2017考研数一真题及解析

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ਭᵨ2017ᐰắẆᐭὃᦪṹ301ὃ⚗1.⚪ὃᙠ⚪ᢣ!"#$ᑏὃ&'(ὃ)*+ᙠ⚪ᓱᢣ!"#$ᑏ-ὃᓫ!ஹὃ&'(ὃ)*01ᑏὃ)*234஺2.ὃ6⚪#Ḅᔁᩩ:ṹ;<ᩩ=>;<ᙠ⚪ᓱ”ᔁᩩ:ṹ;

12017ᐰắẆᐭὃᦪ⚪ஹ⌱Q⚪18⚪.⚪4ᑖᐳ32ᑖ.1-cosVx1.ᦪ/(x)={——ᙠx=OᜐIJb,x<0(A)ab=(B)ab=~(C)ab=0(D)ab=2222.£ᦪ/(%)¥z¦ᦪ§¨©/(x)/'(x)>0,ᑣ(A)/(1)>/(-1)(B)/(1)|/(1)|(D)|/(1)|<|/(-l)|3.ᦪ/(x,y,z)=Vy+z2ᙠ4(1,2,0)ᜐ´ᔣ¶஻=(1,2,2)Ḅ·ᔣ¦ᦪ¸(A)12(B)6(C)4(D)24.ᵬஹ»¼½¾¿ÀÁÂÃÁᵬᙠ»·10(ᓫ!ÄÅ)ᜐ᝞ÇAÈÉ⊤ËᵬḄÌÍÎÉV=%(f)(ᓫ!ÄÅ/Ð)ÑÉ⊤Ë»ḄÌÍÎÉÒ=Ó஺)(ᓫ!ÄÅ/Ð)Ôᙽ▢FcᑖḄ☢ØᑖÙ¸10,20,3,ÀÁÂÃv»Ú#ᵬḄÁÛ¸ᑣ()(A)%=10(B)15Ý<20(C)?=25(D)t>250Q5.£a¸஻ᓫ!ᑡᔣ¶E¸஻▤ᓫ!ã▣ᑣ(A)E-aa'Bz⌮(B)E+aa'Bz⌮(C)E+2aa'Bz⌮(D)E-2aa'Bz⌮200ஹ‘210ஹ’100ஹ6.æçã▣A021,B020,c=020,ᑣ001,ஹ°o1,ஹ002,(A)ACSëB,CSë(B)ACSëBSë(C)A,CBSëSë(D)A,CBSëì஺BSë7.£A,6¥¼íîïðñ0஺(4/ᔊḄᐙᑖ⌕ᩩñ¥(A)P(B/A)>P(B/A)(B)P(B/A)P(B/A)(D)P(B/A)

2-1n8.£XóX2,…,X“(஻N2)¸ᩭNü᝱þÿN(஻,l)Ḅᓫ᪵=—ᑣᑡn■=,Ḅ()(A)S(X,.-஻)2%&᮱ᑖ)প)2(X“-KJ?%&/ᑖ)/=1(C)f(Xj—5)2%&/ᑖ)(D)஻(56஻)2%&/ᑖ);=|7ஹ9:⚪(⚪ᐳ6>⚪?>⚪4ᑖAᑖ24ᑖ.BCᫀ9ᙠ⚪FGH)9.JKLᦪ/(x)=O^,ᑣ/ব(஺)=______.l+x10.VᑖWXy"+2y'+3y=0Ḅ^_`.11.aGbᑖcdceᙠfg஺={(i|/+k2<1}ᑁopqrᐵᑣ஺=.12.tuᦪv(61)"7x"-|ᙠfy(_11)ᑁḄzLᦪ`n=\‘101ஹ13.|}▣A=112,%,%`GឋrᐵḄᑡᔣᑣᔣA.,A%)%Ḅஹ஺1L`.14.|XḄᑖ)LᦪF(x)=0.5জ(x)+0.5জ(4)ᐸজ(x)`᪗᝱ᑖ)LᦪᑣEX=•ஹ_C⚪15.(⚪Aᑖ10ᑖ)|Lᦪ/(஻#)ᐹᨵ7▤ᦪy=f(ex,cosx),ᵯ|,^-|..v0dxax

316.⚪Aᑖ10ᑖ43k[khmு—1In11+—஻f00nIfl17.⚪Aᑖ10ᑖJKLᦪyxᵫWXk+y3-3£+3y-2=0.18.⚪Aᑖ10ᑖ|Lᦪ/¥ᙠfy¦o,icHᐹᨵ7▤ᦪ©/প>0,1«4°<0,®:1WX/x=0ᙠfy0,1°±²ᙠ6³´᪷2WX/¥"¥+/'`2=0ᙠfy0,1ᑁ°±²ᙠ¶³·´᪷.

419.(⚪Aᑖ10ᑖ)|ↈᱏºSᙊ┵☢z=Jf+y2¿À☢z2=2xᡠᒘḄᨵ▲ÄᑖᐸHÅ6ÆḄÇÈ`஻=9jK+y2+z2,Éᙊ┵☢oÀ☢ḄÊG`C.(1)CᙠX0V)HḄᢗÍaGḄWX(2)SḄÎ20.(⚪Aᑖ11ᑖ)|▤}▣஺3)ᨵ³·ḄᱯÐÑ©%=4+2a2,(1)®Ór(A)=2(2)£=஺c+஺2%WX4x=Ḅ^_.21.(⚪Aᑖ2ᑖ)|7Öºf(x,x,x)=2xf-x&+axf+2X,X-+2xxᙠÊᣚx=QyḄ᪗Ù`i232234y஺ḄÑÚ6³Ê}▣஺.

522.(⚪Aᑖ11ᑖ)|x,yÛÜÝÞ©xḄᭆ᳛ᑖ)`P{X=O}=P{X=2}=,yḄᭆ᳛ÇÈ`0,ᐸá,(1)ᭆ᳛P(Y

62017ᐰắẆᐭὃᦪ⚪ᫀஹ⌱#⚪$(1)ூᫀ௃A1-COsVxr],/ஹ14,1lim---------=lim-^ߟ=——f(x)(.—=b=ab=—.ூ᪆௃faxD?orlaᙠB=°ᜐEF2a2⌱A.(2)ூᫀ௃C,"(x)>0l/'(x)>0ᡈ?LᨵC⌱⚗OPপROPQ),ᡠU⌱C஺ூ᪆௃(3)ூᫀ௃Dgradf={2xy,x2,2z},^gradf\={4,1,0}=>|^=^0#~={4,1,01-{1,|!)=2.(l20)?ூ᪆௃duU333⌱D.(4)ூᫀ௃Bூ᪆௃1J஺2ᑣo⌕qrᵬ?ᑣf0v,(t)-v.(t)Jr=10f-25'«2',i‘஺”lOP?ᦑ⌱C.(5)ூᫀ௃Aூ᪆௃⌱⚗A,ᵫ(E-஺஻w=஺஺=0x(E—a")x=0ᨵyz?ᦑ{஺஺|=0஺ᓽ~஺"⌮஺⌱⚗B,ᵫ"oa.anlxaa’Ḅᱯn-10,1.ᦑE+a"Ḅᱯ11,2.ᦑ⌮஺ᐸ⌱⚗ᳮ஺(6)ூᫀ௃Bூ᪆௃ᵫ(A)=°Ḅᱯ2,2,1‘100ஹA~0203-"2E-4)=1,...Aᓄ?R1°02)ᵫὡ=°Bᱯ2,2,1.

73-"2£-8)=2,...Bᓄ?ᯠcᓄ,...A~C,RBC(7)ூᫀ௃Aூ᪆௃ᢥ᯿ᩩ¡ᭆ᳛¤¥¦§?ᑣA⌱⚗¨ᔠ⚪ª஺(8)ூᫀ௃Bூ᪆௃X««N(O,1)=>£&-஻)2~/(஻),4¬/=!n(஻—1)S2=£(X,-®)2~%2(஻_]),C¬?/=1=>(¯-஻)~mi),n{X-஻)2~%2(1),D¬,nn~N(0,2),(X“4XJ~/প?ᦑB┯³.ᵫ´¬Ḅµ¶?ᦑB¨ᔠ⚪ª஺·ஹ¸¹⚪$(9)ூᫀ௃/º·-6ூ᪆௃/(%)==-=-=y(-x2)n=y(-i)nx2n1+/i-(-%2)23r(X)=£(—1)"2஻(2஻1)(2஻-2)/'—3=f=0(0)n=2(10)|»ᫀ¼y=ex(c\cos4-csinV2x)2(,”Q½ª¾ᦪ)|᪆¼¿ÀᱯÁÂÃ2+22+3=0n4,2=_+ᦑÄCcos4+csinV2x)2(11)ூᫀ௃a=1dP_-2xydQ_2axydP_dQ_ூ᪆௃ঝU2+r-l)2?Sx(V+yL1ÆᵫÇᑖÉÊËÌᐵঝ&s(x)=——~7(1+Ï(12)ூᫀ௃

8¼(1+X)2|᪆¼W=13=17+13ூᫀ௃2ூ᪆௃ᵫÑ'4?a3ÒឋÌᐵ?Ô▣??஺2,03⌮?ᦑr(Acr,,Aa,Aa)=r(A(a,,a,,

9ä17åூᫀ௃᩽ᜧyäD=i,᩽üNTå=°ூ᪆௃ýþÿ
3x2+3/y,-3+3y'=0পy'=°
x=±i1ᐵx
6x+6yy'+3”+3y"=0ফx=lx=-\0ᦑ7=18᩽ᜧ;<-yD=i>X=T8᩽?;<-MT=O18IB▤ᦪ--°*x..f
xhm----<0H1ᵫ-o,x,᪷L᩽▲ḄNOឋ
,Q<038>0,\7T60»ᨵ7,ᓽ/X<0YZ[€0বᨵ/^_஺`ᵫ/%B▤b-ᡠd/Xᙠ10-Ighijklm3ᙠU-1ogij-ᵫ/p<0,/প>°᪷Lq

10F(x)=/(x)/"(x)+(/'(%))=°ᙠ(0,1)tuᨵ᪷஺
}஺(19)ூH᪆௃Z=Jx2+y222c-,NJ=>x2+y2=2x(1)ᵫ⚪¤ᩩ¦~-CḄ§¨8ெz-=2xJx2+y2=2xᑣCᙠ«-¬☢Ḅ§¨8ெz=°(2)®=JJ஻(x,y,z)dS=jj9ylx2+y2+z2dS=j|9y/2yjx2+y2-JldxdyssD:x2+y2^2xf—f2cos^o=±ᕣ,dr=64~2(20)ூH᪆௃প}¾:ᵫ4=«+2%b
%+2a21a3=°,ᓽ/,%-ḄÂឋ·ᐵ-ÃÄ-1AH2a31=஺-ᓽAḄᱯÇ;hᨵ0஺`Ã8AᨵḄᱯÇ;-ᑣᱯÇ;,Èᨵ10,É᜜Ë0.'4ஹA=4ᵫAhb·¸¹ᓄ-ᑣb¤ᐸ¹¼▣8I°).r(A)=r(A)=2(II)ᵫপ"A)=2,~3-r(A)=l,ᓽAr=°Ḅ×ẠHÙÈᨵ1HᔣÛ-r1'(1]p(a,a,a)2=A2=02t23ᵫ4+2a2-4=0b
I-11,ᑣAx=0Ḅ×ẠHÙ8(7TÝ-|:1(6,02-%)1=`=6Z]+%+,ᓽJপ-ᑣÞ=ᔆḄwᱯH8প-k2+1,&wRÒg-Ó=£ḄÕH8(ߟUপ

1121ூ
᪆௃’21-4ஹA=1—11f(x,x,x)=X'AXᐸ,(-41a,]23ᵫ/(X-X2-X3)=X'AXáâãäᣚæ-
ᑮḄ᪗éê84>>+4%,21-4r(A)=2=>|A|=0=>1—11=0no=2#஺=2%ᐭ-ìíî(A)=2,ÃÄa=2ïᔠ⚪ñ-Äò\~412J,ᑣ2-2-14|AE—A|=—12+1—1=0n4=—3,4=0,4=6-1ᵫ-3E-Ax=°,b
AḄõᱯÇ;-3ḄᱯÇᔣÛ8U0ᵫ6E—Ax=°,b
AḄõᱯÇ;6ḄᱯÇᔣÛ8UJP-'AP^6î=%%-%,ᑣᵫ%,&2-஺3öÄâã-ᦑÈ◤ᓫùᓄᓽb:-y=-(l,-l,l)r,y?=-^-(-1,0,1/,^=-^r(l,2,l)r,2

12111不一0看1。22=(^AA)=一f-zr\1r-6耳正2Aeolx7ᑣx=Qy.úf=-3ᑖ+6%(22)ூH᪆௃প£(y)=[y2ydy=]J஺3P(Y1,ᓽzN3,E(Z)=11,(3)Oீz3ᡠ%&'z0

13(23)ூ/᪆௃প4(z)=P(Z,Wz)=P(|X,—”0,£(z)=P(-zz>0<,ব=1=cr0,z<0&'(?ভAzBJ'=CDEF,2-2஻Vz^cr&-DE471_1«1nE(Z,)=Zz=Rz,=Hx,U஻|Gni=l஻x=l(T=ᵫIJK஺ḄNOPQXYZxḄ஻[᪵]X|,X?,…x">ᑣabḄcXdeḄ᪵]4Z>…z“,4=NU“,i=1,2…஻,Gᐸ᪵]ghZ\,Z»...Z",Z.=|X,--M|(n*L(cr)=\\J27rcr0,ᐸoᑣXjḄkᯠmᦪpqrXᦪ>4>Z2,…z“>°2i஻InL(cr)=nIn—j=----------VZ.2Fc2a2£s3=j+4£zu=oGdbubM

14n1=1ᡠ%>Y"vvhᡠwḄᨬᜧkᯠOP஺