏ±ᦻ³´µஹºµ»2ᡈ½¾¿À.15.(¶⚪7ᑖ10ᑖ)X2ᦪy(x)·1ᑖ,2y+¸=J78ᩩ:y(0)=0Ḅᱯ.(1)¹y(x)(2)¹ly=y(x)ḄÁÂÃÄÅÆÇ.

1113.(1)y(x)=eu/v(Je2^iXdx-\-c)=e2(x+c),Êy(0)=0,12ᦑc=0,Ëy(x)=xeM.(2)yr=ey—x2e=(l-x2)eM_l2(2_l2(xxyn--2xe*-(l-x2)xe2=(x3-3x)e2=x(x2-3)e%%y"=0Cx=0ÍÎX(-oo,-V3—5/3(-V3,0)0(0,V3)V3(V3,+oo)n—0+0—0+yyÂÆÇÁÆÇÂÆÇÁᡠly=yÏxÐḄÁÃÄkÏ—J5,0Ð^ÏÎ,ÒÐÂÃÄkÏF,-QÐ^Ï0,ÎÐ,33ÆÇkÏ0,0Ð,--.-/01,-26”1.16.϶⚪7ᑖ10ᑖÐa,஺kÕᦪᦪ2=2+஺Ö2+×2ᙠÇÏ3,4ÐᜐḄ,ᔣᦪxÚ,ᔣ/=34/Ḅ,ᔣᦪᨬᜧᨬᜧUk10.Ï1й஺,஻(2)¹l☢z=2+of+(>0)Ḅ☢~.z(1)gradz=(2ax,2by),gradz^=(6a,Sb),(34)=——ᓽ஺=b,Ê|graJz|=J(6a)2+(8஻)?=10,ᵫ⚪C,ᡠa=b=-l.1+(à)2+(à)2dxdy-||J1+(ߟ2x)2+(—2y)?dxdydx//+y2a=JJ1+4d+4y2dMyJ1+4P2஺/᜛=21.(1+422)5f=—^/â200123

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