成考专升本高数二课堂笔记

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xJᓫxᨵ]ᑣ\ᨵ᩽▲஺3.ᦪᑡ᩽▲ḄyᑣTUᳮ஺᝞limq=Azijlimy*={ᑣᳮ1.5…"ᙢড~”~3ᨴ±3.12ফ.%K2=Q%Q..ᵨ=43rlimxAEmy,#0"-»tavlimy.B3…&z".2ᦪ᩽▲Ḅᭆ1.XTXoᦪfxḄ᩽▲1X—Xof.X2Ḅ᩽▲ᦪf.X2,᝞X▲ᙢXoᦪf.X2▲ᙢ!ᦪA,ᑣ#X-XOᦪfxḄ᩽▲7A,+,hm/(x)=^rAgᡈf.X2—A.X—>Xo2y=f(x)=2x+lx—>1,f(x)—►?ூᶧ11010102=┐⚪௃X<1X—1x…0.90.990.999...—>1y••,2.82.982.998-3x>lx—1

19x—1.11.011.001…71y…3.23,023.002…—3(2)XTXOf(x)Ḅ¡᩽▲ᦪy=f(x),᝞x¤X஺Ḅ¡¦▲ᙢX஺ᦪf(x)▲ᙢ!ᦪA,ᑣ#XTXOᦪf(x)Ḅ¡᩽▲7A,+,lim_f(x)=AJᡈf(xo-O)=A(3)x—xof(x)Ḅ¬᩽▲ᦪf(X),᝞X¤XoḄ¬¦▲ᙢXoᦪf(x)▲ᙢ!ᦪA,ᑣ#x—xoᦪf(x)Ḅ¬᩽▲7A,+,lim/(x)=Aᡈf(xo+O)=Ax+1x<00x=0x-1x>0¯°•/(»,²⛷᝞ᦪூᶧ11010103=┐⚪௃µ=x¤0Ḅ¡¦▲ᙢ0f(x)▲ᙢ!ᦪloᡃ¸#x-0,f(x)Ḅ¡᩽▲71,ᓽᨵlimf(x)lim_(x+1)=1xfCT¹'x¤0Ḅ¬¦▲ᙢ0,f(x)▲ᙢ!ᦪ-1஺ᡃ¸#x-0f(x)Ḅ¬᩽▲7-1,ᓽᨵ⇵¼=%(ᱏ1)=1¿¹X”Àf(x)

20lim_/(x)lim/(x)lim/(x)ÁᯠᦪḄ¡᩽▲-X஺-ஹ¬᩽▲5LᦪḄ᩽▲-%MNᨵ&pᐵÆ=ᳮ1.6XTXOᦪf(x)Ḅ᩽▲ÉAḄ\⌕ᐙᑖᩩr7lim_/(x)=limf(x)-A1X—>X—>0_67g=᝞X-XOᦪf(x)Ḅ᩽▲ÉA,ᑣ\ᨵ¡ஹ¬᩽▲ÎÉA஺lim/(x)=A`M᝞¡ஹ¬᩽▲ÎÉA,ᑣ\ᨵஹ7”஺ᦇ_1஻x)=J(xwl)x-1X-1RX)T?/(x)=Ô1=(x+l)('T)=x+1x#lx-1x-1x—1fifx)—>2ÖV—1olim----=2xf1x-1᱄-1஻X)=J(XKl)ᦪx-l,x-lf(x)Ḅ¡᩽▲72,¬᩽▲f72஺

21Ø22.X-8ᦪf(x)Ḅ᩽▲(1)XTOOᦪf(X)Ḅ᩽▲y=f(x)x8f(x)—>?1_y=f(x)=l+x1X—>00f(x)=l+X—>1Hm(l+—)=119xᦪkf(X),᝞XT8f(X)▲ᙢ!ᦪA,ᑣ#XT8ᦪf(x)Ḅ᩽▲7A,+,lim/(x)=A—8ᡈf()—A(x—co)x(2)X—+8ᦪf(x)Ḅ᩽▲ᦪf(x),᝞XT+OOf(x)▲ᙢ!ᦪA,ᑣ#X—+8ᦪf(x)Ḅ᩽▲7A,+,Þ/(x)=4_Lᦪᑡ᩽▲ḄàáD᪵ᦪᑡ᩽▲Ḅãn+8Ḅn7å᦮ᦪçèᙠ_ãᑣ⌕éᑏëXT+OO,ìᐸãḄxc7å᦮ᦪè'í<îᦪ஺y=f(x)x+oof(x)xï

22/(x)=2+^=21+1x—>+oo,f(x)=2+&->2ñ(2+e”2=ᦪf(x)=2+e",XT+OOf(x)—?ூᶧ11010104┐⚪௃1µ=f(x)=2+e-x=2+&1x—>+co,f(x)=2+2—2hm(2+@”2ᡠ&ᩗ(3)x—ooᦪf(x)Ḅ᩽▲ᦪkf(x),᝞X-8f(x)▲ᙢ!ᦪA,ᑣ#X--8f(x)Ḅ᩽▲7A,+,x⇪yU)=A0X--oof(x)—►?1ᑣf(xù2+6’(x<0)x—>-00,-x—>+81f(xù2+^/^2

23⇪Q+ü=2/W=2+-IL(X<0)=ᦪ71X,X--8f(x)—?ூᶧ11010105┐⚪௃µ=X—8XT+OO஻x)=2+ஹ-=x-2,ᓽᨵýDþX—*00,X+8,X-"00ᦪf(X)᩽▲Ḅcÿ
X—Wf(x)Ḅ᩽▲Aᐙᑖ⌕ᩩXT+OOXT8ᦪf(x)ᨵḄ᩽▲Aof(x)=1+—᝞ᦪX,XT8f(x)▲ᙢᦪ1,XT+00f(X)/(X)=1+—▲ᙢ!ᦪ1,"#$X—00XḄ᩽▲1,%&+—)=1ᐸ()*+᝞,3ᡠ.஺f(x)=l+X

24lim(1+3ifXlim(1+—)=1xy=arctanxlimarctanx="-,limarctanx=——-co2ߟG2limarctanxHIᙠ஺KLᦪy=arctanxᩭN"Oᨵlimarctanx=——•Ko2ᓽSᯠx—fVXXḄ᩽▲IᙠX—+8fVxXḄ᩽▲IᙠKZ[!᩽▲Hᡃ]^_`x-8aarctanxḄ᩽▲HIᙠ஺VbXᦪ᩽▲Ḅcᳮlim/(X)cᳮ1.7VhឋcᳮX᝞j1%Iᙠᑣ᩽▲mch஺cᳮ1.8V[☢ᜳcᳮXpᦪ,“X8஺X“rXᙠstḄu!vwᑁVty◀᜜X|}ᩩ:limg(x)=lim=g(x)

25lim/(x)=A,limg(z)=Bcᳮ1.9᝞jO஺ijlim[/(x)±g(x)]=lim/(x)±limg(x)=A±Blim[/(x)-g(x)]=(lim/(x))(limg(x))=AB(2)lim/(x)/(x)A11m----=---------——limg(x)=3஺0x-»xog(x)limg(x)B(3)1Aᑣyᑮᨵ▲!ᦪḄᦪḄ¡ᨵ¢££lim[^(x)±^(x)±-±/„(x)]=lim¦x)±lim/(x)±-±lim§ব2lim[c©/(%)]=c-Hm/(x)(2)Xf/X->KQlim[/(x)r=[lim/(x)rবXT%ᵨ᩽▲Ḅᑣ᩽▲,®*:Z¯ᑣ⌕°!±²ḄᦪḄ᩽▲Iᙠ,³ᖪḄ᩽▲µ⌕ᑖ¶Ḅ᩽▲H_O·஺¸᜜᩽▲ḄᑣLX-8Ḅ¡¹ᡂ஺(º)»¼½»ᜧ½1.»¼½(¿$»¼)c+ᦪÀ=/(*),᝞jÂýxᙠu!ÃᓄÅÆÇᦪ/s)Ḅ᩽▲O·,ᑣ$ᙠÉÃᓄÅÆÇ,஺)O»¼½Ê%&lim/(x)=O.ᵨÌÍζ᜜/Ï…ᩭ⊤.»¼½஺cᳮ1.10ᦪ/(”)AO᩽▲Ḅ⌕ᐙᑖᩩ

26Ó஺Xy⊤.OA²!»¼½Ô஺lim/
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28;<=%>)ᓄ@ABḄᓽ"ma=0,lim/=0஺lim—=0(1)᝞EBᑣG)%9/:J▤ḄLM&="?)&lim—=c#0(2)᝞E0ᑣG&*£
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^ᨵaa'£0',_da..a!lrim--lim—=hm——
B2%BHQ᜛aᙠᑣn~8)oa/"cᙳ


29^ᨵa2£᜛a_aa!Fde/7f=limlimlimJaB0d—lim—᜛gឋ00hᵨᙠ᩽▲jkBlmnᑮpᓄjkḄMᵨ஺q%rstu[ST!ᣚv2ᙠ᩽▲Ḅ+◀jkBhᵨ஺0ᵨḄST!ᣚᨵ[X->0\sinxx;tanx;arctanxx;arcsinxx;1-cosx——;ln(l+%)~%;--+x-1(x)yz⌕᩽▲1.z⌕᩽▲Iz⌕᩽▲I%ᢣ}☢Ḅ᩽▲..sinx-..tanx..arcsinx“lim------=1lim-------=1lim-----------=1xfox,x-»0x,x->0x

30tanxsinx1lim------=lim-------goxQOxcosxsinx1v=hm-------hm-------K->0xKTOCOSx=1..arcsinx«,lim-----------=1—0x᜛rsinx=2sin/=xXT0,tT0arcsinxt.1«,hm-----------=lim———=h1m-------=1x->0xt-»osintt->0tsin/0gz⌕ᵨlv2k(ᦪḄ6Ḅ᩽▲⚪஺ᐸ᪀
[hm=1x)TdW(X)X->1x-lsin(x2-1)=(x+1)-sin(x2-1)lim-------------=lim------------------------3x-13(x+l)(x-l)sin(x2-1)Qi)/sin(x-1)=lim(x+1)lim——W-------=233(x-l)2.z⌕᩽▲H

31z⌕᩽▲௃ூ%ᢣ}☢Ḅ:lim(l+-)n=en-»8nlim(1+—)x=ex-»oox1lim(l+t)*=et->0ᐸBe%0ᦪ(0ᦪ)ᯠᦪḄlḄ
e=2.718281828495045.......ᐸ᪀
[1lim(l+.(x))°C)=e0z⌕᩽▲i%6Ḅ;z⌕᩽▲II%“¡”Ḅ;\gyz⌕᩽▲ᙠ᩽▲kBnz⌕ḄMᵨ£¤¥¦l§%¨0r⌕Ḅ஺(©)᩽▲Ḅª«[1.ᑭᵨ᩽▲Ḅᑣjk«ᑣ᩽▲&2.ᑭᵨyz⌕᩽▲᩽▲&3.ᑭᵨḄឋ᩽▲&4.ᑭᵨ(ᦪḄ®¯ឋ᩽▲&5.ᑭᵨ°r±«ᑣ;Ḅ᩽▲&6.ᑭᵨST!ᣚ;ᳮ᩽▲஺᩽▲(1)lime=climx=XQ(2)x7ᓽ

32lim—=0(3)r—8xlim(ax2+/x'T-t-axn~'2+---a)02n(4)282n-1w-2-^Oxo+<31XO+a2x0------1■%¿LḄᨵᐵᭆÃ1Å9601È}ᑡ)ᙠÊ;)ᓄ@AB
Ḅ%sin—(x—>0)A.xBeX(xTO)ln(l+x2)(x^O)cᵪ2ூÖᶧØÙ11010301[┐Û⚪Ü௃ÅÖÈCx->0,--»oo,sin-A.xxàᦣ1_1-xB.x—>0,---->-oo,&—>0x1x—>0+,-->-Hx),ex->+oox

33x-3x-31”3)eD.Q=(X+3)("3)=x+30(2)Å0202Èx-0\ஹã1+»*x9:%A.J▤ḄB.STḄC.¨STḄ>▤D.U▤ḄூÖᶧØÙ11010302[┐Û⚪Ü௃ÅÖÈBå:x-OjnQ+x)**%x-»0,ln(l+x)-xln(l+x)1lrim---------=hm-InQ+x)஺x(Jx=limln(l+x)x=ln[lim(l+x)x]0஺=Ine=1᩽▲Ḅjk[[0611]஺x+1ூÖᶧØÙ11010303[┐Û⚪Ü௃2=lim(x2+3x-l)2c..x2+3x-l.n02+30-lhm------------=r---------------=--------------r->0x+1lim(x+l)0+1å[0

34ÅÖᫀì10¿2.6íᑖåïᑖ᩽▲+x-6lim——z-----(1)Å0208ÈX—2--4ூÖᶧØÙ11010304[┐Û⚪Ü௃5ÅÖÈ,..”+ò6(x+3)(x-2)..x+35lim——z-----=lim-------------=hm-----=—å.rf2x2-4r72(x+2)(x-2)x->2x+24■r2r9..X-x/lim——------(2)Å0621ÈkX—2x-4ூÖᶧØÙ11010305[┐Û⚪Ü௃òö-2=.(x-2)(x+l)=2å.x->2x—4x->2(x—2)(x4-2)43ÅÖ"o¿3.0ᨵᳮᓄïᑖ᩽▲hm÷W(1)Å0316Èkò722ூÖᶧØÙ11010306[┐Û⚪Ü௃1ÅÖÈ2≵

35hmúû=limåx-2r->2(x-2)(jx+j2)x-2,.1=lim-------=----=-=hm-==-r->2(x-2)(y/x+)x72(ü+)1~2^2V27n-3hm(2)Å9516ý4"-2-0ூÖᶧØÙ11010307[┐Û⚪Ü௃⌳ÅÖÈ3ÿT+1+3)(7^+0)1J-\>=1im/?//.r->4(2-J2)(j2x+1+3)(Jx-2+J2)..2(-4)(Jx-2+=lim---------7-----------Tf4(x-4)(j2x+l+3)1.23x—2+->/2)=hm---==-----4(J2x+1+3)_4!_20"#00$4.%%78()8*Ḅ᩽▲..X2-1lim—z----=_______.(1)[0308]X-83/+Xூ4ᶧ67110103088┐:;⚪=>௃@ᙢBᨵ

36o(«rn).hm(1--Uf'/Jhm(3+W3r->oox1X4Y5$5.ᵨZ⌕᩽▲X)᩽▲Qsinx11^sin(w(x))hm----=1hm---------=1x~o'0(x)-00(x)xa1b[9603]Fᑡ᩽▲g,ᡂiḄj..sinx2,hm-----=1A.—஺xtanxlim1B.—oXHmp=1C.xfOx2D.X78Xூ4ᶧ67110103098┐:;⚪=>௃X4YB..sin(x-l)11m—y--------=(2)X0006Y—lx+5x-6

37ூ4ᶧ6711010310┐:;⚪=>௃X4ᶭsin(x-l)sin(x-l)sin(x-l)1hmߟ5----------=hm----------------=.^->1x+5x-6x-»l(x+6)(x-l)x-1x+6x-x—1x->lx+6~7$6.ᵨZ⌕᩽▲II)᩽▲1-lim(1+-)=%lim(l+x)x=&,Q8x—01Hm(1+--/W=e,hm(l+.x))஺ಘẆ>)->80(X)2hm(1+5(1)$0416%vw28xூ4ᶧ6711010311┐:;⚪=>௃X4J?22—=/,X=-X᪆Y8zXtX-8/ߟ0

382!'(=hm(1+i)B=+)21[lim(l+zy]2=e2f->0£X'("lim[(1+-)2]2=[H(i+2)2]2m~8x-x»XX=7hm(l+3+=eab28Xblim(l+ax)x=eabx-»01-hm(1--L)B=e2[0306]-82x2lim(l+x)x-e2[0601]XT஺hm(—)3x(2)[0118]vw-8xூ4ᶧ6711010312┐:;⚪=>௃[4]e'(=Hm(1B+=/8f0*

39$7.ᵨᦪḄឋ)᩽▲limln(l+x2)______[0407]…ூ4ᶧ6711010313┐:;⚪=>௃[4]0limln(l+x2)2>஺/(%)=ln(l+?)D(/)=(-oo,4oo)limln(l+x2)=ln(l+02)=00$8.ᵨᣚᳮ)᩽▲Q1-cosxlim------------[0317f°x+sinxூ4ᶧ6711010314┐:;⚪=>௃[4]0/A1x—>0,1-COSX:%2=lim——2-----------limߟ+—=0xTOx+smx2x->0«anx1+------x$9.)ᑖᦪᙠᑖᜐḄ᩽▲f2x4-1,x<0/(x)=<[ln(l+x),x>0(1)[0307]ᑣ/Xᙠx=0Ḅ᩽▲2/*=ூ4ᶧ6711010315┐:;⚪=>௃

40/(0-0)=lim/(x)lim(2x4-1)=1X᪆YI஺-/(0+0)=lim/(x)=limln(l+x)=0x—஺+x->0+x2+l,x<0/0)=0,ᑣ/ব=(2)0406ூ4ᶧ67110103168┐:;⚪=>௃X4Y1/(0-0)=limf(x)=lim+1)=1X᪆Yߟ0-10-/(0+0)=lim/(x)=limcosx=1x-»0+xT)+v/(0-0)=/(0+0)=l8.lim/(%)=1x-»0$10.)᩽▲Ḅ>⚪Q/+¡+6.lim--------------=5,(1)¢£.11¤ᑣ¥ᦪூ4ᶧ67110103178┐:;⚪=>௃lim(x24-/tx4-6)=0.,.._X᪆Y¦8,ᓽ1++6=0,¨©~7¦.Cx+H+6=(x-l)(x+ª)=¤+(jn-Y)x-mk¨X—«=6¨¬~7.

41¦8(®¯°¦ᑣ)Q/+H+6_2x+k,lim----------=lim------=5,1-x3-1ᓽ—(2+W=5,¨=7..x2+ax+blim-----z----=3,ফ²xfsin(xT))&bḄµ.ூ4ᶧ67110103188┐:;⚪=>௃0X᪆Y6*¶.%xߟ1(Bsin(x2-1)-x2-1zX2+ax+ᓰ=(x-l)(x+w)Qx1+ax+BQ(x-l)(x+w)1+¹c11m----------=lim-------------=-----=3»jXT௃sin(¤—1)(%—l)(x+1)1+1,=5ᓽ/+ax+b=(x-l)(x+5)=X2+4X-5ᡠ½½=4»=-5.sinax—.hm-----=3,a=3[0402¾xூ4ᶧ67110103198┐:;⚪=>௃(x+lim8[0017]^00^-2^ᑣ¿=(4:ln2)ூ4ᶧ67110103208┐:;⚪=>௃

42x(1+À/limIx+k=limÁ____Ãx-2k178Â"JX᪆YXJ=83A:=In8=In23=3In2jt=In2Ä☢ᡃÇÈḄᑁÊ:᩽▲ḄᭆÌÍ᩽▲ḄឋÎÍ᩽▲ḄÏw¦ᑣÍÐÑZ⌕᩽▲ÍÒஹᜧÒḄᭆÌÍÒḄឋνÕÒ▤Ḅ×Ø஺Ù~⁚ᦪḄឋXÛÜὃÞ⌕)Y1.ᳮᦪᙠᜐWßàḄᭆÌBᳮᦪᙠᜐW᩽▲áᙠâßḄᐵäBåæᑨàᦪ(èᑖᦪ)ᙠᜐឋḄé¦஺2.ê)ᦪḄßà஺3.åæᙠëìßᦪḄឋÎêᵨíÇîïðñᓫó⚪஺4.ᳮôᦪᙠᐸöìßḄឋBêᑭᵨᦪឋ)᩽▲஺Xø⌕£ùᑁÊY(-)ᦪḄᭆÌ1.ᦪᙠXoᜐö1ᦪ¾f(x)ᙠXoḄúÑûüᑁᨵöB᝞ý%þÿḄᦋ*(X஺)0ḄᦪḄᦋ0,ᓽ0ᡠ°ᡈ4$/(5+6%)-/(5)%=0ᑣᦪf(X)ᙠXoᜐ"#஺ᦪy=f(x)ᙠXo"#()᝞+,-.,-20ᦪ1f(x)ᙠxoḄ2345ᑁᨵ,-᝞89x-xoᦪy=f(x)Ḅ᩽▲=ᙠ>?X஺ᜐḄᦪf(X஺)ᓽ,-30ᦪy=f(x),᝞8AAᑣᦪf(x)ᙠX஺ᜐB"#C᝞8DE/(x)=/(%),ᑣᦪf(x)ᙠᙳᜐI"#஺ᵫKL,-2(M᝞8ᦪy=f(x)ᙠxoᜐ"#ᑣf(x)ᙠXoᜐB"#I"#஺2.ᦪᙠOPQa,bTK"#

43,-᝞8ᦪf(x)ᙠUOPQa,bTKḄVWXᜐX"#ᑣf(X)ᙠUOPQa,bTK"#,Yf(x)Qa,bTKḄ"#ᦪ஺Z[f(x)ᙠB\a"#]ᢣ_`ᐵb.AᙠI\b"#]ᢣ_`ᐵb.Ac**=ᓽf(x)ᙠB\aᜐ]I"#ᙠI\bᜐ]B"#஺(def.?ᦪᙠᐸ,-ḄOPᑁX"#஺3.ᦪḄPh,-᝞8ᦪf(x)ᙠX஺ᜐi"#ᑣX஺f(x)W3Ph஺ᵫᦪᙠ2"#Ḅ,-(Mjf(x)ᙠX஺ᜐᨵ+ᑡlmnopW.(1)ᙠX஺ᜐf(x)rᨵ,-C(2)ᙠX஺ᜐf(x)Ḅ᩽▲i=ᙠC(3)sᯠᙠX஺ᜐf(x)ᨵ,->ᔛv"=ᙠxᑣXo]f(X)W3Ph஺?-1,x(0/(x)=

44A.O1B.41_C.ID.2ூᶧ11010402.┐⚪௃ᑖ᪆.f(0)=klimf(x)=lim>'+)--x-»ox->ox(Jx+4-2)Cx/x+4+2)v=lim--------==-------x(Jx+4+2)x1=lrim--==——=—…x(Jx+4+2)4/(0)=lim/(x)x-rUD*=L4QᫀTBx<0|3Q0209T04+Xv°ᙠX=0ᜐ"#ᑣ2=ூᶧ11010403.┐⚪௃.f(0)=e°=l/(0-0)=Em/(x)=limd=1x-»0-x->0"/(0+0)=lim/(x)=lim(a+x)=aVf(0)=f(0-0)=f(0+0)a=lQᫀT1(-)ᦪᙠWᜐ"#ḄឋᵫᦪḄ"#ឋ]®¯᩽▲ᩭ,-Ḅ±²ᵫ᩽▲Ḅ³´µᑣ(d¶ᑮ+ᑡ"#ᦪḄឋ஺,ᳮ1.12(¹ᑣ³´)0ᦪf(x),g(x)ᙠxoᜐᙳ"#ᑣ(1)f(x)±g(x)ᙠXoᜐ"#(2)f(x)-g(x)ᙠxoᜐ"#/(x)(3)jg(x)¼ᑣgCOᙠxoᜐ"#஺0,ᳮ1.13(½ᔠᦪḄ"#ឋ)0ᦪu=g(x)ᙠx=x()ᜐ"#y=f(u)ᙠu()=g(x)ᜐ"#ᑣ½ᔠᦪy=fQg(x)Tᙠ*=*()ᜐ"#஺0ᙠÀ½ᔠᦪḄ᩽▲,᝞8u=g(x),ᙠxᜐ᩽▲=ᙠÁf(u)ᙠḄồ=!Äg("0ᜐ"#ᑣ᩽▲Å(dÆᦪÅÇᣚ஺ᓽ

45%/Ig(x)T=/R)I0/IJimg(x)T=f(%)/Qg(x)T=/Qlimg(x)T=/(«,)),31.14(ÊËḄ"#ឋ)0ᦪy=f(x)ᙠ2OPK"#>ÌÍᓫÏÐÑ(ᡈÌÍᓫÏÓÔ)ᑣÕḄÊᦪx=J(y)ᙠOPK"#>ÌÍᓫÏÐÑ(ᡈÌÍᓫÏÓÔ)஺(l)UOPK"#ᦪḄឋᙠUOPQa,bTK"#Ḅᦪf(x),ᨵd+Ö3×ØឋZÙឋdÚX⌕ᵨᑮ஺,ᳮ1.15(ᨵÝឋ,ᳮ)᝞8ᦪf(x)ᙠUOPQa,bTK"#ᑣf(x)ÞᙠQa,bTKᨵÝ.,ᳮ1.16(ᨬᜧ¼ᨬâ,ᳮ)᝞8ᦪf(x)ᙠUOPQa,bTK"#ᑣᙠZ3OPKW,=ᙠᨬᜧ¼ᨬâ஺,ᳮ1.17(ã,ᳮ)᝞8ᦪf(x)ᙠUOPQa,bTK"#>ᐸᨬᜧ¼ᨬâᑖäM¼m,ᑣãm¼MpPḄæçèᦪC,ᙠQa,bTKéÔ=ᙠW3஺ê¶f(4)=Cëì(í,ᳮ)᝞8ᦪf(x)ᙠUOPQa,bTK"#>f(a)Æf(b)î,ᑣᙠQa,bTᑁéÔ=ᙠW3ïê¶f(&)=0(¹)?ᦪḄ"#ឋñᦪᙠWᜐ"#Ḅ,ᳮM,"#ᦪò¯ᨵ▲ó¹ᑣ³´ᡈ½ᔠ³´²¶Ḅᦪᙠᐸ,-ḄOPᑁ]"#ᦪ஺Áᵫ×Ø?ᦪᙠᐸ,-OPᑁ]"#Ḅ(d¶ᑮ+ᑡô⌕õì஺,ᳮ1.18?ᦪᙠᐸ,-ḄOPᑁ"#஺ᑭᵨ?ᦪ"#ឋḄõì(M.᝞8f(x)]?ᦪ>X஺],-OPᑁḄᑣ

46f(x)ᙠXoᜐ"#᯿9প=7;)%ø]ùÀ?ᦪᙠ,-OPᑁ2ᜐḄ᩽▲ú⌕´ûᦪᙠḄᦪᓽ(஺[0407]limln(l+x2)=ln(l+02)=0ூᶧ11010404.┐⚪௃[0611]..x1+3x-1lim---------=_…x+1ᙠ(-co,-1)u(T,+co)ᑁ>?ᙠx=0ᜐA?..x2+3x-l02+3x0-1,1im-------=-----------=-1*~஺x+10+ூᶧ11010405┐⚪!௃#1.%&'()ᦪ+,x3-5x+l=Oᙠ/0(0,1)ᑁ23ᨵ567᪷.ூᶧ11010406┐⚪!௃%:f(x)=X3-5X+1f(x)ᙠ[0,1]?@Af(0)=1f(1)=-3ᵫCDEᳮGHI23Jᙠ5D&G(0,1)MNf«)=0,3-5&+1=0ᓽ+,ᙠ(0,1)ᑁ23ᨵ567᪷஺RSTUVᦪஹ᩽▲Z@A[\]ᑖ_ᨬaRஹᨬb⌕Ḅᭆfg5Ih᩽▲ijk[\]ᑖḄ'ᜧij_ᨬaRḄijg5ImnopqrIstuvwḄxyᡭ{|}ḄaẠ஺s5SḄᑁᙠὃ_ᓰ15%,u22ᑖ஺RSḄ⌕ᑁU᝞E5ஹᭆfᑖbD᩽▲ᭆfITZTḄᭆfI@AḄᭆf஺᩽▲ᭆf&᩽▲[ᙠEᓄ,_VᦪᓄḄឋ᝱I᩽▲[56EḄᦪ஺Vᦪᙠ5D@AឋḄ'6aR⌕¡(1)f(X)ᙠDXoᨵE¢஺(2)Ḙ/ಘJᙠ஺

47T¦/(§=/(4)kJ)«->*&oᵨḄ[f(x()-0)=f(xo+0)=f(Xo)o¦ஹijᑖbD᩽▲IVᦪḄD@AឋḄᑨE஺1.Vᦪ᩽▲Ḅᵨ+¯⌕ᨵ(1)ᑭᵨ᩽▲Ḅ±ᑣij¯ᑣ᩽▲³0´ᕽII¶·E¸IGὃ⇋ᵨº¸ᑖ»ᡈᨵᳮᓄ½¾Cº¿¯஺(2)ᑭᵨÀ6b⌕᩽▲᩽▲³11m^^=1lim(l+—)*=eX*T9x(3)ᑭᵨTḄឋÃ᩽▲³(4)ᑭᵨVᦪḄ@Aឋ᩽▲Äf(x)ᙠX஺ᜐ@AIÆÇÈ(5)ᑭᵨT)ᣚEᳮ᩽▲³(6)tᑖÊVᦪᙠᑖÊDᜐḄ᩽▲³(7)ᑭᵨÌmͯᑣÎE¸Ḅ᩽▲஺2.ᑨEVᦪḄ@AឋIᑭᵨÏ/0?@AVᦪḄCDEᳮ%&+,Ḅ᪷ḄJᙠឋ஺ЦS5ᐗVᦪ\ᑖxÐ5⁚ÓᦪZ\ᑖÔÕyὃ⌕Ö1.ᳮ»ÓᦪḄᭆf×ᐸÙÚÛ¢IÜ»GÓឋZ@AឋḄᐵÞItᵨE¢Vᦪᙠ5DᜐḄÓᦪ஺2.tßà?5DᜐḄᑗà+,Z¯à+,஺3.opqrÓᦪḄaRâ¸ஹ±ᑣij¯ᑣv×ÕᔠVᦪḄÓ+¯஺4.qr◚VᦪḄÓ¯ZᦪÓ¯஺tᑖÊVᦪḄÓᦪ஺5.Ü»å▤ÓᦪḄᭆf஺tçᓫVᦪḄå▤Óᦪ஺6.ᳮ»\ᑖḄᭆfIqr\ᑖ¯ᑣIÜ»G\éGÓḄᐵÞItVᦪḄ5▤\ᑖ஺Ô⌕HêᑁÖ(-)ÓᦪḄᭆf1.ÓᦪḄE¢E¢:Vᦪëf(x)ᙠDX஺ḄìíîᑁᨵE¢IïðXᙠX஺ᜐñNᦋóIVᦪkf(x)ñNôḄᦋõyMk(x+Ax)-f(x),᝞ùï5OBûIVᦪḄᦋ00õyZðḄᦋAxgüḄ᩽▲

48limᒹ=1È&1þ¦ÿgoAxFOAxᙠᑣ᩽▲ᦪfxᙠXoᜐḄᦪᦪᡝfXᙠXOᜐ/1#$y,|fᓾfᡈ*”ᓽ/(%+ᦑ)-/(%)=ᡠ678/(%)=1AxfX-%ᑭᵨᦪ;<=ᦪḄ>⚪@AB1=CDEF=£xo+Ax-fxoEy_—o+Ax-/J2LMAxAx7ᒹ=Hm/%+ஹ-஻J3T᩽▲2஺AxEOAxAyWᦪ᝞Y*EXT஺D[\Ḅ᩽▲ᙠᑣ᩽▲ᦪfxᙠX஺ᜐḄWᦪ,F.x,ᓽ0/'_x=ltmb=HmKL-00ar-MTAxfTO-AXAygᦪ᝞Y*Ex-O,[hḄ᩽▲ᙠᑣ᩽▲ᦪfxᙠX஺ᜐḄgᦪiX0,ᓽ/jx=limb=hm/a+M-g஺0AXTO.AXarTOfAx᝞YᦪfxᙠXoᜐmᯠ⌕=ᙠWᦪpgᦪqᙠrstuvwᡂy஺ᦪ7zᙢ|}~a,bᑁḄ7x,ᦪfXqᨵᦪfXᙠa,b~a,bᑁḄ7xᨵ7ᦪfX,ᦪxḄᦪᦪᦪ஺f\ᦪᦪ/1«$dxax2.ᦪḄ<}Ḅ¡y=fx,ᑣᵫᦪḄ;<£ᦪy=fxᙠ¤X஺ᜐḄᦪPX஺¦ḄMx,yᜐᑗḄ¨᳛ª00/'X=lim—=tanaa¬—ᓽ"DAX'2

49ᵫḄ¨°¡᧕£f(x)¦ḄM(xo,y)ᜐḄᑗ¡0y-yo=f(xo)(x—xo)3.²³´Ḅᐵ¶;ᳮ2.1᝞Yᦪ¸f(x)ᙠXoᜐᑣ¹ᙠXoᜐº;³´஺ᵫ»;ᳮ£B¼ᦪf(x)ᙠX஺½³´ᑣf(x)ᙠXoᜐº;½஺(x(0)y=/À=|Á=¾:(x>0)ூÃᶧÅÆ11020101┐~È⚪ÉÊ௃f(x)ᙠx=0ᜐ³´஺¸(Æ)=ÌÍÎ=mÏ+f)7Ï)11AX-JOAX/Ð=Rmঞ7®)gox-Ñ3/8)(0)=%x-0-X-0v=lim--------=-1Òx-0Óx-0x-0r=lim------=1x->o*x-0Vf.(O)^f'(O)+r.f(x)=IxIᙠx=oᜐ½(×)Ḅᑗ¡ØÙ¡¼ᦪf(x)ᙠXoᜐÚᦪḄ<£F(Xo)⊤ÜݦM(Xo,y)Ḅᑗ¨᳛஺ᡠfݦM(xo,y0)Ḅᑗ¡0y-y=f(x)(x-xo)oo¼f(x஺)ᙠr½tÞᑣÝM(xo,y)ḄÙ¡0

50y-ß7àg")Hmá)7/3)=|¾lâ9704æ}ᦪf(x)çèmoxᑣf(0)=ூÃᶧÅÆ11020102B┐~È⚪ÉÊ௃>BlimXT஺x/(2x)-/(0)-limXTOx=-21imXTO2x-0-2/1(0)-2/'(0)=b/'(0)=-iâÃæ5Em/(ê+2%)-/(ê)¾2â0303æë£ᦪf(x)ᙠx«ᜐrf(xo)=2,ᑣht()A.OB.lC.2D.4ூÃᶧÅÆ11020103B┐~È⚪ÉÊ௃>Bf(x)ᙠXoᜐf(x)=20lim”Æ+2î7^h~-m/(%+2ïð)2117I஺W=2/1(஽)=2x2=4âÃæDᦪḄ<¾3â0410æòóᙠ(0,1)ᜐḄᑗḄ¨᳛k.ூÃᶧÅÆ11020104B┐~È⚪ÉÊ௃â>᪆æö6⚪÷⌕ὃùᑭᵨᦪḄ<çᑖ4ᑖ஺y'=(e'*)'=-e'*>û=ü'|*“="=-1¾2â0616y=x3-xᙠ(1,0)ᜐḄᑗ.ூᶧ11020105┐!"⚪$%௃'y'=3x2-ly'I=i=2xy-0=2(x-l)ᑗy=2(x-l),y=2(x-l)-3,9920ᙠ/=&123Mo,67MoḄᑗ89:;x-2y+5=0,=27

51MoḄᑗ>?஺ூᶧ11020106┐!"⚪$%௃,'᪆BC⚪D⌕ὃGᑭᵨJᦪLMNO2Ḅᑗ>?PQᑖ6ᑖ஺SM(x,y)o00TUV஺=W11,.X32%1Y31_1ᦑᑗ2-5,ᓽx-2y+l=0?y-l=-2(x-1),ᓽ2x+y-3=0(\)JᦪḄ]^1._B`abᦪḄJᦪcd(1)(C)'=0(2)(x")-1ᑁf)(ߟ)'=--4-(3)2N(4)x7(5)(ax)—axlna(a>O,a^l)(6)(ex)-ex(logx)'=lloge=-1-^)0,Qnx)'=laa(7)xxlna(8)x(9)(sinx)gcosx(10)(cosx)--sinxft3nx)=—x—=sec'x(cotx)1=——:—«—=—(11)cos2x(12)sin2x(13)(secx)-secxtanx(14)(cscx)--cscxcotx(arcanx)1=—==(arccosx)'=--==(15)Jl-/(16)J1—-(arctanx)'=—h(arccotx)'=--h(17)1+N(18)1+x22.JᦪḄiᑣk^?ᑣSu=u(x),v=v(x)ᙳxḄmJbᦪPᑣᨵ(1)(u±v)'=u'ov'(2)(u-v)-u^v+uv,(3)(cu)'=cu'(4)(6)(u-vw)-u,vw+uv,w-l-uvw,3.pᔠbᦪ2J?ᑣ᝞su=(p(x)ᙠxᜐmJPty=f(u)ᙠuvḄu=(p(x)ᜐmJPᑣpᔠbᦪy=f(p(x)ᙠxᜐmJPwᐸJᦪ

52axauaxyᳮP᝞sy=f(u),u=(p(v),v=v(x),ᑣpᔠbᦪf[(P(V(x))]ḄJᦪ=/'(«)-P,M3=•axduavax4.bᦪ2J?ᑣ᝞sx=q>(y)ᓫmJbᦪPᑣᐸbᦪy=f(x)ḄJᦪ-I,0008Sbᦪf(x)=sin2+x2+2\2y\ூᶧ11020201┐!"⚪$%௃,'᪆BC⚪D⌕ὃGJᦪḄiᑣk^2pᔠbᦪḄJᦪ஺Qᑖ4ᑖ஺f(x)=(sin2+x2+2x)'=2x+2xln2-2,0602Sbᦪy=e2x+5,ᑣy'=ூᶧ11020202┐!"⚪$%௃y'=(e2x+5)'=e2x.(2x),=2e2x-3[9419]SbᦪV=Jl+#+ln85+27ூᶧ11020203┐!"⚪$%1,'᪆BC⚪D⌕ὃGJᦪḄiᑣk^2pᔠbᦪḄJᦪ஺Qᑖ5ᑖ஺,1-1s,Xsinxx.zy=—==•2%+----(COSX)=------=3£x2J1+/COSXVl+X2COSTJ1+/-4,9712Sbᦪf(x)=(1+x2)arctanx,2©(0)஺ூᶧ11020204┐!"⚪$%௃,'᪆BC⚪D⌕ὃGJᦪḄiᑣk^2pᔠbᦪḄJᦪ஺Qᑖ5ᑖ஺f(x)=(1+x2)'arctanx+(1+x2)(arctanx)'212xarctanx+(1+x=2xarctanx+lf(0)=1_cosx-5,0122SbᦪI-x'-l,2yPூᶧ11020205┐!"⚪$%௃,'᪆BC⚪D⌕ὃGJᦪḄiᑣk^2pᔠbᦪḄJᦪ஺Qᑖ6ᑖ஺,(COSX)'-(x2-1)-COSJT(ª-1)'y-------------------------------------_-sinx(x2-1)-8sx•2x-6,9809Sbᦪ/=$1!1(xD,°Uy=ூᶧ11020206┐!"⚪$%௃,'᪆BC⚪D⌕ὃGpᔠbᦪ2J஺Qᑖ4ᑖ஺

53'?3y=sinu,u—sinv,v=x=cosy1=-V_dydudvdxdudvdx=cosu--3x2=-eosinx3VX'?hy=cosln(/)[ln(/)r=cosln(V).3(Vy=cosln(N)p3/3=Ecosing)x-7[0010]Sbᦪy=lnarcsin²Pᑣy=.ூᶧ11020207┐!"⚪$%௃['᪆]BC⚪D⌕ὃGpᔠbᦪ2J஺Qᑖ4ᑖ஺y'=_Lj=(arcsin³),arcsin-V^---------]—--i1.(´rarcsin"P-(QR•arcsin³.-80223Sbᦪf(x)=e*,g(x)=sinx,wy=fg'(x),2µrூᶧ11020208┐!"⚪$%௃,'᪆BC⚪D⌕ὃGpᔠbᦪ2J஺Qᑖ7ᑖ஺¶g'(x)=cosx,ᡠ¸y=f(cosx)=ecosx,-9,᪵⚪23Sbᦪºe-smxு,ᐸ¼f(u)mJP2᜜ூᶧ11020209┐!"⚪$%௃,'᪆BC⚪D⌕ὃGpᔠbᦪ2J஺Qᑖ8ᑖ஺

54yP=e*ᵫ¿"(sin2Ẇ=ZsM2*)/'(sin2x)(sin2x),=e"*2")j'(sin2x)cos2x(2x),=f(sn2x)./Qin2x)2cos2xe-100318Sbᦪy=6+7,2yPூᶧ11020210┐!"⚪$%௃,'᪆BC⚪D⌕ὃGpᔠbᦪ2J஺Qᑖ6ᑖ஺y^—i=(x+«)=—=஺S1f+124+W2Tx+&2jxx2+xy/x-110420Sbᦪf(cosx)=l+cos3x,2f(x)ூᶧ11020211┐!"⚪$%௃,'᪆BC⚪D⌕ὃGpᔠbᦪ2J஺Qᑖ6ᑖ஺Scosx=t,ᑣf(t)=l+t3,ᓽf(x)=l+x3,ᡠ¸f(x)=3x2-12Sf(cosx)=sin2x,2f(x)ூᶧ11020212┐!"⚪$%௃f(cosx)=l-cos2xÁcosx=tf(t)=l-t2f(x)=l-x2f(x)=-2x-13Sf3)=l+ex+e2x,2f(x)ூᶧ11020213┐!"⚪$%௃f(ex)=l+ex+(ex)2f(x)=l+x+x2f(x)=l+2x5.ᑖÂbᦪḄJᦪ1n(l+x)_Kx«0/(x)=1-14ÃÄsinxx>0ᙠx=0ᜐḄJᦪ஺ூᶧ11020214┐!"⚪$%௃'f(0)=0µ(0)=1"ব7(஺)/3XT஺-X—0KT஺-X11=limln(l+x)“=lnlim(l+x)”KT஺-XT0~=Ine=1

55Æ(0)=.Ç1®=.ᔳ+XTO+X-010+X=1'(0)=7Ê'(0)=1Ë0)=1(i)2J?1.◚bᦪ2J-19919Sºy(x)ᵫy3=x+arccos(xy)ÍÎP2dx஺ூᶧ11020301┐!"⚪$%௃,'᪆BC⚪D⌕ὃG◚bᦪ2J஺Qᑖ6ᑖ஺ÏÐyÑ!x2JPÒ3y2y'=l--j=^=cT+`)7K-3)2(3,<-(zy)2+x)y'=<-(Ṻ)2-yᑣyP=+₹-y_3/J1-ಘ)2+xØ=y,=13)2-yC3y2jl-(xy)2+x-29520Sy=y(x)ᵫex—ey=sin(xy)ᡠÍÎP2yḄJᦪyᙠx=0ᜐḄJᦪÙPlÚoூᶧ11020302┐!"⚪$%௃,'᪆BC⚪D⌕ὃG◚bᦪ2J஺Qᑖ7ᑖ஺ÏÐyÑ!x2JPÒe*-e>/=cosÜ)8+9')ey+xcos(XÝJ/=ex-ycos(xy).y,=©x-ycos(»)ey+xcos(xy)Þx=0ÑPßᐭᡠáPᓽe°-ey=sinO,Wy=0I_â-ãcos(ä)eP+xcos()k஺P)2.!ᦪ2J?-19621Sbᦪy=(Inx)'P2y'ூᶧ11020303┐!"⚪$%௃,'᪆BC⚪D⌕ὃG!ᦪ2J?஺Qᑖ5ᑖ஺adÏÐyÑæçᯠ!ᦪPÒ

56Iny=xIn(Inx)adÏÐyÑ!x2JPÒ—y=ln(ln+x-—•—=ln(lnx)d-yInxxInxᡠ¸(Inx)Tln(lnx)+——]Inx-2,0123Sbᦪë=sinX+X2y'஺ூᶧ11020304┐!"⚪$%௃,'᪆BC⚪D⌕ὃG!ᦪ2J?஺Qᑖ7ᑖ஺'Á/=ë171=sinx,y=2y'=yf+ìM=COSXIn72=6Inx11---Vn=——=lnX+------2mxy”Ê(lnx+2)—2-yJX1ny'=cosx+—=-(lnx+2).x7(ï)ð▤JᦪÎO᝞sbᦪy=f(x)ḄJᦪf'(x)ᙠxmJPòóf(x)ḄJᦪbᦪy=f(x)d2yd2fy"4"(x),TT-Ḅh▤JᦪPõöVa#ᢥ᯿JᦪḄÎOPbᦪf(X)ᙠXᜐḄh▤Jᦪòùúᑡ᩽▲hm(x+Ax)—(x)rw=Ax->0Axf(x)Ḅ▤ᦪy஻=/(X)Ḅᦪᦪf(X)Ḅ▤ᦪd3ydx3!ᙢᡃ$%&f(x)Ḅn▤ᦪ(ᐸn-1▤ᦪḄᦪᓽ᝞-f(x)Ḅn-1▤ᦪḄᦪ.ᙠ01ᦪ(2ᩭḄᦪf(x)Ḅn▤ᦪ/456d”d”ᓽᨵ9y0";'=yn(n=2,3,4……),▤A▤BCḄᦪD(E▤ᦪ஺G190615;Jy=sin2xᑣy஻=

57ூOᶧQR11020305S┐UV⚪XY௃[Sy-cos2x(2x)-2cos2xyn=2(-sin2x)(2x)r=-4sin2xG29910ᦪ\Ḅ▤ᦪy"஺ூOᶧQR11020306S┐UV⚪XY௃9[᪆;^_⚪`⌕ὃcdᓫᦪf▤ᦪ஺gᑖ4ᑖ஺2—r/(r)=In,ᑣiপ=G39613Jᦪ2+xூOᶧQR11020307S┐UV⚪XY௃9[᪆;/(x)=ln(2-x)-ln(2+x)ম=]42+x8x/"«=i(1)=lG49810Jy=axIn2a+a(a-1)xa-2G5031"Jᦪy=x2+e2x,ᑣyḄ50▤ᦪy<50)=ூOᶧQR11020309S┐UV⚪XY௃9[᪆;^_⚪`⌕ὃcdᓫᦪfE▤ᦪ஺gᑖ4ᑖ஺y'=2x+e2x.2y"=2+e2x22ue2x-23y'=e2x-2n(n>3)»50)=p.250(m)nᑖ

581.nᑖḄ%&%&᝞-ᦪf(X)ᙠpXᜐḄr1stᑁᨵ%&᝞-UvwxyᙠpXᜐḄᦋxy{*,ᦪḄᦋxyAy}B⊤(⚗AS{y=A(x)Ax+o(Ax)({x-0)ᐸA(x).XAxᐵo({*)E▤Ḅ_yᑣᦪy=f(x)ᙠpxᜐ}nA(x)Z\x(ᦪᙠpxᜐḄnᑖ(dyᡈdf(x),ᓽdy=df(x)=A(x)Ax2.nᑖḄ&Jᦪy=f(x)Ḅ᝞ᡠM(x,y)(CḄ%pMo,(?#1)axIna(4)d(Inx)=—dxx/r(5)d(a)=----dx(a>0a¥1)rIna(6)d(ex)=exdx(7)d(sinx)=cosxdx(8)d(cosx)=-sinxdx

5921(9)d(tanx)-secxdx=----------dxcos*2x21(°)d(cotx)=-cscxdx=-———sin'x(u)d(secx)=secx-tanxdx(12)

60fê5´ᦪÊ⊤,íᔠìᑣö÷ᝅ஺ᑖëìᑣíᔠ,ᐵ¶ùúÃf஺ÓÈᢣUð,ᦪÉÊ⌕ᱞ஺ñòᐵ¶⌲⚗,üᖪᦪᨬÿ⌕஺ôḄᦪᐳ⚗,UVUV஺ᖪḄᦪᑖᑖ஺ᔠᦪᣵ஺◚ᦪ!"#$y&'()*▤ᦪ▤▤,-./0⌕஺12345᩽▲,HIJKL5,ᑖ9ᦪᑖ9:,MNᔲ=P஺ᦪ;ᑖ<=>,;ᑖQRSTᣵ஺?@ABC,EUVWXY,D./EFᦟ,Z[ὃ]^_஺`aᖛc5d5efghᝯ஺jk⁚ᦪḄmᵨoVὃp⌕5q«“8»1.WUxyᵨz]{|ᑣ50'8'"08”ஹ“8-8”HḄ᩽▲Ḅ|஺2.xyᑭᵨᦪᑨHᦪḄᓫឋ5ᦪḄᓫ1ஹḄ|஺LᑭᵨᦪḄᓫឋᓫḄ=஺3.ᳮ#ᦪ᩽4Ḅᭆxy5ᦪḄ:ஹ᩽4:ஹ᩽4ஹᨬᜧ4ᨬ4Ḅ|L#ᓫḄmᵨ⚪஺4.LᑨḄ¡ឋL5Ḅ¢:஺5.L5Ḅ¤¥¦§¨©¦§oª⌕«¬ᑁ®q(-)z]{|ᑣ5᩽▲01.5Hᳮ2.3(z]{|ᑣ1)᝞²জlim/(x)=0,limg(x)=0XT½0XTX஺ঝf(x),g(x)ᙠXoḄÂÃÄᑁ(:XoÅÆ◀᜜)ÅÉᡈX)Mঞlim'J=A“TX஺g'S)(Aᨵ▲Ðᦪᡈ8)QÑ=)Ò=ᨴ1mᑣXTXog(x)XTXog(x)(ᡈÔx_xoᦋX—8)

61hmx—27-40Ø1ÙÚ:ூßᶧáâ11020403ã┐åæ⚪çè௃lim(x+l)(x-2)3ED:'(=xߟ2(x+2)(x-2)4EGHIJKLᑣNlim2x-l3'(=x—>22x4<.arcsinr-rlim———=----Ø2o9517q5ó°Sin”ூßᶧáâH020404ã┐åæ⚪çè௃0o#᪆q÷⚪ª⌕ὃøᵨz]{|ᑣ53H᩽▲஺ùᑖ5ᑖ஺1úarcsinx-xJ1-arcsinx-xr1lim-=lim---------=lim———sin"D/TTO36x6«-1+X—€511mC——2—Ø3o0417q“ó°xூßᶧáâ11020405ã┐åæ⚪çè௃o#᪆q÷⚪ª⌕ὃøᵨz]{|ᑣ5H᩽▲஺ùᑖ6ᑖ஺1#/1—e
e1_lim=lim-----=lim----x-^Qx-^02xx-^022002ᳮ2.4ᑣ2᝞জlim/(x)=oo,limg(x)=oo;Jx->x0ঝf(x),g(x)ᙠXoḄ()*ᑁ(,Xo-.◀᜜)-123g(X)4ঞlimJ:'=AXTXOg'(X)(A:ᨵ▲=ᦪᡈ:8)f(x)/'(X),ᑣlim----=lim---=Ag(x)2%g'(x)(ᡈBx—Xoᦋ:X70)limIn”+1)K1.LXT+8x2

62ூNᶧPQ11020406┐ST⚪VW௃YZ᪆\]^⚪_⌕ὃbᵨᑣL᩽▲஺Xf+8x2Xf+oo2xr^-oo(x2+l)HmIn(x-y)x7——tanrK2.L2ூNᶧPQ11020407┐ST⚪VW௃YZ᪆\]^⚪_⌕ὃbᵨᑣL᩽▲஺Hmln(x--)1flim2'22cos2ᕴ+-----------=7T+--------=g+-----x——tanxx1x——ஹ⇟99-----n-9hߟjcos2X2cosx(-sinx)k+-sin2x=03.0ooSlOsmn2-.opqrnᓄ:ᖪḄrn2ᓽ-ᓄ:vᡈwmn,ᯠyzᵨᑣL᩽▲஺%•(cos--1)X—8ூNᶧPQ11020408┐ST⚪VW௃YZ᪆\]^⚪_⌕ὃbᵨᑣL᩽▲஺11{|=-,£=_2X—>8,/1«ஹcos/-1-sinzrlimx-(cos—-1)=rlim-----------=livm---------=0xߟ^0xt-^0if•ߟ>014.00~00Sl8—8mn2-ᑭᵨᑖoᐸᓄ:vmn2ᯠyzᵨᑣL᩽▲஺fHm/1ஹL(-------)KXTOx/j1

63ூNᶧPQ11020409┐ST⚪VW௃YZ᪆\]^⚪_⌕ὃbᵨᑣL᩽▲஺.I1ஹe*—1—xrlim(----------)=lim---------xf0x/_1x->0x(ex-1)e"—1—xe*—11=lim--------=lim------=—x->0x2x-02r2KXT9ூNᶧPQ11020410┐ST⚪VW௃YZ᪆\'/+sin/2z+2xcosx21+8lim--------=lim------------=lim~rᵨᑣXT8/KTCO2XXT8lim(1+cosx:,j8ஹ,ᙠ2zᵨᑣ஺,1.21+sinxlimlim——------=1ḄZ:X-»oo281(w)ᑭᵨ1ᦪẆᦪḄrឋ¢1.ᦪḄᓫ¤ឋᳮ2.5¦ᦪf(x)ᙠ§¨(a,b)ᑁ-12ᑣ(1)᝞ᙠ(a,b)ᑁḄ«j,xᜐ2ឤᨵf(x)>0,ᑣᦪf(x)ᙠ(a,b)ᑁ®¯ᓫ¤°±²(2)᝞ᙠ(a,b)ᑁḄ«j,xᜐ2ឤᨵf(x)<0,ᑣᦪf(x)ᙠ(a,b)ᑁ®¯ᓫ¤´µ஺K¶·ᦪf(x)=x-arctanxᙠᐸ¹*ºᓫ¤°±Ḅ஺ூNᶧPQ11020501┐ST⚪VW௃/(x)=x-arctanxD(f)=(-cq+co)=----z->0(x#0)1+//(ᓫPQRᦪ½¾ᦪf(x)ᙠᐸ¹*ºḄ¿À,ᜐf(x)=O(ᡈf(x)ᙠÁÂÃ),ÄÅᐸᓫ¤ឋ஺

64ᑭᵨ1ᦪᑨᦪᓫ¤ឋḄjÇÈÉ(1)ᦪḄ¹*(2)LÊᦪḄ1ᦪy2=F(x)²(3){f(x)=0,LÊᦪᙠᐸ¹*ᑁḄᡠᨵÏ,2Ï,o¹*ᑜᑖᡂÒÓÔ§¨,ᙠÕ¿Ô§¨ᑁÖ×f(x)ḄØÙQ2ÚfᦪḄᓫ¤°´§¨஺y=ln(l+/)(-cq+8)ᑁSx<0.y1<0x=0y'=0x>0y'>0y=ln(l+/)ᓫPT;U(-eq0)ᓫPQ;U(O,+8)2.ᦪḄ᩽Û(1)ᦪ᩽ÛḄ¹¹¦ᦪf(x)ᙠ(a,b)ᑁᨵ¹2X஺(a,b)ᑁḄ(j,2Òᙠ,X஺Ḅj¿)*2zÜSÝ)*ᑁ«j,X(x#x),0জឤᨵf(x)vf(xo),ᑣßf(x())ᦪf(x)Ḅj¿᩽ᜧÛ2ßXoᦪf(x)Ḅj¿᩽ᜧÛ,²ঝឤᨵf(x)>f(x,ᑣßf(Xo)ᦪf(x)Ḅj¿᩽^Û2ßX0ᦪf(x)Ḅj¿᩽^Û,஺o)᩽ᜧÛ4᩽^Ûáß:ᦪḄ᩽Û஺᩽ᜧÛ,4᩽^Û,áßᦪḄ᩽Û,஺(2)᩽ÛᙠḄ⌕ᩩãᳮ2.6¦ᦪf(x)ᙠ,XOᜐᐹᨵ1ᦪ23ᙠ,XoæÜ᩽Û2ᑣᨵ?(Xoè0஺jÇᙢ2ßP(x)=OḄ,:ᦪRx)ḄÏ,஺½¾᩽Û,Ḅ1ᦪᙠ2ᑣ᩽Û,Ï,2ìíÏ,j᩽Û,஺f(x)=x3f(x)=3x2{f(xè0,ÜÏ,x=O¦f(x)=x2P(x)=2x{î(xè0,ÜÏ,x=0xீ0ð2f(x)<0x>0ð2f(x)>0x=0:4x)Ḅ᩽^Û,(3)᩽ÛᙠḄᐙᑖᩩãᳮ2.7(òjᐙᑖᩩã)¦ᦪf(x)ᙠ,xoÂÃ23ᙠ,X஺Ḅ(jóô)*(õjö÷+v)ᑁ-1(x)-.øloᡈᙠ)2ᑣfজ᝞ᙠ(÷jù÷)ᑁ«j,xᜐ2ᨵP(x)>0,fᙠ(ú2÷+3)ᑁ«j,xᜐ,

65ᨵ2(X)<0ᑣf(X஺)᩽ᜧÛ2X஺᩽ᜧÛ,²²ঝ᝞ᙠ(X஺j$2ü0)ᑁ«j,*ᜐ2ᨵf(x)<0,fᙠ(“02“0+þ)ᑁ«j,xᜐ2ᨵf(x)>0,ᑣf(xo)᩽^Û,Xo᩽^Û,;ঞ᝞ᙠ(X0-ÿ)ᑁ(+5)ᑁXᜐP(x)fᳮ2.8(!ᐙᑖᩩ%)&'ᦪf(x)ᙠXoᜐᨵ!▤-ᦪ.f(Xo)=O,f''(Xo)/),ᑣজ6f"(x<09ᑣf(X஺);᩽ᜧ>?0)ঝ6f''(x0)>09ᑣf(xo);᩽B>?ঞ6f''(x())=09ᑣDEᑨX஺Gᔲ;᩽>஺ᑭᵨ-ᦪK'ᦪ᩽>ḄMNO(1)ᐜKR'ᦪḄ-ᦪy'(x)=f'(x),Tf'(xo)=0,KR'ᦪᙠᐸVWᑁḄᡠᨵYZ-ᦪD[ᙠḄXi(i=l,2...,k)?(2)_'ᦪf(x)ᙠஹḄabcWᑁd-ᑣᑭᵨ᩽>Ḅᐙᑖᩩ%ᑨ஺ᓽ6f'(X)ᙠXiḄfgh9i(X);᩽>,Xi;᩽>_f'(X)ᙠXiḄfg9f(Xi)DG᩽>X,DG᩽>஺(3)᝞l'ᦪḄ!▤-ᦪf''(x)m᧕Kᨴ.f''(D)[ᙠᑣdp᩽>Ḅ!ᐙᑖᩩ%ᑨ஺ᓽ6f''(q)>09ᑣf(r);᩽B>;;᩽B>?6f’‘(u<09vlwf(Xi);᩽ᜧ>;;᩽ᜧ>_'x0,ᑣyᦋᵨ᩽>Ḅᐙᑖᩩ%ᑨf(Xi)Gᔲ;᩽>ஹGᔲ;᩽>஺{1|9803~'ᦪy=ln(1+x2)ᙠ(g,+oo)ᑁ()A.ᓫB.ᓫC.DᓫD.Dூᶧ11020502O┐⚪௃|᪆~B⚪⌕ὃᑭᵨ-ᦪẆ'ᦪḄᓫឋ஺¡ᑖᑖ42xty=Tl+XTy'=0,£x=0,

666x<09yz<0,'ᦪy=ln(1+x2)ᓫ,6x>09y'>0,'ᦪxIn(1+x2)ᓫ,ᦑ⌱C஺{2-9903/p¦§¨©ḄG()A.'ᦪf(x)Ḅ-ᦪD[ᙠḄDGf(x)Ḅ᩽>B._xo;f(x)ḄYᑣxoª;f(x)Ḅ᩽>C._f(x)ᙠxoᜐᨵ᩽>.f'(xo)[ᙠᑣªᨵf'(X஺)=0D._f(x)ᙠxoᜐᑣf'(X஺)[ᙠூᶧ11020503┐⚪௃|᪆~B⚪⌕ὃ'ᦪ᩽>Ḅᨵᐵᭆ஺¡ᑖ4ᑖ஺᪷¯'ᦪ᩽>[ᙠḄª⌕ᩩ%y⌱C஺{3-0426/K'ᦪ°xe*Ḅᓫ²³´᩽>஺ூᶧ11020504┐⚪௃|᪆~B⚪⌕ὃK'ᦪḄᓫ²³´᩽>஺¡ᑖ10ᑖ஺O'ᦪḄVW;(-co,-oo)oy'=e"+x(-e-x)=(1-x)e"Ty'=0,£Yx=lµ6xீl9y'>0:6x>l9yz<0»ᡠp'ᦪyḄᓫ²³;(-co,1)'ᦪyḄᓫ²³;(1,+oo)'ᦪyḄ᩽ᜧ>;y(1)=e-'{4-0614/'ᦪ·,Ḅ᩽>;x=ூᶧ11020505┐⚪௃y'=2xTy'=0£Yx=06xீ09yr<0,x>OEbj,yz>0,x=0;¸='Ḅ᩽B>{5-0626/K'ᦪf(x)=x3-3x+lḄᓫ²³᩽>ூᶧ11020506┐⚪௃OD(f)=(-oo,+oo)f(x)=3x2-3=3(x+l)(x-l)Ti(x)=0,£Yx=l,x=l(-8,-1)-1(-11)ஹ(1,+8)f(X)+00+f(x)᩽ᜧX\᩽ZXf(-1)=3*f(1)=-1

67fºX»Ḅᓫ²³;º-00,-1»Uº1,+oo»ᓫ²³;º-1,1»fºx»Ḅ᩽ᜧ>fº-1»=3᩽B>fº1»=-13.½¾Ḅ¿ᔣ´Áº1»½¾Ḅ¿ᔣV᝞lᙠºa,b»ᑁ½¾ÄÅÆÇᐸÈᜐḄᑗ¾ḄÈÊᑣ˽¾Äᙠºa,b»ᑁGᔣÈ¿ḄºÌËÈ¿ÍË¿»?᝞lᙠºa,b»ᑁ½¾ÄÅÆÇᐸÈᜐḄᑗ¾Ḅ¦Êᑣ˽¾Äᙠºa,b»º2»½¾¿ᔣḄᑨÎÏᳮ2.9&'ᦪ°fºx»ᙠв³ºa,b»ᑁᐹᨵ!▤-ᦪজ᝞lᙠºa,b»ᑁḄÒx,ឤᨵÔºx»>0,ᑣ½¾°fºx»ᙠºa,b»ᑁGᔣÈ¿º¿»Ḅঝ᝞lᙠºa,b»ᑁḄÒ•x,ឤᨵFºx»<0,ᑣ½¾y=fºx»ᙠºa,b»ᑁGᔣ¦¿º×»Ḅ஺{º1»ᑨؽ¾y=lnxḄ¿×ឋ?ூᶧ11020601O┐⚪௃y=lnxDজ=º0,+8»ூᶧ11020602O┐⚪௃º2»ᑨؽ¾y=sinxᙠ²³|0,2ᐔ~ÈḄ¿×ឋ஺

68y=sinx[0,2ᐔ]y-cosxy஻=-sinx600¿fy°xᐔ(3)½¾ḄÁV_½¾y=f(x)ÈḄPG½¾È¿¦¿ḄᑖßᑣËPG½¾°f(x)ḄÁ஺K½¾y=f(x)ḄÁḄMNOজKR!▤-ᦪr(x)?ঝKRà!▤-ᦪáÇ0ᡈ!▤-ᦪD[ᙠḄXi(i=l,2,k)?ঞÇpÈḄãäᔜḄfg!▤-ᦪGᔲh᝞GᑣæGÁḄçᙶ᪗?টKRÁḄëᙶ᪗஺{19505½¾y=6x-24x?+x4ḄÈ×(¦¿)²³G()A.(-2,2)B.(-co,0)C.(0,+00)D.(-00,+oo)ூᶧ11020603O┐⚪௃|᪆~B⚪⌕ὃᑭᵨ-ᦪK½¾Ḅ¿×²³஺¡ᑖ4ᑖ஺D(f)=(—00,4-00)y'=6-48x+4x\y"=-48+12x2=12(x+2)(x-2)Ty''=0,£x=—2,x=26-209y”>0,ᡠp½¾y=y3—3x+lḄÁG(0,1)஺{30226K'ᦪy=x3—3x2—1Ḅᓫ²³ஹ᩽>Zᐸ½¾Ḅ¿×²³´Áூᶧ11020605O┐⚪௃|᪆~B⚪⌕ὃK'ᦪḄᓫ²³ஹ᩽>Zᐸ½¾Ḅ¿×²³´Á஺¡ᑖ

698ᑖ஺D(f)=(—oo,oo)y-3x2-6x,y"=6x—6Ty'=0,£x=0,x=2,Ty"=0£x=lᑡ⊤£X(-00,0)(0.1)i(12)2(2,+oo)y'+0———0ᓝy"——0++Á/᩽ᜧ>᩽B>/y(1,-3)nf(O)=-lnUñx-5Uᡠp'ᦪḄᓫ²³;(-8,0)U(2,+oo),ᓫ²³;(0,2),᩽ᜧ>;f(0)=—1,᩽B>;f(2)=-5஺ᐸ½¾Ḅײ³;(-8,1),¿²³;(1,+oo),Á;(1,-3)஺4.½¾Ḅòó¾V᝞l½¾CÈḄôPõḼ½¾÷▲ᙢúûü9PýþÿLḄᑣLCḄ஺(1)x—8f(x)—c(cᦪ)ᓽᑣy=f(x)ᨵy=c஺(2)'x—a(ᨵ)x-a’ᡈx—)ᨵf(x)-8,ᓽᑣx=ay=f(x)Ḅ'(.ᚖ)(ᐸ1aᦪ)஺1y=-X—8X[\]^_hm1—=cox`a]^_~2x~3y=5~561X-1Ḅ,'.ூ9ᶧ;<11020606?┐AB⚪DE௃GH᪆JKL⚪M⌕ὃPQḄஹ'஺

70,x2—2x—3x2—2x—3ᑣSG=௃ᑣS,T௄Ḅ,..xJ-2x-3(x+l)(x-3)lim-------------=lim-----------------2XT-1x2-1*T-1(x+l)(x-1)~2x—3[.(x+DQ—3)l1im----x-------=lim--------------=co5r-1(x+l)(x-l)x3-2x-3ᑣ^=1V=—j------Ḅ'஺x-1(Y)ZᦪḄᨬᜧ(L)]^_▭aᵨE⚪1.ZᦪḄᨬ](1)cf(x)ᙠGa,bJfghiḄᑣf(x)ᙠGa,bJfjklᙠḼᨬᜧ]MoᨬL]m஺qf(x)ᙠGa,bJfḄᨬ]rsᙠGa,bJᑁḄ᩽]vowxyv1Qz஺{|?ᙠ}wxᑁhiḄZᦪ~jkᨵᨬᜧ]oᨬL]஺(2)QhiZᦪf(x)ᙠwxGa,bJfḄᨬᜧ]ḄH⚪?জQZᦪf(x)ᙠ(a,b)ᑁḄᡠᨵv^ᦪ~lᙠvXi(i=l,2...k)ঝfᔜvḄZᦪ]f(xPf(X2),…f(xQ^wxḄyvḄZᦪ]f(a),f(b)5ঞfḄk+2Zᦪ]ᐸ1ᨬᜧḄZᦪ]gᨬᜧ]M,ᨬLḄZᦪ]gᨬL]m஺{|?জ᝞f(x)ᙠwx(a,b)ᑁrᨵj᩽ᜧ]ᨵ᩽L]ᑣ᩽ᜧ]gf(x)ᙠwx(a,b)ᑁḄᨬᜧ]?ᳮ᝞f(x)ᙠwx(a,b)ᑁrᨵj᩽L]ᨵ᩽ᜧ]ᑣ᩽L]gf(x)ᙠwx(a,b)ᑁḄᨬL]஺ঝ᝞f(x)ᙠwxGa,bJfᓫhiZᦪᑣᨬᜧ(L)]ᙠwxyv¡z஺61G0019JQZᦪ£xb*ᙠwxG0,2JfḄᨬᜧ]¥ᨬL]()ூ9ᶧ;<11020701?┐AB⚪DE௃GH᪆JKL⚪M⌕ὃPQZᦪḄᨬ]஺§ᑖ6ᑖ஺y'=(1—x)eT¬y'=0,zvx=l,,12MD=jy(2)=—,®y(0)=0,ee_j(l)=-ᡠZᦪ°*6*ᙠwxG0,2JfḄᨬᜧ]QᨬL]y(0)=0.2.ᨬᜧ(L)]ḄaᵨE⚪QHᨬᜧ(L)]ḄaᵨE⚪Ḅ?(1)±²³⚪´µ⚪|ᑡZᦪH᪆·5(2)AZᦪQ᩽]5(3)ᑨkᨬᜧ(L)]5(4)9⚪஺62.»¼½aḄjᙽ¿ÀÁÂÃÄÅᔜÆÇjᜧLÈḄL¿ÀÁᯠʻļ

71ᢚÌÍjÎÏḄÀÐEÆÇḄL¿ÀÁḄ¼½ÑÒᡠzÀÐḄÓÔᨬᜧÕᨬᜧÓÔÑÒÕூ9ᶧ;<11020702?┐AB⚪DE௃GH᪆JKL⚪M⌕ὃPQHZᦪḄᨬ]_▭aᵨE⚪஺cL¿ÀÁḄ¼½X,ᑣÀÐÖ☢Ḅ¼½a—2x,ØcÀÐḄÓÔV,ᑣV=-2x)2,(o°,62y0஺aax=—ᡠ6à--Ḅ᩽ᜧ]vᓽgᨬᜧ]váᓽL¿ÀÁḄ¼½6ᡠzÀÐḄÓÔᨬᜧÓÔ27஺(Ä)ᑭᵨZᦪḄᓫឋäå~æ·çäx^xOᨵf(x)>g(x)êëìZᦪF(x)=f(x)g(x_F(x)§îïᩩñ?(1)F(x=O5(2)x>xOF'(x)>0,F(x)>F(x),F(x)>0o)0x>x()FF(XQ)F(x)>0F(x)-g(x)>0F(x)>g(x)6lG0026Jäå?1+xÖx+M+K)>-+>°)ூ9ᶧ;<11020703?┐AB⚪DE௃GH᪆JKL⚪M⌕ὃPᑭᵨZᦪḄᓫឋäå~æ·஺§ᑖ8ᑖ஺ä?c஻õ)=1+xln(x+J1+/)-Jl+x

72/(r)=ln(r+Jl+x2)+J—-2L__=ln(r+♦+/)f(0)=0ᑣJi+/+/x>0/3>°J"),ᓫ÷ø...f(X)>f(°)ᓽ1+xln(x+Jl+x")-Jl+x2>0áᓽ1+xln(x+Jl+x")>J1+xz*>0)jx-——02ூ9ᶧ;<11020704?┐AB⚪DE௃GH᪆JKL⚪M⌕ὃPᑭᵨZᦪḄᓫឋäå~æ·஺§ᑖ10ᑖ஺ä?/c/(x)=ln(l+x)-x+—,g(x)=x—In(1+x),i2yx>0ᔢ/(x)=---l+r=—>0,ú1+r1+r1xS(x)=1-------=------>°1+X14-X°/(x)=ln(14-x)-x4--ᡠx>02,g(x)=x—ln(l+x)ᙳᓫ÷ø2xx-——f(0),g(x)>g(0°0,ᓽ2,ln(l+x)02஺Kÿ
•ᐗᦪᑖᙠᑖᓰᨵ᩽⌕Ḅᙠὃᓰ30%,45ᑖ஺⌕ᑁ
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110_2.¬¹y=%®y=x-2ᡠᡂḄ☢Ḅ☢஺ூgᶧij11030702m┐oM⚪qr௃`t᪆b¯°%t±²³f2ly=%1/=X-2,´µḄ¶·A(1,-1),B(4,2)஺ᑣ1/=%®y=x-2ᡠᡂḄ☢Ḅ☢23Q½=Ho+2--¾=(1+2^—À)A=5ÁtHXᑖÂÃA=ᙠ&Ådx+jf`Çx-2bdx34R3_319826b¬ᵫÈᱥT=®ᐸᙠ·(1,0)ᜐḄᑗ]yÎᡠᡂḄ☢Ḅ☢஺ூgᶧij11030703m┐oM⚪qr௃`t᪆b¯°,

111y=-2xj|=-2%=1з(1,0)ᜐḄᑗ±²y=-2(x-l)஺12ᑣᡠ¬ÑÒÈᱥÓ=1*®ᐸᙠ·(1,0)ᜐḄᑗy=-2(x-l)]yÎᡠᡂḄ☢Ḅ☢஺A=(-2*+2)-(1-19=JQ(X-2x+T)dx=io(x-X)2dx_1r1\31_1=y-1)o=3¬ᵫᡂḄ☢☢ÕḄt⚪Ö×m(1)¯₝%¬°Ḅ¶·ᙶ᪗Û(2)ᵨÜÝÞß⌱áXÛ(3)âã-ᦪ®ᑖ'(m(4)cdᑖ஺%=å%/(x)dx="/2(x)dx2.æçèḄè(1)Xᵫ23éêxë0)]x=a,x=b(a

112_1(0028]2,1প¬¹x=0,x=2,y=0õÈᱥÓ=Å+LᡠᡂḄ☢Ḅ☢;ூgᶧij11030704┐oM⚪qr௃(2)¬÷☢íÎæçᕜᡠ´æçèḄè%ூgᶧij11030705┐oM⚪qr௃`t᪆b(1)A=+1ø+ø-(-/+1/3,3ù=(+/O+(b_*)12)242aJO一2X+146=--ᑍ.15(ú)ûᔠ⚪õýþ⚪1.cdýþe_1$0127%,/(▀)=6tan᦮ᦪ)f(3)+f(5)=l/4.(nூᶧ11030706┐⚪௃

113f(3)+f(5)ᦻ=tanxdx+tanxdxᑍZ32=JQtanx(l+tan&x)dxᑍ'+32,=JQtanx-secxaxᐔ,3,=JQtanxdtanx乃14-=-X4041=-42../▲12ᑖ451ᳮ720228:;6S=1-cosx,ᱏ/(;ᜐ=1஺E:;Fᓣ6HভJK6(/"ভᡂ=1-COSX.RSTUVX45Fᱏ/ডᡂ+xf(x)-xf(x)=sinx,ᓽডᡂ=sinx,ᐳX-ᙠ/S[\2,F]^(_`=sin—,ᑍ]^5b=1

1143.ᣚᐗ2ᑖ1ᳮ511Jn%-2x)ix=po")dx73efᦪRx)ᙠhi0,1/jku2ூᶧ11030707n┐⚪௃o᪆qr⚪s⌕ὃvᵨᣚᐗ2ᑖxRS஺yᑖ10ᑖ஺nz.ᣚ,\2x=t,Fx=(l-t)/2,dx=-(lফdt,|x=0t=l}|x=l/2t=0ᑣᨵF6ߟ2ஹTO(=3%=3r4.ᵨ12ᑖᦪḄᭆ749927efᦪf(x)y/ব=m-ὡ/ಘᵨ~7ூᶧ11030708n┐⚪௃\ᵨᵫ:;F/=51"F)"»2/STUVhiব/Ḅ12ᑖF=xdx-A^dxᓽFeA=LA=l/ef=-ᓽ1e5.ᵨᑖ2ᑖx..._/(%)=X-C?f(x)cosxdxஹᓝ¢75.e°f(x)=x+2

115ூᶧ11030709n┐⚪௃:/'«=1JQ/(x)cosxdx=J^/(x)dsinx=/(x)sinx|Q-sinx•/\x)dx=K6sinxdx=cosx|Q=-2/(x)=x-g/(x)cosxdx=x—(-2)=x+2r¥Kᐗfᦪ2ᑖ¦§2ᑖ¦Ḅ᪶©ᑁ«¬Kᙠὃ[®ᓰ32%,®48ᑖ°±s⌕ᑁ«²¥³´᝞¶nKஹᭆᑖ·¸n¹fᦪº»12ᑖḄᭆஹ»12ᑖḄឋ½12ᑖḄᭆºឋ½¾¿hi/ÀÁ2ᑖḄᭆ஺ÂஹÃᑖ·¸nÄKᣚᐗ2ᑖxஹᑖ2ᑖxÅû12ᑖஹ12ᑖ./▲12ᑖÆᐸ45ÈÅÃÀÁ2ᑖḄÅÃ஺ÉஹÊᵨᑖ·¸n12ᑖḄËÌÊᵨ4Í☢ÏÐḄ☢2ÑÒÓÔḄÔ2஺ÄÕÖᐗfᦪ§ᑖ¦×Øὃ⌕4L^oÖᐗfᦪḄᭆÙ4ÂᐗfᦪḄ1ÁÚ஺^oÂᐗfᦪḄËÌÛÁ஺2.^oÂᐗfᦪḄ᩽▲ºjkḄᭆ஺3.ᳮoÂᐗfᦪK▤Þ5ᦪÑᐰ§ᑖḄᭆàáÂᐗfᦪḄK▤Þ5ᦪḄ4x஺àáÂᐗfᦪḄÂ▤Þ5ᦪḄ4xàáÂᐗfᦪḄᐰ§ᑖḄ4x஺4.àá×ᔠfᦪº◚fᦪḄK▤Þ5ᦪḄ4x஺5.Ù4ÂᐗfᦪḄ¾ᩩå᩽æÑᩩå᩽æ஺6.ÙᵨÂᐗfᦪḄ¾ᩩå᩽æÆᩩå᩽æoçᓫḄé▭⚪஺ÄK⁚Öᐗfᦪ(K)ÖᐗfᦪḄᭆ1.ÖᐗfᦪḄ1Á1Á:eDOxyᙶ᪗Í☢/ḄKîhÚ᝞ïðD/ñK¸(x,y),.òzó᯿õKÊö÷²ᨵøKù1Ḅᦪ溬Êᑣúzx,yḄÂᐗfᦪûz=f(x,y)

116ᐸ[DúÂᐗfᦪḄ1ÁÚ஺üýᙢÿ
ᐗᦪu=f(x,y,z)ᐗᐗᦪᐗᦪ஺z=x2+,y2z=x+2y-12.ᐗᦪḄᐗᦪz=f(x,y)Ḅ
D,ᑣᙠᙶ᪗"Oxyz#z=f(x,y)⊤%&'(☢*+,(☢ᙠOxyᙶ᪗-☢Ḅᢗ/ᓽᦪḄ
D஺᝞z=ax+by+c⊤%••,-☢3z=ᡃ2_/_y⊤wᳫyᙠ'z,{|RḄ~{ᳫ☢z=&+/⊤wᔣ~Ḅᙊ┵☢z=x2+2⊤wᔣ~Ḅᱥ☢஺3.ᐗᦪḄ

:-☢5ᐗᦪz=*x,y)ᨵ
Ḅ&ᑗ8Ḅ9ᔠᐗᦪḄ
DᡈDপ஺ᐗᦪḄ
D=Oxyᙶ᪗-☢ᡈOxyᙶ᪗-☢Ḅ>&,?஺@ᐗᦪ
A&ᐗᦪBC◤⍳᯿G,HᑣI(1)ᑖMḄᑖNOP3(2)QᏔST᪷VGḄ⊤WMXYᜧ[ᡈ\[P3(3)]ᦪḄ^ᦪXYᜧ[P3(4)arcsinfi[x,y),arccosf(x,y)#ḄU(")I1஺(5)@_ᔠᦪ
`a[ᵫ᜜dᑮfdgh஺i1.@GᑡᐗᦪḄ
ூlᶧnV11040101I┐]p⚪rs௃224-x-f>0x2+j2<4%)={(")y2+z2{x2+y2<4|l}I>(2)y=ln(x-y)ூlᶧnVH040102I┐]p⚪rs௃

117y=ln(x-y)x-y>0,x>y0c/)={("),»}|l}{(")y<2,2cx+y4/2,2ஹy=arcsin-------------Fln(x+y)ব2ூlᶧnV11040103┐]p⚪rs௃x2+y2>00

118/3x+_y)=(x+y)&ṺD=஻,x+y=vf(u,v)=vf(x,y)=y()ᐗᦪḄ᩽▲
ᦪz=f(x,y)ᙠ8ᱏ()Ḅ>&ᑁᨵ
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Ḅ§ᦪA,ᑣA=ᦪz=f(x,y)¢8P(x,y)£¤[8ᱏ(x஺)`Ḅ᩽▲lim/(x,j)=Af0P=J("xp2+&lim/(r,7)=>lA஺()ᐗᦪḄµ¶ឋ
ᦪz=f(x,y)ᙠ8ᱏ(¸¹஺)Ḅ>&ᑁᨵ
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¥=µ¶ᦪ஺(4)ᨬᜧ(¹)
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119ÊḄ¡஺Ö⁚ØÙᦪAᐰÛᑖÜ-ÝØÙᦪ1.
ᦪz=fHx,yNᙠ8ᱏÜ(XÝḄ>&Dᑁᨵ
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Z=fHx,yNᙠ8ᱏHX஺/஺Ýᜐ]yḄØÙᦪᓽ᝞Â᩽▲.:m/Mm+3)-஻/)11ᒼߟ0Ay@r0Ay⊵=xHNᡈ%5%/dÝóᐔ᝞ÂfHx,yNᙠ?DᑁÃ&8¥ᨵØÙᦪ/Mõᑁ’ᑣ{ö+¸,ØÙᦪ÷
ᐗᦪ§ÊØÙᦪøØÙᦪ஺2.ØÙᦪḄIᐗᦪz=fHx,yNᙠ8ᱏܼ,éÝᜐ]*ḄØÙᦪ/MçÝḄ=Iᙠ(☢2=ᵯúÝA-☢kABûḄ(ü5,ᓽ(ü2=/ý¹Ýþ8ÿ᝞"ᡠᑗxḄ᳛tanaIᳮᐗᦪz=fHx,yNᙠᜐyḄᦪf■'Ḅ!"#$ᙠ%☢z=fHx,yN'☢x=xHN()Ḅ%,2,ᓽ%z=/HXoJN+,-.,0,/%,4NNᡠᑗ3Ḅ᳛tan4஺

1203.ᦪḄ89:ᐗᦪz=f(x,y),;8z=f(x,y)xḄᦪ<=⌕?ᐗᦪ@ḄyABᦪ,.=⌕x8ᓽC஺ᳮ;8ᱏEx,y)yḄᦪ<=⌕?ᐗᦪ@ḄxABᦪ.=⌕y8ᓽC஺zGHIF19515:ூKᶧMN11040107$┐P⚪RS௃dxdzF2[9805]:z=QnyUᑣdx=ூKᶧMN11040108$┐P⚪RS௃W=(1nyUln(ln,y)y=.ylnIny.QnyZtdxA.^Qn/T-iB.Qny)°lnlny/(ln/)XJlnlnjD.xQnyyInlnyc[K\CdzF30005:z=sm(]2),ᑣ^=஺ூKᶧMN11040109$┐P⚪RS௃xycos(xy2)-xycos(xy2)AB-y2cos(xy2)y2cos(xy2)cD[K\D1z-,HF40014:®ூKᶧMN11040110$┐P⚪RS௃ᡭX/

12112[K\zydzz=e',——F50608dxdzxyxy—=ey=yeydxyz=ex,Hlj—qn=________F0114:^'''஺ூKᶧMNH040111$┐P⚪RS௃ae.2.20.1df(x,y)df(x,y)ff(?y,x-y)=x+y,ᑣ--------+--------=F69710dedx®ூKᶧMN11040112$┐P⚪RS௃/(wy)=0hE+29/(w,v)=h+2i1/(")=2x+1/=2,=2ydx------®df(x,y}df(x,y)-------------1-------------=2+2ydxdyA.2+2yB.2-2yC.2x+2yD.2-2y[K\A()ᐰlᑖ1.ᐰlᑖḄn"n"::z=f(x,y)ᙠP(x,y)Ḅphqrᑁᨵn"uvwxx,yḄᦋwxzᑍᑗ᝞|ᦪz=f(x,y)Ḅᐰᦋwxk=/(x+A"+Ay))C⊤~Az=-4Ax+5-Ay4-o(/7)22ᐸ@A,BᐵC#x,yḄᦪ;°=+᝞)70

122#0஺Ḅ▤xᑣ+B஽ᦪf(x,y)ᙠ(x,y)ᜐḄᐰlᑖdz,^dz=ALx+BLyᦪz=f(x,y)ᙠP(x,y)ᜐCl஺tAz=A,Ax+34y+o(Q)(Q-0)dy=+BLyττ=(\)%)8=3”,170)II&(.)=஺0Jo+(,%)4IIញ(᜜)=/&)^+,%)ḄIIdz=f{x,y}dx+fy^y'jdydz=A-Lx+BLyx᝞|z=f(x,y)ᙠrDᑁḄh(x,y)Clᑖᑣf(x,y)ᙠDᑁClᑖᵫCiAE᝞|z=f(x,y)ᙠDᑁClᑖᑣPlᑖn(x,y)Ḅᦪ஺(ᙢᦪz=f(x,y)ᙠ1஺/஺)ᜐḄlᑖCiᳮlᑖᦪdzᙠ“0/0)ᜐḄBdz2.ᐰlᑖᙠḄ⌕ᩩ¢ᐙᑖᩩ¢(1)ᐰlᑖᙠḄ⌕ᩩ¢:z=f(x,y)ᙠ(X஺J஺)ᜐClᑖᑣz=f(x,y)ᙠᜐḄ¤¥ᦪ/¦஺)'/§®஺,஺)nᙠ¨=/ᓰ0%)3=஻«,%)ᡈdz&A=—B=—dx®᝞|z=f(x,y)ᙠrDᑁClᑖᑣᨵ&,ydzX=ZQdyudxy=yoUᐔ᪵᝞|z=f(x,y)ᙠrDᑁClᑖᑣ

123dz=—dx-\----dydxdy(2)ᐰlᑖᙠḄᐙᑖᩩ¢dzdz~~~,nᳮ1᝞|z=f(x,y)ᙠP(x,y)ᜐᨵ±²Ḅh▤ᦪ³,ᑣz=f(x,y)ᙠP(x,y),dz,´az=—ax+—dyᜐClᑖ¨µ᝞3.ᐰlᑖḄ898z=f(x,y)ḄᐰlᑖḄ⊤¶¦Cᐜ8E¤¥h▤ᦪᯠ¹ºᐭᐰlᑖ¼¦ᓽC஺½⌕¾¿ᐰlᑖḄᑣ⌕?'ஹ0Ḅºᐭ?dxᵨAxஹᵨÂḄºᐭ஺22%ÃF1[0404]ᦪz=x+yᙠ(1,1)ᜐḄᐰlᑖoூKᶧMN11040201$┐P⚪RS௃dzdzÄ=2])=2dzdz.—=2Æ—/I-lx=2^^(D)È(1,1)=É(1,1)¼+9(1,1)=2dx+2dyA.dx+dyB.2dx+2dyC.2dx+dyD.dx+2dy[K]B2F2[0221^z=sm(x,y)+2x+y8E஺t(KᶧMN11040202$┐P⚪RS௃dz—=cos(D)y+4xdxdz—=cos(xy)-x+1,dz,dz.dz=——dx+——aydxdy=[4x+ycos(p)]d;v+[1+xcos(xy)]dyF3[9825]:z=xe'+sin(xy),8Ë஺

124ூKᶧMN11040203$┐P⚪RS௃z1=9+Ñ-V.ಔ)+cos(xy).y=e-xye+^cos(xy)1—zy=xe-(-x)+cos(xy)-x=xcos(zy)»dz-z*dx+zydy=[eṺ-Ô+.Xcos(A^)]d?x+[xcos(xy)-e'ᦑF4[9924]:z=f(2x+3y,eX),8dZoூKᶧMN11040204$┐P⚪RS௃Pdfdu^dfdvdf1nadxdudxdvdxdudvᒹᑏ2ᵱxy—=----3+-----&-xdydudvdzdzdz=——dxH----dydxdy=(—•2H-----ye)ax+(—•3H-----xe)aydudvdudv(Ø)Ùᔠᦪlᑖ91.ÙᔠᦪḄÛ¦9ᑣnᳮ$:ᦪu=u(x,y),v=v(x,y)ᙠ(x,y)ᜐᨵ±²Ḅᦪ஺ᦪz=f(u,v)ᙠ(u,v)ᜐᨵ±²ḄᦪᑣÙᔠᦪZ=f[u(x,y),v(x,y)]ᙠ(x,y)ᨵx,y±²ᦪ¨dz&du^dzdvdxdudxdxdzdzdudzdv———.—+—.—dydudydvdyi+¼¦ÙᔠᦪḄÛ¦9ᑣ2.áᱯãäåæḄÛ¦9ᑣ:æ☢áᱯãç¦èᔠ+énᳮ@Ḅᩩ¢$(1)᝞|z=f(u,v),u=u(x),u=v(x),ᓽz=f[u(x),v(x)],ᑣᦪZXḄᐰᦪ:dzdzdudzdv(2)᝞|z=f(x,y),y=y(x),ᓽz=f[x,y(x)],ᑣᦪzxḄᐰᦪ:

125dzdfdfdy---=-----+----------dxdx®dxz=Js”,ᵨëv=x+Æ8ìËF1.:Gxdy஺ூKᶧMN11040205$┐P⚪RS௃3zu9zu—=QsinV,—=QCOSV3udvdududvdv——1,——13xdydzdzdadzdv.uu---------------1-------------esinyy+®cosv13x3u3xdv3x=sin(x+y)+cos(x+y)]dzxy—=e/[xsin(x+y)+cos(x+y)]dy(î)◚ᦪlᑖ9i.hᐗ◚ᦪ:ᵫᐗñF(x,y40ᡠónḄ◚ᦪ4y(x),᝞|F(x,y)x,yᙠ±²ᦪ¨竺Ë=_ax竺3Fdx——w0办ᦔ,ᑣyxḄᦪ2.ᐗ◚ᦪ:ØᐗñF(x,y,z)=0ón◚ᦪz=z(x,y),᝞|F(x,y,z)x,y,zᙠ±²ᦪ¨9Fwdzydzdy"dxdy3F—0u——yᑣZXஹyḄᦪyᒹ஺dzF1[0225]:z=f(x,y)ᵫñõ+§+z=*ᡠón8஺ூKᶧMN11040206$┐P⚪RS௃

126dzdz2y+2z----=x(z+y—)1dz(2z-xy)—=xz-2ydzxz-2ydy2z-xyF(x,y,z)=/+/+z2-xyzdF~—=2y—xzdFdzdyxz-2ydy2z-xydzdzF2[0125]:z=f(x,y)ᵫñø=T+/ᡠón88x஺ூKᶧMN11040207$┐P⚪RS௃dF---=ZdxdFz——=x-&dzdFᵯ$$z.zdx3Fx-ez&z-xdzF3[0025]:z=f(x,y)ᵫñXᡠón8dz஺ூKᶧMN11040208$┐P⚪RS௃

127:F(x,y,z)+z^-2yezdFdFz8xṺ8Fz—=2z-2y&dzdzg2x_xxdxdF2z-2yezyez-2dyù2z-2yezz-ye,dzஹdzஹaz=——ax-\-----aydxdyzx,e-———dx+-------Ṻye-zz-yexdx-ezdyzye-zú▤ᦪ᝞|z=f
x,yᙠrDᑁh
x,yᜐᙠᦪ,ûüy“ᑣÿ
ý¤¥ᦪþnᦪ஺᝞|ý¤¥ᦪḄᦪ´ᙠ,ᑣf
x,yḄ▤ᦪ஺ddzz",ஹ=-0=/xx
xjoxdxdxddz0z"d—=T-r-=f»xjdyoxdxq^ddz@z"d-==/yx"oxdyd^dxddzz"^^^2"dz0zdxdy'dydxfx,y▤ᔠᦪ஺

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y@AᐗCᦪḄ᩽Ei.ᐗCᦪ᩽E1G8Cᦪz=/xjᙠH᧊J,KAḄLMNᑁᨵGP/ᙠNᑁQRST᧊XoJoḄHUXJA,᝞VᨵW"PAY/PᵨAPᑣH᧊=⊈JoḄ᩽ᜧEHP/^_""AḄ᩽ᜧE`᝞Vᨵ஻"Ab/^_PᑣH᧊Ḅ‘J஻"AḄ᩽dEHP஻eJo஻"AḄ᩽dE஺2᩽EfᙠḄ"⌕ᩩiᳮ3᩽EfᙠḄ"⌕ᩩiA᝞Cᦪz=fx,yᙠHjX஺,klm᩽EPnᙠHḄᦪfᙠPᑣ"ᨵ£஽,ᙢ=0,r᝞_=0.

129stPuA=0,4P_=0xyᡂ{ḄH|JoACᦪ2=஻%7AḄHPᵫᳮPCᦪḄ᩽EHMHPPHM᩽EH஺%᝞z=xy,0,0A᩽EH஺3A᩽EfᙠḄᐙᑖᩩiᳮ4᩽EfᙠḄᐙᑖᩩiA8Cᦪz=/xjAᙠHeJ0AḄLMNᑁᨵḄM▤▤ᦪPnH᧊e'ACᦪ/ḄHPᓽ£ePA=°/PA=஺eP_=/P£`5_=£7PA=ᑣজR2-jc<0,n<<0ᡈC<0yP᧊J஺AḄ᩽ᜧEHP¦AW”PAḄ᩽ᜧE`ঝB2_¡C0ᡈC>0yPᱏJಘP“AḄ᩽dEHP“e_஻x,yAḄ᩽dE`ঞ/c>0yP“JJḄ᩽E஺ট§2M5c=CAyP/SoJ0A²᩽E`³²᩽EP⌕ᵨᐸ<µ¶·¸¹஺22%1403255?CᦪPxjA=4x_yA-x_JḄ᩽E஺ூ)ᶧ+,11040301-┐/⚪12௃4¼᪆5¼<¾¿。&-=4-2%=0，5ax&¥=-4-2y=01、mH2,-2A,ÀÁAÃa7ZlI2--2A=c’naÊ?ZIÌ-2A=oc=Ãd2ZIL-2A=-2B2-AC=-4<0,A=-2<0ᡠ/2,-2A=8᩽ᜧE.

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134(C)156(D)169ூ1ᶧ3411050102┐78⚪:;௃=13x12=1561(C)஺(2)ᓝ¡G¢£¤ᓱ¦§ᐸ©Gᔜ«W¤ᓱQ¬~©®ᐳ«W¤ᓱḄ¬ᦪ¯()(A)50(B)100(C)(D)90ூ1ᶧ3411050103┐78⚪:;௃°᪆²³⚪´⌕ὃ·᣸ᑡḄᭆ¹r᣸ᑡᦪcdef஺ºᑖ5ᑖ஺ᓝ¡G¼½¢£¤ᓱᨵ«ᓱ¾ᦈᓱ¼ᑖᓽᨵRSឋÁ᣸ᑡ;⚪஺10EFGᐗI¦L2EᐗIḄᡠᨵFG᣸ᑡEᦪ!=10x9=90ᦑ⌱(D)஺(3)ᵨ1,2,3,4,5,6uᡂÄᨵpqᦪÅḄFGḄt¡ᦪᐳᨵ()(A)120(B)60(C)20(D)216ூ1ᶧ3411050104┐78⚪:;௃°᪆²³⚪´⌕ὃ·᣸ᑡḄᭆ¹r᣸ᑡᦪcdf஺ºᑖ5ᑖ஺~P+~¢Æ!t¡ᦪᨵE¡ஹᓝ¡¾Ç¡¼ᑖᓽLWḄtEᦪžÈÉRSᨵᐵᡠr˯᣸ᑡ;⚪ᵫ᣸ᑡᦪefÌË᪵FGḄt¡ᦪᐳᨵ()¡—6x5x4=120ᦑ⌱(A)»2.⌱⚪(ᨵ▲ᑴᩩÒḄ᣸ᑡ;⚪)(1)ᵨ0,1,2,3uᡂÄᨵpqᦪÅḄÓ¡ᦪᐳᨵ()(A)6E(B)12E(C)18E(D)24Eூ1ᶧ3411050105┐78⚪:;௃°᪆²³⚪´⌕ὃ·᣸ᑡÔᭆ¹?᣸ᑡᦪ”de×஺ºᑖ5ᑖ஺ᓟ|¥|ᓝ|¢Æ!Ó¡ᦪᨵE¡ஹᓝ¡ஹÇ¡¾ᓟ¡¼ᑖᓽLWḄÓEᦪžÈÉRSᨵᐵᡠr˯᣸ᑡ;⚪஺Ù⌕ὃ⇋ᦪÅ0FÛᙠ✌¡ᑖÞßᡂà᣸ᑡᦪefÌË᪵FGḄÓ

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142anBPnc=>inMBn.ᑖÔÊMÕuᑗnc=MRnouMEncPM3PMHn6Uc=MHUGnMBUGYᏔÊMÚ=4nKÛÜ=zuM4PÞ2.ßlᢇqá5âãlqáäÛNåæMᓽçèéãḄqáNêåæ.ëçèéãḄqáêåæ.ᑣ7åæP.4•⊤ìièâᑮíáMi=l,2,3P,ᵨᦻïðñºᑡi°41Pzóூõᶧ÷11050207┐Y´⚪üý௃ÿ4U«Uᙳ⊤ᨵᑮ2°AM2aூᶧ11050208┐"#⚪%&௃(4y⊤ᑮḄ+,30./Uὡ/U/1ூᶧ11050209┐"#⚪%&௃(^⊤4ᨵ5ᑮ4°/7ὡ14ூᶧ11050210┐"#⚪%&௃(A8AU4AAUᜐAA⊤4ាᨵᑮ஺32323<3.>ᢇ@4AB@CDEFGHIJᓽLMAḄ@ENFGOPLMAḄ@NFGOᑣRSFGHITOUV4⊤WiᑮJᔠZi=l,2,3T,Hᵨ4,_O`⊤aᑡUV1°+ᑮூᶧ11050211┐"#⚪%&௃(ᑁdᙳ+ᑮOᓽOeBUV7fghO⊤Siᙳ432°4ᨵ5ᑮூᶧ11050212┐"#⚪%&௃

143(4ᨵ5ᑮOjᕡḼWmWnᑮJ4,2T,WmWᑮJ44T,WnmWᑮJSoTOeBUVᨵBghO⊤S44U4`U4p?4rᨵᑮூᶧ11050213┐"#⚪%&௃(4rᨵᑮOᓽាᨵ•ᑮ஺jᕡḼᑮḄB@4rᨵB,Otᐸv5B,Oᦑxy⊤S44஽{U4E|4°4}ᨵ••ᑮ஺ூᶧ11050214┐"#⚪%&௃(4}ᨵ•ᑮOjᕡḼ4~ᨵᑮJᓽᐰ,TᡈrᨵᑮOᦑxy⊤S4ᙳὡ44444஺<4.⌱⚪J1TAஹBஹCஹ,BUVOAஹBஹC4ាᨵ5BUVghḄU⊤SJTA.A+B+CABC+JiBC+ABCBC•/!+R+CABC+ABC+ABCDூᶧ11050215┐"#⚪%&௃DJ2TA,BS5UVOᑣaᑡᡂḄ,JT,A.4+3=A-\-BB.AB=ABC.ᨴ+B=3+AB0X+S=5+ABூᶧ•11050216┐"#⚪%&௃CJ3TᵬஹnOAஹBᑖ¡⊤ᵬஹ4¢᪗ḄUVON+B⊤JTA.n+~4B.ᨵ~4

144C.n+4D.ᨵ4ூᶧ11050217┐"#⚪%&௃BWn⁚UVḄᭆ᳛ஹᭆ᳛Ḅ©ª«¬1.⚣ᦪ¯⚣᳛«¬ᙠ±7ᩩVaCDn´µHIO᝞·UVAgh¸kOᑣRk¨yJXT=—SUVAghḄ⚣ᦪO»¼▀RSUVAghḄ⚣᳛O¾¿S6T,ᓽ"▀஺ᑡ᝞OᔊÂÃÄᨵ¿ÅÆÇÈÉḄᜧË´µHI஺᝞a⊤ᡠ:HIὅÇÉᦪn☢AÐᦪk☢AÐ⚣᳛k/nÑ•᥅᪷204810610.5181ÔÕ404020480.5069Ö×Ø1200060190.5016Ö×Ø24000120120.5005ÙÚ30000149940.4998>Ã⊤xyÛAO`HIᦪ⌲ÝÞ}fO☢AÐḄ⚣᳛¼,ß«ḄOàᙠ0.5▬â᤮ä஺2.ᭆ᳛Ḅ©ª«¬«¬ᙠ±7ᩩVaO´µCDnHIOUVAghḄ⚣᳛ß«ᙢᙠæçᦪp▬â᤮äOtéêëᩭOnៜᜧO᤮äḄîïៜðOᑣRçᦪpSUVAghḄᭆ᳛O¾¿PJAT=pnஹᭆ᳛Ḅòᐺ«¬1.òᐺᭆô᝞·HIᐹᨵ᝞aö⌕ᱯùJ1TJᨵ▲ឋTLHIrᨵᨵ▲BxüHIý·Oᓽ᪵ÿ
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14521p(A)=-=-ᑣ42D2.nopF)qᙳᒴḄrsMNḄᦪtu-8Ḅᭆ᳛-()ூUᶧWX110503027┐]^⚪`a௃cd᪆fnopF)qᙳᒴrsḄxyᐗ{Ḅ᣸ᑡᐸ:ᦪ-36ᓽ12345611,11,21,31,41,51,622,12,22,32,42,52,633,13,23,33,43,53,644,14,24,34,44,54,655,15,25,35,45,55,666,16,26,36,46,56,6P!Ḅឋ$%ḄᐸMNḄᦪtu-8Ḅ=(,lA7“MNḄᦪtu-8“I36,ᦑ⌱(B)஺lX7“)qrsMNḄᦪtu”ᑣk23456789101112m12345654321P(X=k)%6%%6%6%6%%6%6ஹᭆ᳛Ḅឋᑣឋ1.0P(A)+P(B)

1462.]n-A,ᨵp(&=1->ভ3.]noA,B,C,ᨵP(A+B+C)=P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC)c05.10f¡AḄPA=0.6,ᑣAḄ]£AḄᭆ᳛>ভ=04«ூUᶧWX110503037┐]^⚪`a௃D3.¥¦ᨵ4§¨ᳫ2§ªᳫ«¥n¬ᳫ)¬1§ᑖ)®¯°1ᨵ±²³¬´2µ±²³¬ᙠ'()®¯°¶L¶ᑡḄᭆ᳛জ¬ᑮ2§¨ᳫ´ூUᶧWX110503047┐]^⚪`a௃ঝ¬ᑮ2§¹⁐$%Ḅᳫ´ூUᶧWX110503057┐]^⚪`a௃ঞ¬ᑮḄ2§ᳫ¼½ᨵ1§¨ᳫ஺ூUᶧWX110503067┐]^⚪`a௃cd᪆flA7“¬ᑮ2§¨ᳫ”B7“¬ᑮ2§ªᳫ”C7“¬ᑮḄ2§ᳫ¼½ᨵ1§¨ᳫ”஺1ᨵ±²³¬44164জªভ—x—=—=D663692241P®=—x—=——=—66369415ঝª(4+3)=P(4)+2(3)=]+´=/—12ঞ9(ঢ=P(JB)=1—9(B)=1—§2µ±²³¬43122জª(4)=—x—=—=—653052121P«—x—=—=—653015217ঝ(ᨴ+=ᡝ(ভ+20)=(+t=5ঞP(C)=P(B)=1D20)=1-°᨟D4.)ÆÇÈÉᙢᢗᐭ᪗X-1,2,3,4Ḅ4ÍÎᑣ1,2XÍÎᔜᨵPÆÇḄᭆ᳛Ð

147ூUᶧWX110503077┐]^⚪`a௃cd᪆flA7“1,2ÍÎᔜᨵPÆÇ”஺:ᦪÒ=4=16,AᒹḄᦪm=2!=2,ᑣḄ16Mᦑ⌱C஺D5.ÕᵯᾯØÙÚἠ(36⌱7)ᝄᭆ᳛᝞¶⊤ூUᶧWX110503087┐]^⚪`a௃ᝄ⚗⌱ᦪáâãᝄᭆ᳛ᱯ1]*******⌱77ᝄ568347680.******6Q⌱X+ᱯCå7_1ᝄ೙X5683476801192526æ******Cç9203_16Q⌱Xᝄ%8347680411225Q⌱X+ᱯc2;Ck9609_1*****೙ᝄX'8347680137075Q⌱XᡈèU7U29τ^7^1^2922736_14Q⌱X+ᱯᝄ****೙¬ê68347680—367Xë****4Q⌱Xᡈ433í13255780_15^291^7^1^293Q⌱X+ᱯᝄ***೙ᡈ48347680-33■)î⁚ᩩᭆ᳛ஹñஹḄò£ឋPஹᩩᭆ᳛5617lᨵA,B,óP(B)>0,,Pভ᝾°õöᙢ᝞÷P(A)>0,ᑣB]AḄᩩᭆ᳛-

148D1.%øF)⚩ᙳᒴḄrsᙠMNḄᦪtu-7Ḅúᛀ¶ᨵ•⚩rs-1Ḅᭆ᳛½஺ூUᶧWX110504017┐]^⚪`a௃cd᪆flA7"ᦪtu-7”B7“ᐸP⚩-1”஺A:{(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}
AB:{(1,6),(6,1)}212(3|ᨴ)=±=91:63221P(AB)1p(BIA)=_18_162.ᨵ10ᩈᳫ6ᴻᳫᩈᳫᨵ3!":⁐7!%⁐ᴻᳫᨵ2!&⁐4!%⁐஺)*+,-ᳫᵨA⊤0“,ᑮ%⁐ᳫ”B⊤0“,ᑮᴻᳫ”,4P(B|A)oூ9ᶧ;<11050402┐?@⚪BC௃᪆Fᑡ⊤ᑖ᪆IJᩩ
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A,B,C,ᨵ

149P(ABC)=P(A)P(B\A)P(dtAB)P(A)=1,P(B)=-,`a3.bc
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151ᭆ᳛ᑖµḄឋ·2132¸¹ឋNº~20~=஺,2,…32232»ឋNZ½=13.ᑖᦪ7ᭆ᳛ᑖ89Ḅᐵ;¾x)=P(XWx)=Z¿>Xᦣ?ᑣ஺@1.ABCᨵ6Fᳫ?ᐸC1Iᳫ3J?2Iᳫ2J?3Iᳫ1J?ᙠᐸCLMNJᳫ஺&X⊤,MOḄᳫḄ᪗ṹ?RXḄᭆ᳛ᑖ7ᑖᦪ஺ூTᶧVI11050501-┐YZ⚪\]௃_`᪆bXNᑗ%d
1,2,363ᖝ=33="XḄᭆ᳛ᑖ121/21/3XḄᑖᦪfox3@2.ᨵ3mn2Jop?qnᢗᐭopC?ᵨX⊤,“ᨵnḄopᦪ”?RXḄᭆ᳛ᑖ7ᑖᦪ஺ூTᶧVI11050502-┐YZ⚪\]௃_`᪆bXNᑗ%d
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152XḄᑖᦪ0x2()Ḅᦪᱯ1.ᦪ(1)ᦪḄᭆ-Xᦣ?ᐸᭆ᳛ᦪ(k=l,2,3,-)XkPkfXkPk>ᦪQYᦈ?ᑣXḄᦪ?ᡈᙳ
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1530012Pika0.20.5(1)RaḄ
-ூTᶧVI11050503-┐YZ⚪\]௃(2)REX~ூTᶧVI11050504-┐YZ⚪\]௃(3)RDX஺ூTᶧVI11050505-┐YZ⚪\]௃[`᪆](1)a=l-(0.2+0.5)=0.3(2)EX=OxO.3+lxO.2+2xO.5=1.2ব£)Y=(0-1.2)2X0.3+(1-1.2)2X0.2+(2-1.2)2X0,5=0,76ᡈὅ᝞(`-DX=EX2-Eব2X2014p0.30.20.54=0x0.3+1x0.2+4x05=2.2DX=EX2-(£Z)2=2.2-(1.2)2=0.76[2][0525]XᑖᑡX123P0.2a0.5(1)Ra=?ூTᶧVI11050506-┐YZ⚪\]௃(2)RXḄEXூTᶧVI11050507-┐YZ⚪\]௃`:(1)a=l-(0.2+0.5)=0.3(2)EX=1X0.2+2X0.3+.X0.5=2.3@2.XḄஹᑖÅE(X),D(X),ÆY=aX+bᑣᨵE(YD(Y)=஺ூTᶧVI11050508-┐YZ⚪\]௃_`᪆b(1)EY=E(aX+baEX+b,(2)DY=D{aX+b)=a1DX@3.ÉÊE(X)=-1,D(Xᡝ3,R*[3(¡2-2)]ூTᶧVI11050509-┐YZ⚪\]௃[`᪆]E(X2)=DXÎQ2=3+(-1)2=4+E[3(XZ-2)]=3[£(Z2)-2]=3(4-2)=6

154@4.ÏCÐᨵᑖÅ᪗1,2,3,4,5ᦪḄᳫ?ÑCLM3J?ᵨX⊤,ᡠM3ᳫCᨬÔḄᦪ?(1)RXḄᭆ᳛ᑖ~ூTᶧVI11050510-┐YZ⚪\]௃(2)EX,DXூTᶧVI11050511-┐YZ⚪\]௃_`᪆bXNᑗ%d
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