2021-2022学年吉林省吉林市高三（上）第二次调研数学试卷（理科）（附答案详解）

《2021-2022学年吉林省吉林市高三（上）第二次调研数学试卷（理科）（附答案详解）》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2021-2022
ᔡ᪍ḕᔡ᪍Ẇᦪᔁᳮ1.ᔠ4={(%,y)|y=2%—1},B—{(x,y)|y=ᑣ4n8=()A.0B.{1}C.{(1,1)}D.{1,1}2.12ᦪz=r(cos0+isin0)(r>0,0GR),ᑣ<=>?@AB2ᦪzḄD?@EᐸGrH2ᦪzḄI,஺H2ᦪzḄKDEᑣ2ᦪz=L+᜛ḄD?@NOḄP()ATT..7T07T71ᔆ71..7TT-X7T7T,cos-4-isin-B.sin-4-tcos-C.cos-+isin-D.sin-+icos-666633333.Vaeg,1,2},Z[ᦪ\=]Ḅ^_`PR,aHᏔ[ᦪḄᡠᨵaḄeP()A.2B.1,2C-?2D.|,1,24.ᔣgh=(1,i3),h=(-1,3),ᑣkᑡmn┯pḄPA.a//bB.1LqrstHiuvwC.a+b=0D.xixLyhᔣz{2x—y>01|ᦪx,y}~Ex-2y+1S0,ᑣx+yḄᨬeH%<1A.-B.1C.2D.326.hi┵EᑮḄ᝞ᡠEᑣḄH8.ᔜ⚗ᙳHNᦪḄᦪᑡa”GE<12=3,a3a4a5=3%ᑣCZ3=A.6B.9C.27D.819.2020
5ᨴ28xEᓝ¤ᐰ¦§ᜧ©ª«ª¬®¯G°§±ᐳ³¦±´ᐺ¶E·2021
1ᨴ1x¸¹º.»᪥u½ᐰ᪥2000¾¿ÀÁ®“±´•᪛ÅÆ”Çȱ´ÆÉÊEËÌÍÎ200¾¿ᡂÐÑÒ᦮ᳮÔÕÖ⚣᳛ᑖÚÛh᝞ᡠE1ᡂÐÜÝÞ400¾ḄßrsàᝄâEãÒàᝄßḄᡂÐᨬäᑖH

1A.70ᑖB.80ᑖC.86.5ᑖD.87.5ᑖ10.[ᦪf(x)=2X+2-x,1a=/(0.5-11),b=/(log2),c=/(logi3),ᑣ()32A.cb>0)ióíE,ð2PñᙊḄஹõᯖíE÷“øð2=ùESp=4V3ý÷èþPF1Ḅᑮytan"iPF2=%AF1F2ᑣᯅ+ᯅḄ!"()|pa[|PF|2A.[i,-]B.C.[i,-)D.[i,-)L23J'15'3'L2157l23713./᪷523Ḅ45678ᙠ:;<=>?@A>BḄCDḄ3EFGH22Ḅᭆ᳛K.14.“a=l”"“7P(1ᑐ+2)/+1=0T7PU+(+1))/-2=0VW”Ḅᩩ(1Y(Z“ᐙᑖF]⌕"'']⌕Fᐙᑖ”“ᐙ⌕”ᡈ“aFᐙᑖbF]⌕”).15.cdᳫ஺ḄghK1,A,8"ᳫ☢Ck408=90஺CKmᳫ☢Ḅ.nop┵஺-4BCḄrsBᨬᜧA,B,CoḄv☢ᙊḄ☢sK.16.cdyᦪ/(%)=x(ex-1)-Inx,ᑣ}Ḅ~yᦪy=/஺)ḄᦪKᙠx6(0,+8),BFf(x)

218.“ᜩ”¡ஹ“£¤”ᝂᨴஹ“§¨”©ªஹ“«T”©ᨴ……®¯°±²³ᑮ´µᡂ·8Ḅ¸ᜩ¹º»¼½¾µ¿/À/ÁᓺᙢÄ᥎ÆÇÆ®ḄÈᝍᝯᐸ»WᘤᐸÍÎ=ஹ▬YஹÐ⊤ᡠᵨᑮḄᔜÕᩞᧇ"¸ᜩØᢈÚ½¾ḄÛÜឋÞßà/.áâãäåæçḄAè¸ᜩᩞᧇ"»WᘤḄé⌕Y,mᩞᧇêᵨëìᓝᑖîïmâãKðñAè¸ᜩᩞᧇòWêᵨᦋ⌼᪷õö÷øẆúûüBᑮêᵨᦋ⌼ᢗᐭxÿᐗ
Ḅᦈyᐗ
Ḅᦪ᝞%ᐗ
23461011yᐗ
122226415365Ẇ⊤ᦋ⌼ᢗᐭxᐗ
Ḅᦈyᐗ
ᐹᨵឋ!ᐵᐵ#.&
᪷⊤(ᦪ)*ᦈyᐗ
ᐵ+ᦋ⌼ᢗᐭxᐗ
Ḅ,-./y=bx+a1&
23456ᢈ89:;ᵨᦋ⌼ᢗᐭ=>+15ᐗ?@ABCDE⊡G5ᐗHDEᦈᦈ+@A⊡G
Jᑮ90ᐗLᦋ⌼ᢗᐭM>JᑮN>ᐗOPᑮ0.01ᐗ
QRὃDTb=UVa=y-bx%RὃᦪW=i஽%=1685,=286.19.᝞Z2[ᙽ]^_ᩈᧇᐸc☢ABC஺fgAB1AD,AD//BC.1
⌕ij☢CGD1CᑁḄ[lPm^B3nᩈᧇop,ᙠᩈᧇ⊤☢;st᪵vQwxyz{Z|ᑏ*{Z~◤
2
H=AB=2,BC=441=1,:lPᙠlCᜐ?)APj☢CGA஺ᡠᡂḄ.20.ᦪᑡᓽḄ«⚗m2SnneN*,ln,Sn
ᙠᦪ/X
=X2+XZ.

3(,))ᦪᑡḄ⚗DT1(&)Hᦪᑡ“fg1=¡5eN*),)ᦪᑡ¦Ḅ஻⚗m21.©ᱥCy2=2px(p>0)[lG%)ᑮᯖlḄ³´2*(&))©ᱥCḄ᪗¶./1(&)HlA,B2©ᱥ¹+xº.=»Ḅ¼l0A,08Ḅ¾᳛ᑖÁ2Â,ᦇ2ÄfgḄ2—4=4Â+4%2)A8iÇl.22.ᦪf(%)=xlnx,g(x)=ax2+1.(1))ᦪf(x)ḄᨬÌ1(2)H=ÍT(Î+l)lnx-2(%-1)>7nḄÑG(1,+8)ឤᡂÓ)mḄÔÖ1(3)Hᦪ/(x)ḄZg(%)ḄZᨵ8(%2ஹ2)¼Û=»ḄÜl:>16.(RὃᦪIn2yo.69,In5«1.61)â4⚓ᐳ15⚓

4åᫀmç᪆1.ூåᫀ௃Cூç᪆௃ççëìTîL4nB={(1,1)).ᦑ⌱C.óç./ô¡:-1ᯠöᓽóî*4nB.W⚪ὃø3ùᔠḄûüýḄÇþÜùḄÇþÿ
ὃ
Ạ⚪.2.ூᫀ௃Aூ᪆௃z=^+ஹḄ1,#$g226ᑣ(ᦪZ=?+Ḅ,$-.cosg+isinp2266ᦑ⌱A.᪷89:ᩩ<=ᔠ(ᦪḄ,$-.Ḅ?@ᓽBCDE.F⚪G⌕ὃ(ᦪḄ,$-.Ḅ?@Ạ⚪.3.ூᫀ௃Aூ᪆௃ᵫaeg,1,2),Na=Oy=PḄ?@QR0,+8),UVᔠ⚪WXNa=lZy=xḄ?@QR,^᜻`ᦪUVᔠ⚪WXNa=2Zy=MḄ?@QR,JL/(-%)=(-x)2=X2=/(X),ᑣf(x)Ꮤ`ᦪVᔠ⚪W.ᦑ⌱A.ᵫ`ᦪḄ?@QḄEklᏔ`ᦪḄ?@Bm=n.F⚪ὃ`ᦪḄ?@Ql᜻ᏔឋḄᑨqὃrᳮẠ⚪.4.ூᫀ௃Bூ᪆௃uᔣwx=(1,—3),K=(-1,3),ᡠ|}=-~ᓽ஻⌱⚗4~Xuᔣwᐳᡠ|U⌱⚗B┯Xu3=—ᡠ|x+}=6,⌱⚗C~Xux=2ᡠ|xxḄᔣ⌱⚗O~.ᦑ⌱B.

5᪷8☢ᔣwḄᙶ᪗
ឋ⊤ᑖᑨq⌱⚗Ḅ⚪¡ᔲ~ᓽB.F⚪ὃ☢ᔣwḄᙶ᪗
ឋ⊤£ᵨ¥⚪¡Ạ⚪.5.ூᫀ௃Bூ᪆௃ᵫ¦§ᩩ<¨BQ᝞ª,ὶ¬1°mᡃ¯°2=x+y,ᓄy=-²+z,ᵫªB:NCy=-x+z³AZ,Cᙠyµ¶Ḅ·¸ᨬºzᨵᨬº¼+|=1.ᦑ⌱B.ᵫ¦§ᩩ<¨BQ°2=¯+᜜ᓄC¿ḄÀ·.ᦪ-=ᔠmᑮᨬ,ÂᨬḄᙶ᪗Ãᐭmᫀ.F⚪ὃÅᓫḄឋÇᑜὃᦪ-=ᔠÉÊ¡Ạ⚪.6.ூᫀ௃Cூ᪆௃ூᑖ᪆௃᪷8,˪ḄᱯÍ:⍝Ï˪Ъ-ḄÏÑᔣÒÑÓÓᑮÔ~-Ḅ☢ᙠ☢¶ᨵᩩÕ$Õ$¡ᵫÏÖ$ᑮÒ¶$Ḅmᑮ=×.F⚪ὃØÙª-Ḅ,˪ὃÏ˪ḄÚkF⚪¡ÔẠ⚪ὃḄᑁÜÝÞÅᓫB¨ßḄ┯¡Õ$ḄᔣB¨┯.ூ௃Ï˪Ъ-ḄÏÑᔣÒÑÓÓᑮÔ~-Ḅ☢ᙠ☢¶ᨵᩩÕ$Õ$¡ᵫÏÖ$ᑮÒ¶$Ḅᦑ⌱C.7.ூᫀ௃Aூ᪆௃tan(a+£)==2W,3l-v3tana•7tana=y/3f,V3•tana=—,6⚓ᐳ15⚓

6ᦑ⌱4á⚪Wᑭᵨã$lḄ~ᑗᓽBEmᫀ.F⚪ὃã$låḄ,$`ᦪẠ⚪.8.ூᫀ௃Bூ᪆1•.ᔜ⚗ᙳ~ᦪḄéÝᦪᑡëaì஺2=3,îïÝq,n*,•a3a4a5=a,*q,*3*cj—3óq=3,ᑣ&3=a-q=3x3=9,2ᦑ⌱:B.ᵫ⚪WᑭᵨéÝᦪᑡḄឋöஹ÷⚗ï.ᐜEmïÝùE¨஺3Ḅ¼.F⚪G⌕ὃéÝᦪᑡḄឋöஹ÷⚗ï.Ạ⚪.9.ூᫀ௃Dூ᪆௃î⚣᳛ᑖýCªiḄ⚣᳛/X,ᑣþ=0.005x10=0.05,5=0.015x10=0.15,f=0.030x10=03,f=0.040x3210=0.4,f=0.010x10=0.1,5ᐰ᪥2000400ḄᝄᡠᝄḄᭆ᳛=0.2,ᦑᝄḄᨬᑖᙠ!"80,90),&ᝄḄᨬᑖa,ᑣ)0.05+0.15+0.3+(a-80)x0.040=0.8,1)a=87.5,ᦑ⌱)D.᪷5⚣᳛ᑖ789:;<=>Ḅ⚣᳛?&ᝄḄᨬᑖ”ᵫ⚪Cᑡ9E;<ᓽ.G⚪ὃIJ⚣᳛ᑖ789:ḄKᵨMNOẠ⚪.10.ூRᫀ௃cூ1᪆௃1)Vᦪ/'(X)=2ஹ+2rḄ]^_R,/(-x)=2T+2X=f(x),/(%)cᏔVᦪ,•1-c=/(logi3)=/(-10g3)=/(log3),222f(x)=2xln2-2-/2=(2/-2-x)

72,lx>0n2X-2-x>o,>o,/(%)=2X+2rᙠ(0,+8)oᓫq⌴s•••0.5-11>2,0

8ᦑ⌱)c.ᑭᵨ]^ᑨxVᦪf(x)ᏔVᦪᑭᵨyᦪᑨx/(zᙠ(0,+8)oᓫq⌴s{|}~ᦪḄᜧ.G⚪ὃIᦪḄᜧḄᑨxὃIVᦪḄᓫqឋஹ᜻ᏔឋஹyᦪឋOẠὃI;1}?cOẠ⚪.11.ூRᫀ௃Cூ1᪆௃1)8/)X+7-2=0ᙊ஺)/+=J1NB45,ᡠy1:4(1+—,B(I-,1+%1%ᓝy-z=u$n$$ᡠ-OA=(-3V2,372)(1+,1-ᑶ)=-3V2-9+3ᡈ-9=-18.ᦑ⌱)C.ᑖ;

91,18ÂÂ121"Ð+Ð=ÑÒᦑ⌱)A.&ÓÔ|=771,ÓÖ2|="ᐜᵫ⚪C;<ᙊḄ᪗Ì9EÙ+3=1ÚÛ|+Ü=yᵫm+n=8;<124rnnW16,ᓽ;<ßà.G⚪§⌕ὃIJᙊḄ]^á᪗Ì9EὃIJâãVᦪḄឋnὃIJḄ;1}?MN᫏⚪.13.ூRᫀ௃|ூ1᪆௃1)å“нḄçèéN2ߟ’ìíA,ᑣî}ᙠïðнñò2óḄôõoöxᓽᙠ!Ḅ1÷ḄôõoöxøùöнḄçèéN2ἔᡠᵫûüᭆýḄª«ᑮìí4þḄᭆ᳛P(4)=iᦑRᫀ)ÿ
5᪷ḄᑖᡂᜐḄᐸ.⚪⌕ὃ!ᭆ᳛Ḅ$%ᭆ&ᐵ()*+ᭆ᳛,&*+-.Ḅ/
01
ஹ☢4ᡈ647ᩭ9ᑮᭆ᳛.14.ூ?ᫀ௃ᐙᑖCD⌕ூE᪆௃EGHIa%+2y+1=0QHIR+(a+l)y-2=0WXজZa=0[HI\]^ᓄy=-ᢓy=-x+2,a[HICWXঝZQ60[ᵫHIa%+2y+1=0QHI%+(a+l)y—2=0WX9”eᱏ?E9a=lᡈh2,ja=1")"HIax+2y+1=0QHIx+(a+l)y-2-0WX”ḄᐙᑖCD⌕ᩩ.ᦑ?ᫀGᐙᑖCD⌕.ᵫHIaᐝ+2y+1=0QHIx+(a+l)y-2=0WXᑖa=஺Qa*0rstuv,aḄ᪷wᐙᑖᩩ.QD⌕ᩩ.Ḅxyᑨ{ᓽ^.⚪⌕ὃ!}HIWXḄ~ᐵὃ!}ᐙᑖᩩ.QD⌕ᩩ.Ḅᑨ{Ạ⚪.15.ூ?ᫀ௃ூE᪆௃EG0)ᳫ4408=90°,ᡠ☢AOB)ᳫḄᜧᙊᡠᙠW☢

10ᦑZC஺C1W☢A08[┵஺-4BCḄ64ᨬᜧ஺A=OB=0C=1,ᦑAB=AC=BC=V2,ᑣ4BC)¡¢1A,B,CḄ☢ᙊḄᙊ0,ᑣᙊ0,Ḅ£¤r=0,C=|x^xV2=y.ᦑ1A,B,CḄ☢ᙊḄ☢4ᐔXª)2=«ᦑ?ᫀGy.᪷wᩩ.+x☢A03)ᳫḄᜧᙊᡠᙠW☢,a^+xCᜐ®~[┵஺-4BCḄ64¯9ᨬᜧᯠ±ᓽ^²³1A,B,CḄ☢ᙊḄ£¤´9?ᫀ.⚪ὃ!}ᳫḄ☢Ḅឋ¶·¸³᫏⚪.16.ூ?ᫀ௃l[l,+oo)ூE᪆௃E:f'(x)=ex-1+xex—G=ex(x+1)—G—1,¿g(x)=ex(x+1)——1»gr(x)=ex+ex+xex+Â>0,ᑣÄᦪg(x)ᙠ(0,+8)ÆᓫÈ⌴Êᵫgপ=2e-2>0,g(}=|Î-3<0,g(Ð)g(l)<0^ÑÒḄÓÄᦪy=f'(x)ḄÖᦪ1ᓽe*஺=—,XQᵫxG(0,x)=f'(x)<0,%G(x,+00)=/'(x)>0^900Äᦪ/(x)ᙠ(0,Ù)ÆᓫÈ⌴Úᙠ(3,+8)ÆᓫÈ⌴Êᓽ/'(x)min=/(Þ)=X(ex°-1)-lnx=x(^-1)+lnex«=1,ᓽa21.o00ᦑ?ᫀG1Ð[1,+oo).Ó¿g(x)=/'(x),ᑭᵨÓᦪâᔠÖäᙠឋxᳮᑨ{Äᦪy=f'(x)ḄÖᦪᵫf(x)Ḅᨬæ9çᦪaḄ¯é.⚪ὃ!}ÄᦪḄÖäᙠឋxᳮ᫏⚪.17.ூ?ᫀ௃EG(1)ᙠABC஺ᵫëìxᳮ^ÑBD2=BC2+CD2-2BC-CDeos$BCD=l+4-2xlx2x(-i)=7,■1•BD=V7,ï10⚓ᐳ15⚓

11DB_ᙠZB஺ᵫìxᳮ^Ñ,sin/.BADsinZTlB஺'ᓽò=2sinz_4BD'2V21•sinZ-ABD=—.(2)ᙠABCᵫëìxᳮ^9GBD2=AD2+AB2-2AD-ABcos^BAD,ᓽ7=4+AB2-2AB,E94B=3ᡈ4B=-1(ó)ᡠ4BDḄ☢4S=\AB-ADsm/LBAD=|x3x2Xy=^.ூE᪆௃ô1
ᙠBCDᵫëìxᳮ^Ñ9BQ,ᙠ4BDᵫìxᳮ^9sinz•õBDÐ2
ᙠõBCᵫëìxᳮ^9AB,ᑭᵨ☢4ö÷9õBDḄ☢4.⚪ὃ!E¡øùúûìxᳮëìxᳮ)E⚪Ḅᐵ(ὃ!üýþᳮÿ
᫏⚪.1oᐜY/ᔣஹ-2+3+4+6+10+11~12+22+26+41+53+65,ூᫀ0
%=-------------------=6,y----------------------------=36.5r,66,_£%□%_1685-6x6x36.5_371__„-S-LiXf-nx2-286-6X62-70-,a=y—bx=36.5—5.3x6=4.7ᡠ"#$%&'()y=5.3%+4.7.*+,ᵫ⚪.5.3%+4.7>90-5,.%>15.15,ᵫ15.15215,0ᔠ234567⊡9:;ᡠ<67ᦈ>?ᑮ90AᐗCDᦋ⌼ᢗᐭIJ?ᑮ15.15Aᐗ.ூ᪆௃*+,᪷NOD⊤ᦪN"R᪵TUᙶ᪗"b,a,XR#$%&'(.*+,YZ5.3x+4.7N90-5,XR[\,.ᑮ[].T⚪ὃ_#$%&'(Ḅ"abcᵨὃ_DefẠ⚪.19.ூᫀ௃*1
ZhPi%&EF஻CC0ᑖlmCOஹG5EஹF,noBEஹB௃Fp2
<44iAB,4஺ᡠᙠ%&ᑖl)xஹyஹzstuvw%xᙶ᪗y4xyz,

12ᑣ4(0,0,0),D(0,0,2),Dt(1,0,2),C(0,2,l),•••P(0,2,l),AP=(0,2,1),CD=(0,-2,l),=(1,0,0),☢Ḅaᔣ)ᐗ=(x,y,z),n.£D=-2y=0ᐗ;ট,ᑣ+zpn-DD=x=0r%&APb☢CCiA஺ᡠᡂx)sine=|cos(n,^)|=1^1=i,ᡠ<%&APb☢CGD௃DᡠᡂxḄ¡¢£)¤ூ᪆௃(1)ZhP¥%&EF//CGᑖlmC£¨ஹG5EஹF,noBEஹBJ,ᓽ¬.ᫀ(2)<4A1AB,40ᡠᙠ%&ᑖl)x,y,zstuvw%xᙶ᪗y4—xyz,ᑭᵨvwᔣ"ᓽ¬.T⚪ὃ_¯&&°
&☢xḄD᫏⚪.20.ூᫀ௃(+)•.•h5Sn)²ᙠ³ᦪ/(X)=/+µ¶·¸AS=¹º+,nn»=1¼½=Si=2,»ºi>2¼a=S-S_i=n24-n-[(n-l)2+(-1)]=2n,nnnQi=20ᔠ¸Á•ᦪᑡÃaÅḄY⚗6Áe=2n(neN*)pn(0)•••ᦪᑡûÅÉÊlog2Ì=Í(n6N*),•••b=n-2n,n7p=1x21+2x22+3x23+-+n-2"জ27p=1x22+2x23+-+(n-1)-2n+n-2'+iঝজ-ঝ.஻=1x21+1x22+1x23+…+1x2n•2n+1=2(1~2|1)-n-2n+1=1—22n+i-2-n-2n+i=(1-n)-2n+1-2,஻=(n-1)•2n+1+2.ூ᪆௃(+)ᑭᵨ0=S—Sn-i"Y⚗6Ápnn(#)ᑭᵨ┯ØÙÚa"
.Û12⚓ᐳ15⚓

13T⚪ὃ_¯ᵫS""ᓽ
┯ØÙÚ"
᫏⚪.21.ூᫀ௃*2,h*ᡭ஺,ᑮᯖhḄàá):•,•[+=.P=2,ãᱥ&Ḅ᪗å'()V=4x.*+,çè'a*9/1,ஹ8*ë■%,%>஺í2>஺ᑣî=—,k=ï2yiyz%&A3Ḅ'()%=my+b*m^O,,%&A3Ḅó᳛k=&ὶu'(çᘤ+b^y2-4my-4b=0,ᑣ•••yi>0,ù2>04=16m2+16Z?>0,%+%=47n>0,yy=-4b>0,12••¸ü4=4kl+4k2,TV-1=^+ᓽ4-y2=4y2+4yly2yiஹ2ᡠ<4+4b=16m,ᓽb=4m—1,ᑣ%&ABḄ'()x=my+4m-1=mFy+4,-1,Zþh*—1,—4,,ᡠ<%&ABZþh*1,4,.'a—•8*%2ஹ2,ᵫ⚪ÿi%2yify?>0ᡠIk>0,b>0,ABḄy=kx+b,ὶ12”A?/+F2kb—4x4-h2=0,A=F2kb—42—4k2b2>0,-2kb+4Xi+%2=o..2>(yiy2="pbvkk-4=4kl+4k2,±2ᓽ"/4=4"+4ḂX1XXix22•••yiy-4%IX=4yx+4y2/22x2᦮ᳮb=k—4,.♦•ABḄy=/ex+fc-4=fc7x+1-4,89:7/1,—4,ᡠ<AB89:7-1,-4.ூ>᪆௃7AB8:7:%ᑮᯖ:ḄEFGH>p,ᑮIᱥḄ᪗L.2“2AAv7NO/4P,ஹB7S,᜜yi>o,y>0,ᑣ1=V,k=~,A82244yiyzḄx=my+b77nK0,ὶ\21]+2^ᔠ`a9ᳮbᓄH>def^g.Oh87i2ஹ2ᵫ⚪lX1M2,m2>0ᡠ0ᓃ>0,ABḄy=kx+b,ὶ?2]"ᑭᵨ`a9ᳮefrs-4=4r+4k2,ᯠuH>dᑮ^g.

14v⚪ὃxIᱥḄyᓫឋ|Ḅ}ᵨ~IᱥḄᐵdḄ}ᵨ᫏⚪.22.ூᫀ௃>পᦪ/(%)=xlnx,9(0,+8),(%)=14-Inx,/>x>/(()<0>01),ᑣm<¥(x)¦§lḄx6(1,+8)ឤᡂ"(%)=Inx+—1,ᦪ9(X)=Inx+-1(%>1),ᑣw'(%)=®>0,ᡠ"(1)=0,ᓽ”(%)>0,ᡠ<¥(X)ᙠ(1,+8)Vᓫ⌴ᡠ<¥(%)>¥(1)=0,ᡠ<°i0,ᓽ±Ḅ¢³(/8,0].(3)µᦪ/(%)Ḅ¶·~9(%)Ḅ¶·ᨵ4(%1/1),8(¹,º)»¼½¾Ḅ¿:ᡠ<ᐵÀxḄa/+1=%]nx,ᓽax=Inxᨵ»¼½¾ḄÂ᪷x»2ᡠ0,ᓽÔIn%>2¦§lḄxe(1,+8)ឤᡂÕ1½Ö%2>5>0,ᑣ×>1ᡠ2,X-X1x^-1X2ttᓽln(;qx2)—Þf>2ឤᡂX1X2µ×஺62)-ᓩà2,ᓽ—>>1Nxlx2Nxlx2ᦪG(%)=In%—jᑣG(%)ᙠ(0,+8)Vᓫ⌴åG(4)=ln4-1=21n20.88<1,G(5)=ln5-1«1.21>1,ᡠ1PQ>4,ᓽ%1½>16ᡠ<è½àéê.ூ>᪆௃(1)ᐜHfìᦪ(஺)ᑮᦪ/'(%)ḄᓫឋíîHf/(Ḅᨬ¡¢.(2)h(x)=(x+l)lnx—2(%—1)(%>1),ᑣm<¥(%)¦§lḄG(1,+8)ឤᡂᑭᵨìᦪHfh(x)>/i(l)=0,ïîHfmḄ¢³.(3)ᵫ⚪l(Õᡠ<ᐵÀxḄa%=Inx-ᨵ»¼½¾ḄÂ᪷%ix,ᓽ=In%!-2ñ14⚓ᐳ15⚓

15ax=lnx-ÏГln(x1X2)-Ûô?àInḆ^ᔠ(2)Ḅ^ö(,22÷Inx>2¦§lḄxG(1,+8)ឤᡂ᪀⌼ᦪG(x)=lnx-p᪷úᦪG(x)Ḅᓫឋᓽ(ê^ö.v⚪û⌕ὃxýᑭᵨìᦪẆÿᦪḄᓫឋᨬὃឤᡂ⚪᫏⚪.