成考高数二概念大全

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ᦪஹ᩽▲§1.1ᦪ
ஹ⌕ᑁಔᦪḄᭆ1.ᦪḄy=f(x),xGD#D(f),$#Z(f).f/(x)xeDy=1ீ2.ᑖ)ᦪ[g(X)XGZ>23.◚ᦪF(x,y)=04./ᦪy=f(x)fx=4>(y)=f1(y)y=f-1(x)ᳮ:᝞5ᦪy=f(x),D(f)=X,Z(f)=Y89:ᓫ<=>(ᡈ@A)ḄBᑣDEFᙠ/ᦪy=f'(x),D(f')=Y,Z(f')=XIJ89:ᓫ<=>(ᡈ@A)Ḅ஺ಕᦪḄMNᱯឋ1.ᦪḄᓫ<ឋy=f(x),xGD,Xi>xGD2RXiVx2T,Uf(xi)Wf(X2),ᑣWf(x)ᙠDᑁᓫ<=>()BUf(xj(X2),ᑣWf(x)ᙠDᑁᓫ<@A()BUf(X1)

1ᑣWf(x)ᙠDᑁ9:ᓫ<=>()BUf(X|)>f(x),2ᑣWf(x)ᙠDᑁ9:ᓫ<@A()o2.ᦪḄ᜻ᏔឋD(f)ᐵ_`abWᏔᦪ:f(-X)=f(x)᜻ᦪ:f(-X)=-f(x)3.ᦪḄᕜdឋᕜdᦪf(x+T)=f(x),x£ᕜ8,+oo)ᕜdT——ᨬkḄlᦪ4.ᦪḄᨵnឋ:|f(x)|WM,xG(a,b)ಖstuvᦪ1.wᦪᦪy=c,(cywᦪ)2.zᦪy=xn,(ny|ᦪ)3.ᢣᦪᦪy=a',(a>0ஹaWl)4.bᦪᦪy=logx,(a>0ஹaWl)a5.ᦪy=sinx,y=conxy=tanx,y=cotxy=secx,y=cscx6./ᦪy=arcsinx,y=arcconxy=arctanx,y=arccotxಗᔠᦪuvᦪ

21.ᔠᦪy=f(u),u=6(x)y=f[<1>(x)],x£X2.uvᦪᵫstuvᦪᨵ▲Ḅᑣ(>ஹ@ஹஹ◀)ᔠᡠ᪀ᡂḄIᵨ
ᦪ¡⊤£Ḅᦪ§1.2᩽▲
ஹ⌕ᑁಔ᩽▲Ḅᭆ1,ᦪᑡḄ᩽▲lim%—An—>coWᦪᑡ¥%§¨wᦪAy᩽▲BᡈWᦪᑡ§ᦈ«_A.ᳮU¥>஻§Ḅ᩽▲Fᙠ=y஻§Eᨵn.2.ᦪḄ᩽▲পRX—8T/(X)Ḅ᩽▲limf(x)=Aஹᓅ
00Aolim/(x)=Ahm/(x)=AX—>00x—>+00JফRxf/Tf(x)Ḅ᩽▲:

3lim/(%)=AXf%0"lim/(x)=A°᩽▲:X-^XQlim/(x)=A±᩽▲:Xߟবᦪ᩽▲FḄᐙ⌕ᩩµ:lim/(x)=A=lim/(x)=lim/(x)=Aᳮ:0Xfgಕ¶·ᜧ¹¶·k¹i,¶·ᜧ¹ᓅº/¼½¾1=+8Wᙠ¿ÀᓄÂÃ/¼X¾y¶·ᜧ¹஺XÄÅÀᓄÂ8ᢣX--->—00X-->+00,X---00,X,JC,JC?2.¶·k¹lim/(x)=0Wᙠ¿ÀᓄÂÃf¼Æ¾y¶·k¹஺3.¶·ᜧ¹Ç¶·k¹ḄᐵÈ:1lim/(x)=0<=>lim=+00,(/(x)஺0)ᳮ/(x)

4lima=O,limJ3=04.¶·k¹ḄÉÊ:পU“m£
ËᑣWB8É஺ÊÌ▤Ḅ¶·k¹;lim2=CফUa¼cywᦪ¾ᑣWBÇaº▤Ḅ¶·k¹;বUHÐ=1ᑣWBÇa8vÑḄ¶·k¹ÒÓ—ভUli/=00ᑣWB8ÉQÊÕ▤Ḅ¶·k¹஺ᳮU%~Bia?~×2Bᑣ1>=HmᜓಖÙ☢ᜳᳮ1.ᦪᑡ᩽▲FᙠḄᑨÝᑣÞß
y2—¼=K2ஹ3-¾nálim/=limz=anq-஻
ã8nslimx-anᑣ:஻-00

52.ᦪ᩽▲FᙠḄᑨÝᑣÞb_aX஺ḄÅä#ᑁḄ
ᑗa(aX஺◀᜜)ᨵg(x)

6ಘÙò⌕᩽▲ìsin%1ìsin(p(x)]lim-------=1hm------------=11.%—0xᡈ(p(x)11lim(1H—)'=elim(l+-e2.x->oo1%—0§1.3
ஹ⌕ᑁಔᦪḄឋ1.ᦪᙠ᳝)ᜐ/(X)ᙠ᳝)Ḅä#ᑁᨵ1°limAy=lim[f(x+Ax)-f(x)]=O1Ar->0x-^0oolim/(%)=/(%)°2"x)=/(x஺)±᝞"x)="x஺)2.ᦪᙠᜐḄE⌕ᩩµᳮ/(X)ᙠ᳝)ᜐ/(%)ᙠ/ᜐ᩽▲Fᙠ3.ᦪᙠõ)ᜐḄᐙ⌕ᩩµ:

7limf(x)=/(᳝))olimf(x)=limf(x)=/(x)07Eùx->xX^XQxfú04.ᦪᙠû/(/)ᙠûü
aý஺ᙠþa஻஻8ᢣlim/(x)=/(^)
ArCllimf(x)=f(b)…—ᩈᜐᜩ…-''
஺---g---1----6-------►a'0bx5.ᦪḄ!"#$/(X)ᙠX0ᜐ()ᑣ+0,-পḄ!"஺!"ᨵ0123:r(X))ᙠᜐ678;2᯿/<(=ᙠ;3஺anᙠ@)ᜐᨵ78)A=ᙠ,lim/(x)^/(x)0Dx-^x஺GEF!"Ḅᑨ":

81°HIF!":ᱯ#K”MNO/পP=ᙠ஺QR!"#%;T)=ᙠ)Dlim/(x)^/(x)^0(x)xᙠX஺ᜐ678஺2°HUF!":ᱯ’ᔳ"YZ/ಘ\ߟᡈ1_"I)`₩(=ᙠ஺lim/(%)lim/(x)6b!"#c.dNX—E\eᨵIf,8ಕᦪᙠ᳝)ᜐḄឋk1.ᦪḄlᑣmn:lim/(x)=/(x)limg(x)=g(x)00oX-^XQ)X-lim[f(x)±g(x)]=f(x)±g(x)00i%—plim[f(x)-g(x)]=f(x)-g(x)002X—>X0

9limqপ=£(s)(Xlimg(x)w03஺iog(x)g(x)I%I%஺)o2.tᔠᦪḄឋ#y=/(஻),஻=o(x),y=/[஺(%)]%#%())())(°));(pQo)y(w)=/[^(x)]0limf[(p(x)]=f[lim^(x)]=/[y/)]zIJ%oN3.{ᦪḄឋ#y=f(x),x=|প)y=fM0lim/(%)=f(x)olim|(y)=|(%)0%->%())'->y஺ಖᦪᙠ[஻)Ḅឋk1.ᨬᜧpᨬ7ᳮ#

100'abxm-M0ax2.ᨵ7ᳮ#/Rᙠa,U^/%ᙠ஻)bI7ᨵ஺3.7ᳮ#/XᙠUᙠ“0ᑁ\e=ᙠI:f&=C,ᐸ#m

11#f%ᙠ஻)ᓬ,A/஻p/Snᙠ஺/ᑁᒹI)#/C9=°஺4.ᦪḄឋ#ᦪᙠᐸ7¡¢!ᑁP£Ḅ஺

12HU¤Iᐗᦪ¦ᑖ¨§2.1©ᦪp¦ᑖIஹ«⌕ᑁಔ©ᦪḄᭆ°1.©ᦪ#y=/”ᙠ“0Ḅ±f²¡ᑁᨵ78)lᒹ=l”c஺+&I.“஺imimAx-»oAX=lim/d(x஺)XfXoX—X()¶஺=஺·X=Xo—im2.
©ᦪ:Xf¸x-x0/(x)-/(x)/+(x)=lim00©ᦪ#X->XQx-x07ᳮ#/Xᙠ/Ḅ
ᡈ²¡ᙠᐸᑁQ©)A᩽▲=ᙠ;

13ᑣr(x)=lim/7x)0„/"(x)=limf\x)(ᡈ#J+'0("xfx”')3.ᦪQ©Ḅ»⌕ᩩ½:7ᳮ#/(X)ᙠ“஺ᜐQ©n/(%)ᙠ“0ᜐ4.ᦪQ©Ḅᐙ⌕ᩩ½:7ᳮ#yx=x=f("())=ᙠ=/_(”())=/+(%0),0A=ᙠ஺5.©ᦪ#XG(஻,5)/(x)ᙠ(஻)஻)ᑁᜐᜐQ©஺y/Vo)6.©ᦪḄÂÃឋk:AyÄ(+0)£ÅÆy=/(%)AxM(Xoy())ᜐᑗÆḄÈ᳛஺OXoXಕË©Ìᑣ1.ÎÏË©ÐÑ:2.©ᦪḄlᑣmn#rr1஺(u±v)=u±v2஺(஻u)'=஻"+஻•Ó

14ru\_ur-v-u-vf2(3)3஺V3.tᔠᦪḄ©ᦪ:y=/(஻))u=(p(x),y=f[(p(x)]dydydu----=-----•-----dxdudx?ᡈ{/1஺(c)]}'=/'[[(%)]•᜛'(%)ਮ×Ø{/s(x)]}'prs(x)iḄ¢Ùu⊤ÛtᔠᦪÜ_ÝcË©;/>(x)]⊤ÛtᔠᦪÜ!_Ý஺(X)Ë©஺4.Þ▤©ᦪ#f”gᡈ/1বপ/(஻)()="5T)(x)r,(஻=2,3,4…)ᦪḄn▤©ᦪàᐸn-1©ᦪḄ©ᦪ஺ಖ¦ᑖḄᭆ°L¦ᑖ#/(%)ᙠcḄ±f²¡ᑁᨵ78)Ay=A(x)-Ax+o(Ax)ᐸ#4(x)pAx6ᐵ)஺(Ar)£âAxãÞlim3=0▤Ḅ6bÝ)ᓽ:Ax->0

15ᑣåy=/(“)ᙠ*ᜐQ¦)çè:dy=A(x)Axdy-A(x)Jx(Ax—>0)2.©ᦪp¦ᑖḄéᐵê:x7ᳮ#f()ᙠ2ᜐQ¦n/(%)ᙠ+ᜐQ©,A#/\x)=A(x)3.¦ᑖëÑ(_ឋ#dy=ff(u)du(u£_Ý)ì£!_Ý)ᦪḄ¦ᑖdvPᐹᨵîïḄëÑ஺§2.27ᳮ©ᦪḄðᵨIஹ«⌕ᑁಔ7ᳮi.òó7ᳮ#/(%)ôõᩩ½:1°ᙠYöᙠ(G,A÷\e2°ᙠ(ᓽ஺)ᑁQ©;=ᙠI33°/(«)=f(b)./'(4)=0AyÄযf'4)/(X)

162.ùúᨽü7ᳮ#/%ôõᩩ½:ᙠ3ᑁPᙠ[஻,þ,]=2°ᙠ3,ᑁjnᙠ஺b-a0ooಕᛞᑣQ-!"!ᳮ/X$gX%&ᩩ(:lim/(%)=0(ᡈ8)x—a1limg(x)=0(ᡈ8)x->a2°ᙠaḄ9:;<ᑁ=g'X஺0

17lim‘V=A,(ᡈoo)3"XFQ(8)g'(x)limgUHm3=A,(ᡈ00)%I&:xfa(oo)g(x)%-3)g'(x)ਮCDrᑣḄDEFGᦪIJḄ᩽▲ᓄᡂOPQᦪIJḄ᩽▲஺2°RS%&ᑣḄᩩ(STᵨᑣ஺000ᓽSW஺ᡈXYSZ஺3°[ᵨᑣY⌕ᑖ^_ᑖ`ஹᑖbZcSW_᦮:ᑖ"Z஺4஺Re(%)$g'(X)f%&ᑣḄᩩ(,ghiᵨᑣᓽ/(X)Hmj..f(X)./Tஹlimlim—-------=A(ᡈ8)fxfa(oo)g(x)xft(oo)g(X)g(x)5஺RGᦪW0-OO,00-00kᵨlᦪm0800/\00nᓄᡂdᡈoRWpU8000kᵨ_ᦪᡈᢣᦪmnᓄᡂ6ᡈo஺ಖᦪḄ[ᵨi.ᑗtu$tu:

18vy=fM,M(X0,J0)ᑗtuJ-Jo=/"(xo)U-xo)1tu'V-JVn()=-----y----r-(--x-----)(x-xn),(/'(%n)0w0)02.{tḄᓫ}ឋ(i)/'(%)>0XG3*=>/(%)ᙠ(஻,A)ᑁᓫ}/r(X)<0*£(஻/)=/(%)ᙠ(஺ᑁᓫ};(2)/(%)>0Xᙠ3ಘᑁᓫ}//(X)<0X£3,)=>ᙠ3,)ᑁᓫ}o3.GᦪḄ᩽প᩽Ḅ!Ev/পᙠ("ᑁᨵ!E/W("ᑁḄR_%°Ḅ9:;<ᑁḄD',10,ᨵf(x)>/(x)[W(^o)^f«]o

19ᑣW/C'9Ḅ"᩽ᜧᡈ᩽j,“஺OXḄ᩽ᜧᡈ᩽j஺ফ᩽ᙠḄ⌕ᩩ(i°jaᙠ᩽%஺=>/(%)=஺2°./'Cx஺ᙠ஺7EX஺fx஺1\Ḅব᩽ᙠḄᐙᑖᩩ(!ᳮ:l°JCx9ᙠ3ᜐi;/%W᩽;2஺/%=0ᡈf%Sᙠ;>n%W᩽஺3°.Cx9Ym¡஺¢X£¤'஺Y/পᵫ+m-ᑣ/C%9᩽ᜧ¢§£¤'஺Y"Xᵫ-m+¨IJ᳝᩽j஺l°.frCx9=O]=/C%9W᩽o2°.஻59ᙠjn/W᩽஺!ᳮª:

20R(o),¨ij(o)᩽ᜧRᑣ/(X஺)᩽j.ਮCDS!W᩽᩽«S!W஺4.{tḄᔣ¯°পR()()¨ij()^(2()ᑁW±Ḅ(ᡈḄ)(U)ফR/(x)<°,xᑣ/(')ᙠ("b)ᑁW³Ḅ(ᡈ´Ḅ),(n)i°./7x)=o,1(%,/(µ))o.2°J஻পx0Ym¡ojOপḄ°஺(3)5{tḄ£¸tOপ¹º£¸tRlim/(%)=Al»=AWf(x)Xf-00I——JJᡈlim/(%)=AḄ¹º£¸t஺xf+00>ফ½¾£¸tR5/প=°°]X=CC+JÁÂÃᐗGᦪÅᑖÆ

21§3.1S!ÅᑖஹÇ⌕ᑁÈಔÊ⌕Ḅᭆ̯ឋÍ1.ÎGᦪv/Ï,"প,XEDRF\x)=/(x)ᑣWḄ:ÎGᦪÒ“")+'WḄᡠᨵÎGᦪ,ᐸÕCWDÖᦪ஺2.S!ÅᑖGᦪ/(")ḄᡠᨵÎGᦪḄᐰØGᦪḄS!ÅᑖÙÚj/(x)rfx=F(x)+CᐸÕ/(“)ÛÅGᦪ;f(%)diÛÅ⊤Ý"xÅᑖmÞ஺3.S!ÅᑖḄឋÍ:

22[j/(x)rfx]=/(x)(1)ᡈd[^f(x)dx]=f(x)dxj/\x)rfx=/(x)+CফJ#(x)=/(x)+CJ[/1(%)+/2(x)+…+/(x)]rfxবn=Jfi(x)dx+j/(x)rfx+--+j/(x)Jx2nᑖ⚗Åᑖjkf(x)dx=k^f(x)dx&àáÖᦪ)(4)4.âãÅᑖµ"ಕᣚᐗÅᑖ1.Áᣚᐗ(å“æçᐗ”)[f[(p(x)](pr(x)dxèJ/[O(x)We(x)Jæçᐗ=J/(O^=F(C+C#t=(p(x)=F[(p(x)]+cîl=0(x)ÖᵨḄæçᐗGᦪᨵ:

23dx=—d(ax)=—d(ax+b)iaa3,AÖᦪ,awO)iixmdx=-------dxm+i=-----------d(axm+i+b)2°m+1a[m+1)(᪷Öᦪ)exdx=d(ex)=-d(aex+b)3aaxdx=ª(a>0,aw1)Ina—dx=d(lnx)4°xosinJx=-J(cosx)cosxdx=d(sinx)5sec2xdx=rf(tanx)esc2xdx=-rf(cotx)ஹ1dx=d(arcsinx)=-d(arccosx)26஺71-x1------=(arctanx)=-rf(arccotx)1+x2

242.Áªᣚᐗjf(x)dx=^f[(p(t)]d(p(t)ðx=8«)=F[(p-\x)]+Còl=᜛1(%)ÁªᣚᐗÇ⌕W┐_öᨵ᪷"ḄÛÅGᦪᐸÚᵨW÷᪷"ᨵᳮᓄ஺øᨵg³ùúlᣚrx=஻ᏔᦪY">0(¢ÛÅGᦪÕᨵY)2°x=asin£,(ᡈx=acosx),0<^

251.ᑖþÅᑖµ":^udvu-vftu^uvrdxJurvdx2.ᑖþÅᑖÇ⌕┐_Ḅÿ:sinxdx.পJ(”)cosxdxJpxexdxফ|pxlnxrfxব|pxarcsmxrfx,JPXarccosxdx4Jpxarctanxftr,|pxarccotxdxeaxsinbxdx^eaxcosbxdxমJJ“T+•••+”஻(⚗)ᐸP
x=+஻1%3.⌱u:পᙠ!"#ᦪ%⚗&'P(x)=ufᐸ()*dv-./“!⌱0ফᙠᢣᦪ#ᦪ%⚗&'P(X)=U,ᐸ()*dv;./“ᢣ⌱”஺বᙠ⚗%6ᦪ#ᦪ&'In%=஻&

26ᐸ()*dv;./“6⌱6”஺ভᙠ⚗%8!"#ᦪ&⌱8!"#ᦪ9u,ᐸ()*dv;./“8⌱80মᙠᢣᦪ#ᦪ%!"#ᦪ&;<⌱=#ᦪ9u,ᐸ()*dv;./“ᢣ!<⌱0ಗ.ᓫᨵᳮ#ᦪBᑖDஹP(x)1.ᨵᳮ#ᦪ2(2)ᐸP(x)F஺(G)H⚗஺2..ᓫᨵᳮ#ᦪP(x)P(x)প/(%)=/(%)=1+X1+x2P(x)ফL)=(X+Q)(X+8)(X)ব/M=(%+஻)2+b§3.2NBᑖ=.O⌕ᑁR(=).S⌕ᭆUVឋX1.NBᑖḄNZ:0

27ff(x)dx=li)Ax.&£]^_1/`m-0i=ln—>ooNBᑖklmᑖᒘஹopஹqFஹr᩽▲஺NBᑖḄuvwZHxyxz&{by=f(x),abx=a,x=befᔜhᑖ☢BḄjᦪF஺2஺J(x)ᙠa~ᨵᨵ▲=f;3஺./(%)ᙠᓫᨵ-!J/(%)ᙠ]஻,;B஺Bᑖᙠ&ᑣBᑖVᐵ1°VBᑖᐵ&ᓽয-2஺Vᙠ]%஺Ḅᑜᑖᐵ&ᓽb,

28BᑖVB#ᦪf(%)V¡fH¢ᨵᐵ஺3.£¤——¦§¨ᐻª(“)H«¬#ᦪ/(X)ᙠ[஻,)®Ḅ

293°£[/(x)±g(x)}?x=£f(x)dx±£g(x)rfx4°£/(x)rfx=O5°£/(x)=£f(x)dx+Æf(x)dx(a

309஺BᑖNᳮ/1(%)«¬X£"ᑣ:Îᙠ=Ï£,Ð],(0)NBᑖḄ½¾i.ᣚᐗBᑖÓ(%)«¬&xG[a^b],x=(p(t)«¬&ÃÔ&Õaᑮ×Ø,/(&)ᓫᙢÕ஻ᑮ஻&&a)=aᵨ()=b,“:f"=1/[஺("—'M2.ᑖhBᑖ

31udvafvduf'3.ÛZBᑖAJ_QQAJ_QQÝf(x)dx=Ý/(x)rfx+Ýf(x)dxJ-00J-00Jb4.NBᑖḄàᦪª1஺1/«”=/%2஺]Ý"প□l=/bxå."x3°]]-/পÄL=/]᜛2%å&G-7]%Xå•஻"!NBᑖḄëᵨ1.ì☢íḄ☢B:

321°ᵫ)=/(%)>0,x=x=b,(ag)Vx-ax=8ᡠñᡂḄíḄ☢ByS=f(%)-g(x)H%3°ᵫ=0(y),x=e(y),(஺ó(p)2Vy=c,y=dᡠñᡂḄíḄ☢Bs=&]஺(ô)=஺(ô)ᔊ4஺.qì☢í☢BḄmöজ.qø{bḄù&úø₝í-ঝ.ýNBᑖ&ᵫùýNBᑖ▲;ঞ.ëᵨªᑏ
ᑖ஺2.Ḅ
1°y=/(x)>0,X=a^x=bXᡠXᡠḄ
iᓃ=f2(x)dx

330a•b2°ᵫ$=஺(7)>0,y=c,y=d&ᡠᡂyᡠḄ
:*+,-ᐗ/ᦪ1
ᑖ23§4.189ᦪᐰ1ᑖ;.<⌕ᑁ?(-).-ᐗ/ᦪḄᭆC3.Eᐗ/ᦪḄFGz=f(x,y)(X,J)GDFGHD(f)4.Eᐗ/ᦪḄIJKGEᐗ/ᦪL;MNO☢஺(Q;ᐗ/ᦪLR☢SḄ)(E).Eᐗ/ᦪḄ᩽▲VWX1.᩽▲FGYz=f(x,y)^_ᩩa

341°ᙠc
o,yoḄdM⚞HᑁᨵFG஺gc
%o4oh◀᜛k2limfx,y
=Ax—>x0yflkᑣnZ=/g%"kᙠgrk᩽▲sᙠtuv4஺2.WXFGYz=fgx,yk^_ᩩa1°ᙠcg%஺,y0ḄdM⚞HᑁᨵFG஺2lim/
X,J=/
XJ090y.xᑣnz=/
yᙠgy,xkᜐWX஺ಖ.89ᦪFG/%,7,ᙠ2030c/(Xo+Ax,yo)-/(Xo4o)/6(x^)=lim00Ax/
Xoo+Ay—/%oyo/6(xj)=lim090Ay

35ᑖ|}/ᦪᙠgk0kᜐᓰkḄ89ᦪ஺z=/gykᙠ஺ᑁKcgx,ykᜐḄ89ᦪ}:df(x,y)dz==zdxdxஹSf(x,y)dz,f(y)=——==ySydyಗ.ᐰ1ᑖ:1.FG:Z=f(x,y)=/(x+Ax,y+Av)—f(x,y)=AAx+B/Sy+o(p)ᐸAஹ5AxஹAy2ᐵ,o(᜛)Lp=JA/+Ay?▤Ḅ஺(J:dz=df(x,y)=AAx+BAyLz=/(”)ᙠcgx,ykᜐḄᐰ1ᑖ஺3.ᐰ1ᑖ89ᦪḄᐵ£

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