数学专接本(高数)

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ᐗᦪᑖஹஹᦪஹᦪ⊤ஹᦪᦪḄᦪᢣᦪᦪᦪᦪᦪᦪᦪḄ▭ᦪ

1!ᔠᦪᦪஹஹᦪஹᦪ⊤#⚪1ஹ(01-3)/(x)Ḅ+[0,1],e(x)=/(x—1)+/(*+4)Ḅ+OB.8C8.Dᓽ2ஹ(02-3)Ḅ;()XA.[-l,l]B.[1,0)u(0,1]C.[-l,+oo)D.[0,+oo)3ஹ(03-3)ᦪ஺஺)=F7+J16-x2Ḅ;()A[0,7i]B[-4,-4]U[0,»]C[-4,4]D[-MN]

24ஹ(04-2)ᦪ/஺)=OPḄ;______________Inx5ஹ(04-2)ᦪy=VḄᦪ;X-16ஹ(05-2)ᙠYZ(0,+8)ᑁ]^ᦪ/(x)=71ᓛ`Ḅᦪ()AlnxB^Inx2Cln|x|D|lnx|7ஹ(06-2)ᦪy=arcsin(2x—1)+hḄ+()InxA.(0,1)B.(0,l]C.(O,2)D.(0,2]8ஹ(06-2)ᦪ)]=h-+ij2Ḅ+()x-377+1A.(-l,+oo)B.(l,+oo)C.(-l,3)U(3,+oo)D.(1,3)U(3,+oo)9ஹ(06-2)ᦪy==T+sin4Ḅ+஺A.[0,l]B.[0,l)U(l,3]C.[0,+oo)D.[0,3]

310ஹ(07-3)mnᦪ/(x)Ḅ+[0,2],ᑣ/(Inx)Ḅ;()Aஹ[l,e2]Bஹ[l,e]Cஹ(0,e]Dஹ(0,+oo]11ஹ(07-3)ᦪ/(x)=1+ln(x-1)Ḅ+()V4-x2Aஹ(1,2)Bஹ(1,2]Cஹ[-2,2]Dஹ(l,+oo)12ஹ(07-3)ᦪ/(x)=-J+ln(x-l)Ḅ+()V4-x2Aஹ(1,2)Bஹ(-2,2)Cஹ(l,+8)Dஹ(2,+oo)||x13ஹ(08-2)q/(x)=U,g(x)=/]ᑣ/(g(x))=14ஹs08-2tᦪ/sxtḄ+[0,1],ᑣ”x+ltḄ+stA[-2,-1]B[-l,0]C[0,1]Dfl,2]

415ஹ(08-2)ᦪy=arccosx+21nxḄ+16ஹ(09-2)ᦪ/(x)=᝞jᓰḄ+()x+4A[-4,4]B[-4,4)C(-4,4)D(-4,4]17ஹ(09-2)mn/(x)=L,ᑣ/"(2)]Ḅ;()\-x18ஹ(10-3)yᦪ/(ᐵ)Ḅ[1,3],ᑣᦪ/(1+{2)Ḅ;()A[1,3]B[0,2]C[-V2,V2]D[-V2,0]19ஹ(10-3)ᦪy=Ji||+arccosw-Ḅ;()A(-3,2]B[-3,l]C(-a),l]D[-l,3]20ஹ(10-3)ᦪ—21Ḅ;()V9-x2

5A(2,3)B(2,3]C[-3,2)D(-3,2)}ᓄ41ஹq/(x)Ḅ[0,1],ᑡᦪḄf(ex)/dnx)f(arctanx)f(cosx)2*_12ஹᦪḄᦪ;,ᦪḄ;2+13ஹq/'(sin?x)=cos?x,ᑣ/(x)=jஹᦪḄ᜻Ꮤឋ᜻ᏔᦪḄឋ

6ᑭᵨᦪᑖḄឋjஹᦪḄ᜻Ꮤឋ#⚪1ஹ(04-2)ᑡᦪ]᜻ᦪ+஺X.-XAf(x)=-------Bf(x)=x3+lC.f(x)=--—Df(x)=cosx+12ஹ(05-2)ᙠYZ-1,1]qᦪ/(x)+Ꮤᦪ]-/(x)()A+᜻ᦪBஹ+ᏔᦪCஹ+᜻ᦪ+ᏔᦪDஹᑨ᜻Ꮤឋ3ஹ(05-3)᝞ᦪ°(x)=,ᦪ/(x);᜻ᦪ]ln(x+71+x2)xு0/(x)=«0x=0°(x)=x<04ஹ(07-2)q/(x)=x(2x+l)(2x—l),x£(—oo,+8),ᑣ¡⚪¢

7£Ḅ+()Aஹ/(x);᜻ᦪBஹ/(x);ᏔᦪCஹ“X);ᨵ¥ᦪDஹ“X)¦᜻ᦪ§¦Ꮤᦪ5ஹ(09-2)qᦪ/(x,y)ᙠ(-co,+oo)ᨵ]ᑣᑡᦪ;᜻ᦪḄ+()A/(Ixl)Bl/(x)lCf(x)+f(-x)D/(x)-/(-x)}ᓄ1ஹq/(x);RḄ¨ᦪ]ᑣAy/(X);Ꮤᦪ]ᑣ/'(X);ᏔᦪBy/(*);᜻ᦪ]ᑣ©(x);᜻ᦪCy/(X);ᕜ«ᦪ]ᑣ/'(x);ᕜ«ᦪDy/(x);ᓫᦪ,ᑣ/'(x);ᓫᦪஹ᩽▲᩽▲°ᙠḄ±²³ᑣ

8±²´⌕᩽▲᩽▲¶ᑣ·¸ᑣᑭᵨ!ᔠᦪ᩽▲¹º»¼½¾¿ᣚᳮÂÃᑣᦪ᩽▲^ᦪᑡ᩽▲ḄᐵÄÅ▲ᑖḄᦪ᩽▲

9ᢣᦪ᩽▲ᑖÆÇ{᩽▲᩽▲(᩽▲°ᙠḄᐙ⌕ᩩÊ)ஹ᩽▲⚪1ஹ(01-3)lim2;=()xfOA.OB,+ooC.ooD.°ᙠ2ஹ(01-3)sin(x2~1)()lim=—X-lA.-B.lC.2D.O23ஹ(02-3)ylimf(x)=8,limg(x)=8,ᑣÎᨵ()

10A.lim(/(x)+g(x))=ooBlim(/(x)-g(x))=0X—»«x—>aC.lim-----i-----=0Dlim4f(x)=oo,(kw0)Ï/(x)+g(x)x—>«4ஹ(02-3)qlim)+'”=3,ᑣa,bᑖÆ;()XfIX-lA.1,1B,-l,2C.-2,lD.1,-2]e-'2dt5ஹ(02-10)᩽▲lim%H—6ஹ(03-3)lim(|)_2]=()XTXX+1AlBooC1De37ஹ(04-2)]jm(/+//)=.11111"TOO7771AA7T2777^8ஹ(04-3)ᑡØÙ¢£Ḅ+()

11Aᓫᨵ¥ᦪᑡÎᨵ᩽▲B᩽▲°ᙠḄᦪᑡÎ;ᨵ¥ᦪᑡClim/(x)°ᙠḄᐙᑖÎ⌕ᩩÊ+Ç{᩽▲Ú°ᙠDO+º»¼Û9ஹ(04-3)ᑡØÙ¢£Ḅ+()AJifQXsin—=1BJjj^xsin—=1ciimd+4)=iDlimxsin—=0"Too"10ஹ(04-10)]im(Jl+2x—y/l—x11ஹ(04-2)lim•90cÝsin5x12ஹ(04-2)hm-----x->0-sin2x

1213ஹ(04-2)lim(l+-)"=______________஻á8஻14ஹ(04-2)ᑡØÙ¢£Ḅ+()Alimxsin—=1B.hmxsin—=1X—á8XXC.limxsin—=0Dlim(l+-)w=1x*X15ஹ(04-2)qf(x)=â]ᑣlim/(x)=()x1஺A.lB.-lC.OD.°ᙠ+—16ஹ(04-10)lim(—+—)”á81-22-33-4஻("+1)817ஹ(05-2)q4+Za1᩽▲lim%=n-xcn=lAஹ¨°ᙠ]¨°ᙠBஹ°ᙠCஹ°ᙠ]V᩽▲º£Dஹ°ᙠ]äå᩽▲;1

13ÝJ()coszsinrJr118ஹ(05-3)æ0ç2rI119ஹ(O5-io)qlim(1,—axᑗ=0]஺éḄX->00X20ஹ(05-2)ᙠᑡᔜ]¢£Ḅ+()sinx.sinxAlim------=1Blim----=1x->0xx-*sinx.sinx{Clim------=1Dlim----=1XT-00x18X[(arctanf©é21ஹ(05-3)lim7x2+122ஹ(05-10)᩽▲limব11smxKfOx23ஹ(05-10)qlim(02í1_᝞_î=0,஺éIX

1424ஹ(06-2)1î("hï=()is3ᑍ252-3A.03B.0c.eD.ef(ev+siny-l)dy25ஹ(06-8)--------------x

15(l+x)226ஹ(06-3))r=____________18%+J27ஹ(06-8)lim-…2x(1-cosx)28ஹ(06-2)ᑡ᩽▲¢£Ḅ+()1A.lime”=ooB.limex=+ooX->8x->04sin(x2-1)C.limᔳ=1D.lim----------=1XTlXXTlX-\

1629ஹ(06-8)᩽▲lim'smxiox-sinxtanx-x30ஹ(07-7)᩽▲]imx->0x2sinx31ஹ(07-7)᩽▲limtanxrx-sinx|sin"é32ஹ(07-7)᩽▲limx->0x-sinx33ஹ(07-2)ᑡ¢£Ḅ+()Ýsinx[sinxAஹlim——=1Bஹlim=0XTOXxCஹJjjYlxsin—=0DஹJjjYjxsin—=0A-»0%.V->00X

1734.(08-2)ᑡ¢£Ḅ+()AAஹlim-s-i-n--x--11Bóஹlimxs.in—I=IXT8XX->00XCஹlim(l—)'=eDஹIim(l+—)'=cx—>ooXx—>ooX35ஹ(08-2)᩽▲lim/(x)°ᙠḄᐙᑖÎ⌕ᩩÊ+/(x)ᙠx0ᜐAõöBÇ{᩽▲÷ø²°ᙠCÇ{᩽▲Ú°ᙠDÇ{᩽▲°ᙠå`36ஹ(08-7)᩽▲limùúᓃ20x-sinx37ஹ(08-2)ᦪᙠᜐÇ{᩽▲°ᙠ+᩽▲°ᙠḄ()Aᐙᑖ¦Î⌕ᩩÊBÎ⌕¦ᐙᑖᩩÊCᐙ⌕ᩩÊD¦ᐙᑖ§¦Î⌕ᩩÊsn(v2)38ஹ(08-4)lim-12X-5X+67_ar40ஹ(08-7)e2x—5

18[(1-cosf)df41ஹ(09-7)᩽▲limx->0x342ஹ(09-2)᩽▲lim(l+x)1=()XTOAIBeCeoAxA0B1C-1D2Y'44ஹ(09-4)᩽▲lim—=_____________v-—X[t2tantdt45ஹ(09-7)᩽▲lim»~-——r2+x—2ಗ2)᩽▲*(46ஹ7rA-3B-2C1D2

19/ஹ$1ஹ47ஹ(10-3)lim(l+x)r+limxsin—=()x->0x-+oo%AeBe_1Ce+1D/+148ஹ(10-3)lim(xsin---sinx)=()xxA-3B-2C1D-149ஹ(10-3)lim2sm&=3,ᑣk=()3x249A-B-C1D139450ஹ(10-10)᩽▲lim2xTi)(2x)xsinx51ஹ(10-10)᩽▲lim.—I஺+,-ᓄ/0i..sincox1lim-------x->0x

20ctanx2Iim----.SOxcvsin2x3lim-----9஺sin5x4limxcotxA->01-cos2x5lim--------xsinxY6lim2nsinio2"-tan3x7lim------2஺2x8limSm(X<)1஺(sinx)n..tanx-sinx9lim----------iosin'xsinx-tanx10limXTO(#1+r—1)(Jl+sinx-1)

2111lim(l-x)r12lim(l+2x)7lim(—)2xX14lim(l--)faXfooXln(l+x)limXTO161in/Iosinxsin%-sin஺171im--------------x-ac..sin3ᐗ118lim-------XTAtan5x

22Insinx19limn(AB2x)2rw-am20lim--(awO)•fxn-anIntan7x21lim-----------zo'Intan2xtanx22limXTtan3x2ln(l+-)23lim--------xfyarccosx24limInQ+x?)secx-cosx25limxcot2xx->026limx2e'2x->0

232127lim(-F-------—)…x2-lx-l281C(1+D0+Xxcosx-sinx30lim-----------------iox331iox(ex-I)l+cos^x32lim-----------—x-2x+lx-arctanx33limx->0ex'-1^axbxe—e34limx—>0X

2435lirnC--------)-Inxx-\(2x~-x+136hm(---------)x—2x+x-l4arctanX-TC37lim----------------21X-138E/প=0,Gপ=2,ᑣ1H42=xfX-1X+1—391im(q~)2=_________18X-1A1B/C0De-1->3rt^dt40lim—----------*,Q_sinM41EIJK=2,ᑣBAa=2,b=4Ba=4,Z?=-5Ca=\,b=—2Da=—4,Z?=5

2542lim/.=——.2஺Jl+xsinLBJcosx£(tanVr-43lim±-------------------—°f'(tanj-sint)dtxln(l+-)44M/(x)=(B—,X<°,lim/(x)sinQ,,xNORஹSTDUVWSTḄYZSTḄᐙ⌕ᩩ^ᑖ`aᦪḄSTឋ

26deDSTḄᐵghᔠaᦪḄSTឋUVWḄYZjklRஹSTDUVWm⚪)1ஹ(01-3)/(x)ᙠ(—1,1)ᑁᨵYZr

272ஹ(02-3)aᦪy=|x-l|ᙠx=lᜐ()A.STஹdeB.tSTஹtdeCSTஹtdeDtSTஹde3ஹ(03-3)M/*)ᙠ/WᜐtST<ᑣ()A/'஺஺)zuᙠBlim/(x)zuᙠC/'(x0)ztuᙠDlim/(x)ztuᙠ4ஹ(04-2)Mf(x)={|}$<~YZf(x)ᙠx=0ᜐḄ0).xST6ஹ(05-2)᝞aᦪ/(x)ᙠW/ᜐST0,()Aஹ/()2஺Bஹ/(x)>00

28Cஹ4))=0Dஹ/(x)<007ஹ(05-2)Maᦪ/(x)ᙠWx°de0),/(0)=x9ஹ(05-2)Maᦪ”X)ᙠU(-+8)ᑁᨵYZ

2910ஹ(05-2)Maᦪ/(%)=B1|,ᙠWx=lᜐ1ᦪ/(X)ᙠWX=1ᜐST12ஹ(05-2)MaᦪᙠU(fo,+oo){ᨵYZ6

30sin2x+e2ax-113ஹ(05-3)Maᦪ/(x)=´ᙠU{ax=0(-oo,-i-oo)ST,a=sin2x14ஹ(06-3)Maᦪ/(x)=(xx>0ᙠx=0WᜐST<ᑣx2I4-ax<0a=Jl+x—V1—xXG[T<°)U(°

31Aஹ0BஹeCஹeDஹ®ÀÁᦪ18ஹ(07-3)Maᦪ/(x=(1B2Â<)x’°ᙠ(BÃ+8){ST<ᑣ[ax=஺a=()Aஹe2Bஹ/cஹeDஹ-2x2x<019ஹ(08-7)Maᦪ=|1B/_]ᙠST<஺Ḅ஺—~~-----,%>0a,x=020ஹ(08-4)Mf(x)={1ᙠx=0ᜐST<ᑣ஺Ḅ(1+3ᜩG<Æ஺0x+a.x>021ஹ(09-2)M/(x)=iᙠ1=0ᜐST<ᑣaḄ(l-2x)x,x<0Ç()Ae2B/C"2D1

32—sinx+a,x<022ஹ(09-2)Eaᦪ/(%)=0x()A2B0C1D-1Incosx---------xw023ஹ(10-3)ÈÉ/(x)=4%2ᙠx=0WST<ᑣ஺=()x=024ஹ(10-3)Eaᦪ஻x)=N+xQᙠx=0ST<ᑣa=()a+%2%"஺A2BeC-Dy/e225ஹ(10-3)Maᦪf(x)ᙠx0ᜐde

33A|B-C1D--3326ஹ(10-3)Maᦪ/(x)=sin|x|,ᑣ¦ᑡͨªḄ()Aᙠx=0ᜐ=2

34᩽▲uᙠÕ(2)kǯ0,ب஻x)ᙠx=0ᜐḄSTឋe'+/3,x<04ஹElim/(x)=aᑣzᨵA/(x)ᙠ/WSTB/(x)ᙠ/WᨵÀZC/(x)ᙠ/ḄrᑁᨵYZDa=/(x0).1Ùஹxsin—

35X6ஹM/(x)=10,x=0,ᑣx=0/(x)Ḅxcos—,x>0XASTWBdUVWCÛÜUVWD◫₩UVW7ஹM/(x)={/4,ßà=1ᜐaᦪ/(x)2,x=1AtSTBSTtdeCdeseᦪSTDáeeᦪtST8ஹبaᦪy=—<ḄUVWḄklâஹãஹãᜧjãḄ▤ḄæçãḄYZãḄ▤ḄYZjk▤ãḄYZ

36¾ᵨḄvéãã▤Ḅêëv▤ãḄìíîᣚYᳮãwãᜧḄᐵgâஹãஹãᜧjãḄ▤m⚪1ஹ(04-3)«x->0

37A.ãñòḄªᦪB.ãᜧñòᜧḄᦪC.ãᜧñḄ᎔ᦪãñD.BòḄªᦪḄ᎔ᦪãᜧñ3ஹ(05-2)Ma(x)=ln(l+X?),£(x)=2xsinx,«xf0<()Aஹôsõᨵ᩽▲Bஹd(x)Döx)véã)x)Cஹ0(x)DG(x)÷▤ãDஹd(x)æ᜛(x)ù▤Ḅã4ஹ(05-2)«x>0<᝞x"Dxsin஺véã<”=()A3B4C5D65ஹ(06-2)«x->0<¦ᑡãñ©æxù▤Ḅãñ()A.sinxB.x+x2C.VxD.1-cosx6ஹ(07-2)Maᦪy=f(x)ᙠWx=x0Ḅeᦪ/'(%)*0,dyḄÚaᦪᙠWx=x()Ḅúᑖ

38Aஹ«Ax->0,dyæAyù▤ḄãBஹ«ߟ0,dyæAyþ▤ḄãCஹ«—0,dyDAyvéãDஹû{üýᙳ
7ஹ(08-2)x-»0ᑡ()11,Axsin-B—sinxCInx~De'xx7ஹ(09-2)ᑡᦪ0Ḅ()»-2Ax2sinxB3x2Csinx2D——38,(09-2)xfO,ᑡᦪsin(/)Ḅ()AxBx2CsinxD1-cosxᓄ

391ஹᑡ⚪"#ḄA$%&ᦪᜧ()ᜧB%ᜧ()C*ᦪᜧDᜧḄ᎔ᦪ2ஹ,a=^~—>p=1-Vx,xf1,1+xAa-Ba.᜛0▤Ca.42▤Da᜛3▤3ஹ,/(%)=6ஹ+3*-2,xf0/(x)x8ஹ9ᦪ:ᑖ<=>ᐹ@ᦪA9BCᦪA9◚ᦪA9

40EᦪA9
ᦪA9ᢣᦪA9ᑖGᦪA9HᑣA9>ᑣJᔠᦪA9LᦪA90▤A9

41▲)ᑖA98ஹ9ᦪ:ᑖN⚪1ஹ(01-3)/(x)ᙠx=x0P9Q")=3ᑣ”->0h/,(x)=()0A.3B.2C.lD.Ox22ஹ(01-3)°(x)=Rinx2dxᑣ°(x)=()oA.sinx4B.2sinx4C.cosx4D2xcosx43ஹ(02-10),y=l+—Ay”4ஹ(02-10),஻^———,Wy=Qsinx,z=cosx,AX.஺[+1dx

425ஹ(04-2),ᱏp(x)=[sin/2]^llp'(x)=6ஹ(04-10).,y=xJl-x?+arcsinx,Ay'7ஹ(04-2),y=arctantx,^ljdy=8ஹ(04-3)ᑡ_`"#ḄOA.dlnx=—dxB.dcosx=sinxdxx132C.darctanx=------dxD.dx=3xdx1+x29ஹ(04-10),y=ln(x+J/+Y)Ay'10>(04-10),abarctanc=InJ/+d#

4311>(05-3),ᦪy=/(x)ᵫabn-2+2,=0#<pq/(0)=12ஹ(05-2),ᦪf(x)ᙠrxᜐP9pqf(x+h)7(x-7h);()lim/i->0hA./(x)B2/'(x)Cf'(x).D8f'(x)13ஹ(05-2),ᦪ/(x)ᙠwx(-8,+oo){|}pq"J7(x)dx()Aஹ/(x)Bஹ*(x)dxCஹf(x)+c(c&ᦪ)Dஹf(x)dx14ஹ(05-3),ᦪf(x)ᙠr/P9pqᓝ)-'஺)=XfX0

44—te■f6,-.,pqy=ledu(0)=________16ஹ(05-10),ᦪy=/(x)ᵫab2"'=x+y#<pq0)=________17ஹ(06-2)y=xsinx,^ljdy=()A.(1-cosx)dxB.cosxdxC.(sinx+xcosx)dxD.(sinx+cosx)dx18ஹ(06-2)Ḅ◤AᦪP=10-?,ᑣ஺=30Ḅ▭ᦈ¡()A.-2B.-3C.2D.38ஹ(06-8)^y=e~xsinx,Ay"

4519ஹ£06-2¤,ᦪ/£x¤ᙠrx=lᜐP9Q∎""2?প4ᑣ§প¨£¤20ஹ(06-2)3᝞஺=Lx>0,ᑣ/(x)=()d(x")xA.2x+cB.2y[x+cC.ln|x|+cD.21nx+cx=ln(l+)21ஹ(06-3),|,ᑣª=_________dxy=arctanx22>(06-8)y=71+x2+Incosx+e2Ay'23ஹ£07-2¤ᖪḄ◤AQ£ᓫ²³´µ¤¶p£ᓫ²:

46ᓟᐗ¤Ḅᐵ¼Qp
=15”pe[0,10],ᑣ¶9ᓟᐗḄ◤A½ឋ£¤Aஹ3Bஹ-3Cஹ9Dஹ-924ஹ(07-3)y=e%sin(3+5x),ᑣ:ᑖdy=()Aஹe-2v[-5cos(3+5x)-2sin(3+5x)}/xB^-2A[5COS(3+5x)+2sin(3+5x)]t/xCe-2x[-5cos(3+5x)+2sin(3+5x)]dxDe-2v[5cos(3+5x)~2sin(3+5x)]dx25.(07-8)¿ÀḄEᦪabÁ=%:ÂÃIe“Ä+=0y-2e2dxdx~26ஹ(07-4),ᦪy=y(x)ᵫabcos(xy)=e-*=lnyᡠ#<ᑣdy__dx

4727ஹ(07-7),ᦪy=y(x)ᵫab/+n-e2=0ᡠ#<Ay'(0)28ஹ(07-7),/(x)P9ᦪQÆÇ(È“Ê=/+/(x),A/(x)29ஹ(07-2),/'()Ëᙠ,ᑣᑡ4᩽▲Í/'(/)Ḅ()Aஹ/(x0-Ar)-/(x0)Bஹ/(X஺)-/(/+Ð)Î?-----Ï-----limhCஹlimVÑDஹlimXfXoᑍ”(Jhf(x+2h)-f(x)30ஹ(08-2),ᦪ/(x)P9,ᑣlim20h

4831ஹ(08-7)ᦪ/(x)ᙠ0,1
P9/(x)>0,/(0)=lQᙠ0,1
ÆÇÓ/(x)ߟÔR"")=0,Aᦪ/(x)x-132ஹ(08-2)y=y(x)ᵫabn+lny=0#<ḄᦪAdy__dx33ஹ(08-2)ᖪḄᦈᐭᦪ=▭ᦈᐭ%2=________34ஹ(08-2)ᦪ/(x)=xcosx,ᑣ/d)=V=“Tr35ஹ(09-4)Eᦪab{Ö-ᡠ#<ḄᦪḄ-▤9ᦪy=arctant

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529ஹRᦪ/*)=ST@""I,ᑣ஻x)ᙠx=lᜐḄX2,XZ1AP\#ᦪ]ᙠBP#ᦪᙠ^\#ᦪ7ᙠCP#ᦪ7ᙠ^\#ᦪᙠDP\#ᦪ]7ᙠ10>Ry(_=sinx2sin2xy'(x),y"(x)11Z:ᦪy=y(x)ᵫ<=e@-`=eEF@G@axaxx=f-ln(l+f)d2y12ஹ432@bTy=t+rdx~13ஹy=*c,dy

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73©ᓄ«¬1ஹᙠQ-.জ®)±f'(x)<0,f"(x)

74Irr4ஹeᦪy=asinx+-sin3xᙠx=—ᜐ¾᩽A¿Ua=33AOB1C2D35ஹx>1AÀLex>ex6ஹ)ᦪ/(Á=Â-2|/ᙠ0,3
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7613ஹLM:Ú>0,ex-(l+x)>1-cosx14ஹe/(x)ᙠ[0,1]*ghAᙠ(0,1)*xyAi”0)=1,஻1)=0,)Lᙠ(0,1)ᑁᨵd4,^/Þ)=-ß2—Inx,—

7717ஹ/(x)eC[O,1],0

78/'c)gc)=/e)g'c)21ஹQRx>00SC(x2-l)ln^>(x-l)2h—nb-n22ஹQ---

79ᣚᐗ^ᑖbᑖc^ᑖbஹ#$%ᑖ⚪1ஹ(01-2)^f(x)dx=tan—+c,hlJ/(x)=_2ஹ(02-2)i/(x)Ḅj_ᦪCWO\xf(x)dx=()A.€A(1—x)+cB.cK(1+x)+cCe1(x—1)+cD-cA(1+x)+c3ஹ(03-2)/(x);ABᦪCᑣt72(x)4*)=

80x4ஹ(04-2)f,dx=()5ஹ(04-2)vᑡxU]yzḄi()Af—dx-arctanx+cBjsec2xdx=tanx+cJl-x2C.arcsinx+cD.[cos2xdx=-sin2x+cJ26ஹ(04-10){|jxsin2xdx7ஹ(04-2)f—____________JCOSX8ஹ(04-10)}

819ஹ(05-3)10ஹ(05-3)/~஻=11ஹ(06-2)/(x)+C=pinxdxh()A.OB.lC.sinxD.cosx12ஹ(06-8)}(LᓾxJ77^713ஹ(06-2)/(x)+c=jsinxdx,ᑣy'(;=()A.OB.sinxC,——D.cosx2Jfin*14ஹ(06-3)

82dx15ஹ(06-8)}]-^ᑖJx2\lx2+916ஹ(06-8)}]-^ᑖ■dx17>(07-7){|]-^ᑖ(cosx+f'Mx18ஹ(07-7)}]-^ᑖ19ஹ(07-7)}]-^ᑖJarctan4dx20ஹ(08-2)vᑡᔜCyzḄi()

83cjsinx^r=cosx+c21ஹ(08-7)ᦪ/(x)Ḅj_ᦪ;cosx+xsinx,}^ᑖ^x+f(x))ff(x)dx22ஹ(08-2)ᦪ=}C'஺>◘X23>(08-7)}]-^ᑖJ2x(cosx-e)dx24ஹ(08-7)*i/(ᐗ)Ḅj_ᦪ,\xf\x)dx

8425ஹ(09-2)/(x)Ḅj_ᦪ;Cᑣ/''(x)dx=()A2sinxsinxAcosx-------B----+CXX\sinxc2sinx\C2cosx-----Dcosx--------FCXX26ஹ(09-2)]-^ᑖinxcosxdx=().2sin2x-)AAB^-^+CDCOS-X22227>(09-7)}]-^ᑖ-7=2=~~dxJVx+l+328ஹ(10-4)/'()=sinx,ᑣJ/(x)dx=29ஹ(10-10)}]-^ᑖJxe2dx

8530ஹ(10-4)᝞(x)dx=᮱+c,ᑣ(12Mx=()A2(l-2>+cB-2(12)2+CC-(l-x2)2+cD--(1-X2)2+C22ᓄ¢£1ஹ\e5,dt2ஹJ(3-2X)3(/X3ஹ¤Jl-2x5ஹ1(sinax-e^)dx

867ஹJsin2xcos3xt/x8ஹfcosxcos—JxJ29ஹJsin5xsin7xJxI஺ஹ¥dx11ஹ(x+l)(x—2)12ஹdx13ஹ1+Gdx14ஹ1+71-x215ஹvᑡᔜyzḄi

87A\f(x)dx=F(x)+c,hijj-/(Inx)dx=F(lnx)+cdB区f(t)dt=2xf(x2)Cd瓦£/(x)Jx=/(x)D若1J/(x)dr=arcsinx+c஺ᑣ/(x)16ஹᦪ/(x)ᐹᨵABḄHᦪCᑣJ[M"(x)+/(x)Mx=Axf(x)+cB(2x+1)+cC2(2X+1)2+CD|(2X+1)2+C17ஹ;(x)=2,/(0)=l,ᑣ/(x)/(x)dxA2(2x+l)+cB|(2X+1)+CC2(2x+l)2+cD-(2X+1)2+C18ஹḄx

88fj2x+\20>jedx21ஹ/(x)Ḅ•jᦪisinxh1J/''(x)dx=22>j/(x)dx=ChijC/(•!•+l)dr=A2±প+cBF(|)+cC´+l)+cD2F(|+l)+c(•ln(x+l)+c23ஹJx(x+l)dx=____________A-ln2(l+x)+cB--ln2(-^)+c22xc1i2/Xஹci/X+l\C—In(----)Dln(----)+c2l+xx24ஹarctanyfxdx

89256”iḄ_ᦪ/(%),ᑣj\஻x)dx=Ae-X(l+x)+cBe-*(1-x)+cCe~x(x-l)+cD-e-x(x+l)+c26ஹJxalnxdx,a;¸¹ᦪ27ஹiভ»(ḄABᦪCᑣ/(%)ᨵj_ᦪ;28ஹ29ஹ”x)i(fo,+oo)ᑁḄᏔᦪC±(x)i½Ḅj_ᦪCᑣ__________ᑣᗞ30ஹIn/(f)=costAZcos/-sin/4-cB£sin£—cost+cC£(cos£+sin£)+cDfsinf+c

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92d(f/ÒO)xcosx.A.=/(X)B.[-------ax=0dx11+x2Ccos2xdx=0D.(f/ÒO)C=f(x)-f(a)•ᑍ6ஹ(04-10)ÓJ/_]dx7ஹ(04-2)JInxdx=8ஹ(05-3)/=[cos"xsinxdx,ÔÕ()A/>0B/<0C1=0DI=7i9ஹ(05-3)£(x3+1)Isinx)dx=10ஹ(05-3)ᦪ/(x))*1/VOÔÕ/(D=______

93/\/\f1+sinx,\11ஹ(06-2)--------dx=()L1+%A.--B.-C.--D.224412ஹ(06-2)vᑡ1yzḄi()f/(xRx=/S)B.ff/(x)Jx=/(x)dx&dx*dAd2sxtC.—\f(x)dx=f^D.—ff(t)dt=f(cosx)dx&dx&13ஹ(06-8)}14ஹ(06-2)vᑡ^ᑖCᐸ:;ÖḄi()A./dxB.£-~~dxcj'1—3×D.[xsin2AZ/X

94yf11+sinx,/ஹ15>(06-2)-----—dx=()L1+/16ஹ(06-7)}-^ᑖÙsinx^x17ஹ(07-3)7஺Ú=/,h1Û\3)=()Aஹ0Bஹ3Cஹ6Dஹ918ஹ(07-3)vᑡ-^ᑖCᐸ:;0Ḅi()Bஹ^(x3+3x+\)dxDஹj(eC+L19ஹ(07-3)-^ᑖÐ(4+ᡃ057+1)ÑḄ:;()Aஹ0Bஹ1Dஹ2

9520ஹ(08-2)^e2xdx=^h×=21>(08-7)f(x--)=x24--^,{|L(x3cos2x+/(x))dxxx22ஹ(08-7){|23ஹ(09-4)/(x)=x—ff(x)dx,ᑣ/(x)=24ஹ(097)}1/পÝᐹ/(%)=/X+1,1

9625ஹ(09-2)ᦪ/(x)ABC/(Þ)=᮱+2(/஺×Cᑣ/(x)=()99Ax2Bx2--Cx2+-DX2+233.32“lஹX28ஹ(09-7)}-^ᑖf2xlnxdx29ஹ(10-3)“(x+i)cosxdx=()~2AOBlC3D230ஹ(10-4)/(x)iGHḄᦪC/(0)=1ᑣ)*âã

97^f(t)dt=xfM-x2Ḅᦪ/(x)=31ஹ(10-10){|-^ᑖ'QcosVLix7132ஹ(10-10)fQ2}XḄ:(Ä)-^ᑖḄÅᵨQ☢^ஹÍ^1ஹ(02-10)}V=2xᙠ(-0.5,1)ᜐḄbåZ/=2xᡠçḄ☢^2ஹ(03-10)èå”/஺)(é஺,ு)ᜐḄᑗåë᳛;Þ+1,Xíèåîï(1,L)2(1)}ᦪஹ=/(x)(2)}ᵫèå)>=/(x),y=0,x=lᡠçÉÊñËÌᕜᡠPËÌÍḄÍ^V

983ஹ(06-2)ᵫèå)C=3-Þ2#Þ=2%ᡠçÇ☢ÉÊḄ☢^S=()A.£(3-X2-2X)dXBஹ〈—J3—y2ᑁCஹy?dyDஹ.L(3X2-2X)JX4ஹ(06-8)}ᵫèåy=lnx,yñZóåy=lng,y=ln5ᡠçÉÊḄ☢^஺5ஹ(07-3)ᵫèå)C=1117#óåô=2,)C=0ᡠçᡂḄÇ☢ÉÊöôñËÌᕜ÷ᡂḄËÌÍḄÍ^V=()AஹfInxdxBஹ7ifIn2xdxCஹTCf

992xdxDஹfInxdx

1006ஹ(07-3)ᵫøᱥåy=x2#x=VçᡂḄÇ☢&úḄ☢^i7ஹ(07-8)}øᱥåy=fZóåy=xᡠçᡂḄÇ☢ÉÊḄ☢^ûíÉÊöxñËÌᕜᡠçᡂḄËÌÍÍ^஺8ஹ(08-7)óåx=aüøᱥåx=VZóåÞ=1çᡂÇ☢ÉÊᑖ;☢^ý1Ḅþcᑖ஺}஺Ḅ:9ஹ(08-7)èåy=«y=VᡂḄ☢Ḅ☢10ஹ(09-2)ᵫy=6ᙶ᪗x=1ᡠᡂḄ☢Ḅ☢#()A1—eBe—\C1—De—l

10111ஹ+09-10,ᙠy=6-f+xு0,0123453ᜐḄᑗᙶ᪗ᡂḄ☢Ḅ☢ᨬ9:;ᨬ9<஺12ஹ+09-7,;ᵫ—=2yy=x+4ᡠᡂḄ☢Ḅ☢஺13ஹ+10-4,V=xy=x-2ᡠᡂḄḄ☢B14ஹ+10-10,;y=|lnx|x=,x=e,y=0ᡠᡂḄḄ☢

102315ஹ(10-4);y=±x+y=4ᡠᡂḄḄ☢xFᓄHI1ஹJK=['«-1)2«-2Oᑣᫀ1=஺2ஹRA/1-COS2xdx-"2AOB1C2D43ஹ4ஹ;y=/Ry2=xᡠSxTUᕜᡠᡂWXḄX

103xdx5ஹ1Vs-4x26ஹJ/+x,=+t2dt,ᑣ/'")=arctanx_7ஹ---=_______________£1(1+x)9ஹJe*=f,ᑣ['dx=_____0ex+e~xA^/"dtB[-l=dt1cr.1dtDb0cde47?TT10>£(x271-x2+x3J)+XஹMx=

10411ஹᓃ|sinx|rfx=212ஹlᑡnopq1Ḅ#A—

10516ஹJuᦪ/w)ᙠx2yz0{|x3f(x2)dx=£xf(x)dx£xf(x)dxC21xf(x)dxD£xf(x)dx17>^4cos46l/^218ஹ}~ᑖ(__________ᦈ19ஹ⁐^'f(t)dt=ex,ᑣ/(%)=__________dxᓽA-x-2Bx2Ce-2xD-e2x20ஹJ/(x)B{|uᦪᑣlᑡᡂWB"xf*)

106Cj-ff(x)dx=/(«)ᖽ£7/=/(X2)21ஹlᑡᑖq1Ḅ#A^"=——1=-2BKsinxdx=2[2sinxdxJ-'x2x-1J-ACx2sinxdx=0Df]y11-x2dx=2fP1-x2dx=7r22ஹ-cosx\dxᐗuᦪᑖᓝஹᐗuᦪḄᦪ

107ᐰ+ᐰᑖ,sḄᐵᔠuᦪ;ᑣ+oᑣ,ᐹXuᦪ;uᦪ;◚uᦪ;

108sḄᐵᓝஹᐗuᦪḄᦪ¢⚪1ஹ+01-3,lᑡ¤q1Ḅ#+QA./+x,y,ᙠ3+x+,,yo,{|ᑣ+/¦0,£§+¨ᡭ,ᙳ«ᙠB.fr+Xoyo,f§+Xoy+¦,ᙳ«ᙠᑣ/+X,y,ᙠ3+ᐭ0,{|c./x+Xoyo,,f§+Xoyo,ᙳ«ᙠᑣ/+X,y,ᙠ3஺0%,sD./'+/,,,¯஺0%,ᙠ3஺0ᡭ,{|ᑣ/+x,y,ᙠ3+x஺,%,{|V2ஹ(01-10)J/(஻/)s,z=/(—,²),;dz.y

1093ஹ(02-3)Jz=/(x,y)ᨵµ▤ᑣ()d2f_d2fd2fd2fABzdxdydydxdxdydydxCzᙠ(x,y)ᜐsD·¸{|·=¹dxdydydxdxdydydx4ஹ(03-10)Juᦪz=z(x,y)ᵫº»¼+2y2ᦪ=0ᡠ-.,;dz'(°5-3)J½¾¿+g3-----------6ஹ(05-10)J⁐=lnÁ(x+zwO),;Ä2Åzydxdxdy7ஹ(05-10)Juᦪ/(«)suᦪ=(p(x,y)ᵫº»

110a7a,x-az-/(KÆ)12^a—+h—oxdy8ஹ(05-10)Juᦪ/(஻#)ᨵ{|ᦪz=f(xy,-),;)ydxdy9ஹ(06-3)Jz=z(x,y)ᵫº»/+y2+/-2x+2y-4z-10=012ᑣ——10ஹ(06-8)Jz=/(x+y,y2-x),ᐸp/ᐹᨵµ▤{|ᦪ,;---dxdy11,(06-2)Juᦪy=y(x,z)ᵫº»xyz=e"ᡠ12ᑣÉ#dx()

111A.*C,D,1-yx(l-y)X(l-y)x(l-y)12ஹ(06-8)Jz=/(x+yF—ᐸpÌ=/(஻ᑗᐹᨵµ▤{|ᦪ;ÍÎdydx13ஹ(06-3)Jz=z(x,y)ᵫº»xy+yz-e»'=012ᑣdz_14>(07-4)Juᦪz==xy,u=y,ᐸp/ᐹᨵ{|ᦪᑣ⊵

11215ஹ(07-3)Jµᐗuᦪz=e*ᑣÒ=()dxdyAஹV/Bஹfe"Cஹx*Dஹ*(l+xy)16ஹ(07-7)Jµᐗuᦪz=ᵯ/;u=2x-y,v=x+2yo;ᵯᒹv-dxdy17ஹ(07-3)Juᦪz=e%ᑣ×a,o)=()Aஹ1Bஹ0CஹeDஹe-'18ஹ(07-7)Jz=f(Q//Ú2)jᐹᨵ{|ᦪ,;dzdzy+x—dxdy

11319>(08-7)Juᦪz=z(x,y)ᵫº»X?+V+/-6z=012;dxdy20ஹ(08-7)Juᦪz=/(஻#),“=²,vᨵ{|ᦪ;dz%21ஹ(08-2)z=/2+"ஹ'ᑣÞ=(L2)22ஹ(09-2)lᑡßàáâq1Ḅ#()Auᦪ/(x,y)ᙠ3(x,y)sᑖᑣ/(x,y)ᙠ532{|஺Buᦪ/(x,y)ᙠ3(x,y){|ᑣ/(x,y)ᙠ532sᑖ஺Cuᦪ/(x,y)ᙠ3(x,y)ḄᦪÉãᙳ«ᙠᑣ/(x,y)ᙠdxdy53•2{|஺

114Duᦪ/(x,y)ᙠ3(x,y)Ḅᦪå%ᙳ«ᙠᑣ/(x,y)ᙠoxdy532sᑖ஺Q2Z23ஹ(09-7)Jz=/(x+%æ),/("/)ᐹᨵµ▤{|ᦪ;Uoxoy24ஹ(09-2)Jµᐗuᦪz=x'+e%ᑣᒹ=()dxA/è+/>'ByxT+y/Cxvlnx+e"Dx'lnx+ye”25ஹ(09-7)Jµᐗuᦪz=z(x,y)ᵫº»x+y+z=sin(²z)ᡠ12,4a226ஹ(09-7)Jz=sin(jy)+x+y,;———dxdy

11527ஹ(10-10)íuᦪf(x)#{|uᦪ/(2)=3,î2)=0ï/(x)dx=2ð;^x2f"(2x)dxå/(஻)µ▤s;ᙠ28ஹ(10-10)Jz-)29ஹ(10-3)íz=In(æ),(x>0,y>0),òUxᒹ^ô=()dx'dyAxBæCx+yD030ஹ(10-4)Jµᐗuᦪz=arctan)ᑣ=_______xdxdyFᓄHI

1161ஹJt=lnZ,;ᒹzydy2ஹuᦪz=/+x,y,ᙠ3+÷,ᡭ,ᜐḄᦪ+ᐭ0ø,ஹ/ð+x+,,yo,{|#uᦪz=/+xy,ᙠ3+%,ù,«ᙠᐰᦻᑖḄAᐙᑖᩩýBþ⌕ᩩ
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3ஹ/,,ᐹᨵḄᦪyᒹ+!ᒹoxdy4ஹ#ᐗ%ᦪz=/(x,yᙠ(+,ᡭᜐ./Ḅᐙᑖᩩ
0A/(x,yᙠ(1,3ᜐBfVWx,yQ,ᙠ(+,ᡭḄ567ᑁ9ᙠCAz-f'Wx,yAx-/<(x,yAy=>?+᝞-0A,00000BCD

117Az-/<(x,y)Ax-/<(x,y)Ay0000lim-------------=^=---------D-fOJ(Ax)2+(Ay)2Ay->05ஹ஻+ᐸR/ᐹᨵ#▤ᦪᑣeita஻Xk—r-*V+WXYZ6ஹ2sin(x+2y—3z)=x+2y—3z,_!ab+b=__________8xdy7ஹ%ᦪ/(x,y=f+y4,ᑣᙠd(0,0ᜐ(0,+e=oAᦪ9ᙠB>ᦪg9ᙠCg>ᦪ9ᙠDghᦪg9ᙠ

1188ஹz=x>'lmnoḄ0()Apd2z--^=0----->0nBALdxdydydxdxdydydx„S2zd2zd2Znc----n-----<0D---------WOdxdydydxdxdydydx9ஹᵫuv++=\ᡠoxḄ◚%ᦪz=z(x,yᙠd(1,0,-1ᜐḄᐰ/ᑖdz=10ஹz=/(x,y)0ᵫuvz-y-x+xeLL*=0ᡠoxḄ#71s%ᦪᑣdz=11ஹ%ᦪz=f(x,y)ᨵᔞ=2,h/(x,0)=lJ(x,0)=x,ᑣ5y-f(xy)=()9Al-xy-y2Bl+x+y2Cl-x2y+y2Dl+x2y+y2

11912ஹ+Jᐹᨵᦪ஺,y%13ஹ:&.f(x+y,-)=x2-y2,ᑣ/(x,y)X14ஹ#ᐗ%ᦪf(x,y)ᙠd(x,y)ᜐḄᦪ00£(%,V)(/ᡭ)9ᙠ0ᙠdḄAᐙᑖ⌕ᩩ
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12017ஹᑡ⚪noḄ0Az=/(x,yᙠ(%0%ᜐ./ᑣ!‘஺,W"<஺,ுᙠdᜐBz=/(x,yᙠ(%,%ᜐ./ᑣ/<(%00/<(ᐭ009ᙠCz=/(x,yᙠ(+,ு0ᜐ!,ு஺஻/ு஺9ᙠᑣ/(x,yᙠ(%,%ᜐDz=/",ᙠ(XoyoᜐḄ#▤ᦪ9ᙠ(B0’0/(*0ᑣᙠ(+,ᜐ18ஹ_U"M(ij.i=ᓝஹ¥ᐗ%ᦪᦪḄ¦ᵨ᩽©+ᨬ©(ᒹ«ᩩ
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121¬¦ᵨ®¯°±Ḅᑗ±+³´☢®¯°☢Ḅᑗ´☢¶³±uvᓝஹ¥ᐗ%ᦪᦪḄ¦ᵨ·⚪1ஹ(01-2)ᳫ☢W2+>2+¹=6,ᙠᓰ(1,2,-1)ᜐḄᑗ´☢uv02ஹ(02-2)°☢Z=x2+y2~\ᙠ(2,14)ᜐḄᑗ´☢

1223ஹ(03-2)°☢"-[+=3ᙠd(2,1,0)ᜐḄᑗ´☢uv4ஹ(04-3)f(x,y)ᙠd(Xoy0)Ḅ67ᑁᐹᨵ▤#▤ᦪhfx(/jo)=0,f¼½0)0)=0A=¾(%+>0)B=<(Xo+yo)C=H<(Xo+yo)H=B2-AC,/(+ᡭ)᩽ᜧ©ᑣ()A.H>0,A>0B.H>0,A<0C.H<,A>0D.H<0,A<05ஹ(05-3)°☢2xy+z=3ᙠd(1,2,0)ᜐḄᑗ☢uv6ஹ(05-3)ᙠd(1,1)ᜐ᝞Áz=Â2+2+2#ᐗ%ᦪÃÄᨬ©ÅÆ()Aஹa=—l,b=—1Bஹa=l,b=—1Cஹa=-l.b=lDஹa=l,b=1

1237ஹ(07-2)Çᳫ☢/+>2+822=16ᙠd(2,3)ᜐḄᑗ´☢uv()Aஹx+y+4^=-8Bஹx+y+4z=8Cஹ2x+y+4z=16Dஹ2x+y+4z=-168ஹ(09-2°☢x2+y2_z_2=0ᙠ(2,1,3ᜐḄ³±uv%(09-7Èd஺2Éh+ʱË

124ÎᓄÐÑ1ஹ#ᐗ%ᦪz=/y(4-x-y)ᙠᵫʱx+y=5,xÒyÒᡠÓᡂḄÕÖ7஺×Ḅᨬᜧ©ஹᨬD©஺2ஹÇᳫØf+y2+8z2=16ᙠd(2,2,1)ᜐḄᑗ´☢uv3ஹÇᳫ☢/+2/+3^=6ᙠd(1,1,1)ᜐḄᑗ´☢uv272QÙ4ஹ°±x+ு+“ᦇᙠd(i)ᜐḄᑗ±uv0______U2!3e+5[—4=05#ᐗ%ᦪf(x,y)^x+xy-x*2-***y2ᙠÂ

1250(0,0),A(1,0),8(1,2),E(0,2)⚔dḄÕÖ7×஺Ḅᨬᜧ©¶ᨬD©6ஹ#ᐗ%ᦪz=/(x,y)ᙠd(Þ,ᡭ)ᜐḄᦪ(Xo%)=fஹ(Xo%)=O.ᑣd(½°%)x0%ᦪf(x,y)Ḅ()A᩽ᜧ©dB᩽D©dC᩽©dDàdᓝ#ஹ#áâᑖÊãᙶ᪗æḄX-çâᑖÖ7Êãᙶ᪗æḄè-çâᑖÖ7

126᩽ᙶ᪗æḄ-çâᑖÖ7ᓝ#ஹ#áâᑖ·⚪122x\I1ஹ(01-10)ᦋê#ëâᑖ/=^dxJJdy+JdxJeᔆdyḄâᑖëí,oxix2îïð/I4x4y/x2ஹ(02-2)ñᣚâᑖëíJdxI/(x,y)dy-^-]dxJf(x,y)dy______0-ó1x-2

1273ஹ(03-3)Ö7Dl

1287ஹ(05-10)°☢2="1+>?2=0,/+ு2=û2ÓᡂḄüýḄýâV8ஹ(06-3)ñᣚ#ëâᑖḄâᑖëí1dx£/(x,y)dy=9ஹ(07-7)´☢Ö7D0ᨵᙊᕜV+y2=iᡠÓᡂḄÕÖ7,ïð#áâᑖÙÿ
10ஹ(08-7)ᑖ^y-x2\dxdy,ᐸD={(x,y)IO

12911ஹ(09-4)ᣚᑖḄᑖW4=----------12ஹ10-10£0127'/'"ᓄ$%1ஹ&ᵫ┵☢2=17*+,-ᱥ☢z=6-/—>2ᡠ4ᡂḄ67Ḅ72ஹᣚᑖḄ89dx&y(x,yM)=

1303ஹJJ(2x-y)dxdy,ᐸBᵫCDy=l,y-x-l=0*DX+y—3=0ᡠ4ᡂḄH☢IJ4ஹ+,ᐸ஺={(x,y)l/+y244,yZ0}D5^\\xydxdy,ᐸ஺BᵫCDy=l,y=x*x=2ᡠ4ᡂḄHD☢IJ6ஹQᑖJ஺BᵫRDy=f*y=2_fᡠ4ᡂᑣJ//(x,y)dxdy=()DA^dx£]x'f(x,y)dyCXdyj^/(x,y)dxD[9'd)£/(x,y)dx

1317ஹ\஺:14^+_244,/ᙠ஺ab,ᑣJJf(M+y2)dxdyᙠ᩽ᙶD᪗fgh()AI=2ᾓ/f(r)drBI-27r[^r2f(r)dr-^r2f(r)dr]CI=24rf(_)drD/=2^[J9rf(r2)Jr-£0c1=2(//(x,y)dxdyl0

132Dnoᙳqr11ஹ&ᙊt☢/+y2=2yu┵☢z=gT7xH☢Z=0ᒘz{ᑖḄ☢஺ᓝ}ஹRDᑖ~RDᑖ~RDᑖᓝ}ஹRDᑖஹR☢ᑖ1ஹ(01-10)\RDᑖL=*+/(%)]"-/প
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133&/(x)xḄL2ஹ(03-10)RDᑖ[(/+/)+2ᐸLB-ᱥDy=/ᵫo(0,0)ᑮA(1,1)஺3ஹ(02-10)&RDᑖJyeZx+(/+3y2+l)dy,ᐸL(0,1)/ூ(2,2)Ḅ¡ᩩᐝ¤RD஺4ஹ(05-20)\z¥ᑖᙠᐰH☢oᐵ;3Y2L-y2(p(x)dx+S(x)-—]ydy

134ᐸ¨ᦪMx)ᐹᨵabᦪª«1)=1পஹ&¨ᦪ᜛(X)(2)ஹ&ᑖ/Q®2/=1(0,0)2yz(p{x)dx+W°)--]ydy5ஹ(06-3)\LBᓫa²IJDḄ³´µ¶ᔣDḄ☢A,¸U45ydx+3xdy=6ஹ(07-3)\H☢RDCBº(1,1)ᑮº(2,3)ḄCDᑣrᙶ᪗ḄRDᑖ\lxdx+(y-x)dy=()Aஹ-4Bஹ4Cஹ2Dஹ6

1357ஹ(08-4)\Lᢥ⌮¾┐ÀᔣÁÂḄᙊᕜd+y2=i,ᑣRDᑖ\xy2dx+x2ydy=8ஹ(09-7)\LᨵᔣÅᢚDOABO,ᐸO,A,BÈBº0(0,0),A(1,1),B(0,1),ᑖjxe-y2dy9ஹ(10-4)\L⌮¾┐ÀᔣḄᙊᕜV+y2=9,ᑣJ(2xy-2y)dx+(x2-4y)dy-"ᓄ$%1ஹ\ᨵ´ÅIJDᵫᑖᐝ¤RDLᡠ4ᡂLµÊᔣ¨ᦪP(x,y),Q(x,y)ᙠDoᐹᨵ▤abÌᦪ,ᑣᡮ/x+QdyA1Dᗔa°Xbc*I*f(dÎy-dÏxÐy

136cUW-ÑộyD!ÕÖ×ÓDoxoJy2ஹ\LÊᔣḄᙊᕜx?+y2=4,ᑣRDᑖ^y(ye2+Y)dx+(2yex-x)dy=3ஹ\ᙠRDLoᨵÙÚabLḄÛᦪÀÜ°"),(aWfß᜛),ᐸ᜛à,஻àᙠ8a,â[oᐹᨵ▤abᦪ9'2(f)஻'(f)wO,ᑣRDᑖJ/(x,yMs=()LA/(᜛஺)஻(஺)
Bdf(9প&পgপW’2পjC/C°(f),pà)J”(t)W)dtDk(p(t)"(t))dt4ஹ/=j(çsiny+y)é+(e*cosy-x)dyᐸLy=_54-VᵫA(2,0)8(2,0)Ḅìí

1375ஹRDᑖJPdx+Q/yᑖL(AB)ᐵḄᐙ⌕ᩩðL(AB)6ஹ\LBᙊᕜx2+y2=-2xḄÊÀᔣᑣRDᑖ-y)dx+(x-y39=()3A-2ñB0C—71D2427^ᑖ/=k'siny+y+7r)dx+(e*cosy-x)dy,ᐸLBLº4(1,0)òzóᙊᕜ0-4)2+?2=91º8(7,0)Ḅ8ஹ\LBºA(l,g)RD2y=/ᑮº8(2,2)Ḅíᑣ

1383A-3BOC-D329I=(^2(x2+y2)Jx+(x+y)2Jy,ᐸLBnºA(1,1)B(2,2)C(1,3)⚔ºḄ}õöÊᔣ³´ᓝ÷ஹøùú᪆ü¡ᔣýþᦪᔣýHÂᚖḄᐙ⌕ᩩᔣḄᦪ☢Ḅ

139Ḅஹ☢Ḅᐵᓝஹᔣ᪆⚪1ஹ(01-2)☢&'Ax+By+Cz+D=0,☢.xx}*2'&X++C2Z+஺2=01'2'312ᚖḄᩩ5()A.AjA+B4-C]C=0B.AA++CC+=0222212c^'=^'=DA]=5]=G=3ABCABCD22222222>(02-3)=ᨵ☢“Jx-y+2z=6,E2'2x+y+z=5,ᑣ()A.n,//nB.n,1n22

140C.E|E2ḄᜳLMfDfhE2ḄᜳLM3^(03-2)☢x+2y-z+3=0NO=NP=QEḄ3-11ᐵ5()ARSᚖBRSVXUᙠ☢NCTUVWUᚖDᙠ☢N4ஹ(05-2)=a,᜛5[\ᔣ]^_`=2,a=VIax£=2,bc|axd=Aஹ2Bஹ2V2ICஹ77Dஹ15ஹ(05-2)±f=ᓃf==☢3x-2y+7z=8Ḅᐵ3-275_________AஹVXUᙠ☢ᑁBஹᚖj☢Cஹᙠ☢ᑁDஹ☢TUᚖWUV

1416ஹ(08-2)lm(2,3,1)_Vjᙶ᪗pyozḄ☢7ஹ(08-4)=ᔣa=(1,1,0),᜛=(2,0,1),ᑣ஺tḄᦪ58ஹ(09-2)vwᔣx=(1,2,1),£=(2,1,2),ᑣz£=()A-6B6C(3,0,-3)D(-3,0,3)9ஹ(09-7)|lm(1,2,1)_}~}'ᚖḄ☢

142ᓄ->1ஹᔣa=1,3,1ypᚖḄᓫᔣ52ஹ2="=☢m+y+EḄᐵ5A///☢B/ᙠ☢஻C/ᚖj☢D/☢3ஹN}☢x+y+z=3Ḅᐵ5314AVBᙠ☢NCDᚖ4ஹ|idx+'+'=lḄmᔣ2x-y+3z=65ஹ☢z=4-/-y2ᙠmᜐḄᑗ☢Vj☢p2x+2y+z—l=0,IJmPḄᙶ᪗5A(l,-1,2)B(-1,1,2)C(1,1,2)D(-1-1,2)