2021-2022学年天津高二（下）期末数学试卷（附答案详解）

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2021-2022
ᜩᓝᦪᔁ1.ᐰ஻={-2,—1,0,1,2,3},ᔠ#={_1,0,1},B={-1,1,2},ᑣ(C/)US)=()A.{-1,1}B.{-2,3}C.{-1,0,1,2}D.{-2,0,2,3)2./⚪“Vxe[-2,+8),%+3N1”Ḅᔲ=>()A.”VxG[-2,+8),%+3V1”B.W[-2,+8),%O+3N1”C."YxG[-2,4-°°),x+3>1”D.3%oG[—2,+8),&+3<1”3.4,beRJa>0,L|J"a>b”>“T<1”Ḅ()A.ᐙᑖST⌕ᩩWB.T⌕SᐙᑖᩩWC.ᐙ⌕ᩩWD.XSᐙᑖYST⌕ᩩW4.Zᦪ/஺)="᮱Ḅ]ᑖ^_ᜧa>()5.=cᙠReḄ᜻Zᦪ/(x)ᙠ(g8,0)e>hZᦪija=-/(log1)-b=/(log4.1),22c=/(20,8),ᑣa,6,cḄᜧoᐵqr()A.c()A.-B.-C.—D.24557.Zᦪ/(x)=Inx+x2-bx+a(b>0,a&R)Ḅ^_ᙠu(bJ(b))ᜐḄᑗxy᳛Ḅᨬot>()A.2V2B.V3C.1D.2

18.Zᦪ/(x)=-2x2-ax+3{|}~x6[a-2,a\,ឤᨵf(x)>0,ᑣᦪḄt>()B.(-1,).5-5+A.(-1,1)C.,1)D.(1,)339.Zᦪ/஺)=ig(x)=^(erᯠ}ᦪḄᦪiznG/?),jf(x)=g(x)ᨵSḄ᪷iᑣᦪi஻Ḅt>()A.(04)U(4e2,4-oo)B.(0,e)U(4e3,+8)C.(0,1)D.(4e2,4-oo)10.ᔠ4=—3|V1},^={x|3x-7>8-2x},ᑣACIB=.11.1VQV3,2.12.jZᦪf(x)=e”sin2x,ᑣ/(0)=.13.Zᦪ/(x)>ReḄ᜻Zᦪiᨴ/஺+2)=-/(%),£XE(0,2)¦i/(%)=/,ᑣ/(7)=.14.jQ>1,Z?>0»ᑣ1+a+Ḅᨬotr____.ab-b15.©f(x)=xex+^+e2,g(x)=—x2—2x—1+a,jªᙠ/G/?,xG(-1,+°°),2«¬/(xi).16.¯°ᑡᔜ⚪³(´)2a=58=VTU,µ5+£Ḅt·(´)µ(21og43+log3)(log2+loggZ)Ḅt.8317.Zᦪ/(x)=ax2+(b-2)x+3(a஺0).¸)jS¹f(x)>0Ḅºr(g1,1),µa,஺Ḅt·(´)j/ভ=2.(i)a>0.b>0,µ¼+9Ḅᨬot·zab(ii)jS¹/(%)V1ᙠReḄºr½iµᦪ஺Ḅt.18.Zᦪf(X)=Inx-ax(a6R,erᯠ}ᦪḄᦪ).(´)£a=³¦iµf(x)Ḅ᩽t·(´)Zᦪg(x)=/(%)-2x+l,jg(x)S0ᙠᐸ=cÀᑁឤᡂ®iµᦪaḄᨬot·(´)jᐵÂxḄf(x)=/ាᨵÄḄ᪷Åi%µᦪaḄti2,ÆÇÈXl%2>1.É2⚓iᐳ10⚓

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3•••Xe(0,5cos2x>0,/(x)>0,ᦑ᣸◀B,C⌱⚗.ᦑ⌱3D.ᐜ56!ᦪḄ
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4ூ9I௃93ᵫ/(x)=Inx+——bx+a,µ(x)=3+2rb(x>0),.¶•r(b)=J+b>2,b==ᓽb=l“="ᑗ¦«᳛ḄᨬuY2.bᦑ⌱3D.8.ூIᫀ௃Cூ9᪆௃93!ᦪ/'(X)=-2M—º+3Ḅ@A»^¼ᔣᔣ¾e¿ÀÁ=-3ᓽa>:1/(x)=f(a)=-2a2-a2+3=-3a2+3>0,9gQ—1,ᓽ£10,9ÉÊËᦪ஺ḄÎY(É,1).ᦑ⌱3C.ᵫÏÐ7/(X)min>0,e4ᑖÑÒÓᑭᵨÔÕ!ᦪḄ@Aឋi56/(X)Ḅᨬuᓽ759஺ḄÎ.:⚪<⌕ὃ?!ᦪឤᡂØÙ⚪ὃ?ÔÕ!ᦪḄឋi@AḄwᵨὃ?ᑖÑÒÓÚÛfg59}~DE᫏⚪.9.ூIᫀ௃Aூ9᪆௃93⌕Þf(x)=g(x)ᨵàáâḄËᦪ᪷,ᑣ◤⌕¼å”•ç=mᨵàáâḄËᦪ᪷ᓽ!ᦪè(%)=é3•e”y=ᨵàáëḄìᐳ¨èí2-☜Ôïð"')(x-1)2x-1(x-1)2ñ:(%)>0,Á<0ᡈ%>|,ñ"(%)<0,0VXV1ᡈ1V%V|ᡠBh(%)Ḅᓫq⌴Zõö(—8,0),(÷+8),è(øḄᓫq⌴ùõö(0,1),(1,|),x—8ft(x)—CO,xûh(x)T—00,X1+,h(x)-»+oo,ú+8,è(x)T+00,

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6ூL᪆௃L:/'(x)=ezsin2x,ᡠf'(x)=e*(sin2x+2cos2x),ᑣ1(0)=2.ᦑ?ᫀ2.ᐜ.ᦪnᯠx=0ᐭn.B⚪⌕ὃEv.ᦪḄn7ḄUᵨWX~Ạ⚪.13.ூ?ᫀ௃-1ூL᪆௃Lᵫf(%+2)=-/(%),fQ+4)=f(x),ᡠ.ᦪḄᕜ4.ᡠ47)=஻3)=/(T).ᦪ᜻.ᦪ£x6(0,2)¤/(x)=x2,ᡠ/1)=—/(I)=-1ᡠ/(7)=/(-1)=-1.ᦑ?ᫀ-1.ᵫ/'(x+2)=-/(%),ᑮ.ᦪḄᕜᯠᑭᵨᕜឋ᜻ᏔឋḄUᵨn/(7)ᓽ.B⚪⌕ὃE.ᦪᕜឋḄᑨ¨w.ᦪ᜻ᏔឋḄUᵨ⌕n©ª«¬.ᦪឋḄᔠUᵨ.14.ூ?ᫀ௃2V2+1ூL᪆௃L£a>l,b>0¤,11-r-r+a+Vb=—-----—+(a-1)+®+1ab-bb(a-1)ᡠ+a+Ḅᨬ°+1.ab-bᦑ?ᫀ2±+1.'²ᑭᵨ~B)+ᓽn;³+a+´Ḅᨬ°.ab-bB⚪ὃEvᑭᵨ~B)+nᨬḄUᵨµ⚪ὃEvyznL{|3¶ᓄST}M᫏⚪.

715.ூ?ᫀ௃¹2,+8)ூL᪆௃ூᑖ᪆௃B⚪ὃEvᑭᵨᦪẆ¼ᓫ¾ឋᨬஹÀ².ᦪḄᓫ¾ឋஹ+Á¶ᓄFÂὃEvÃᳮ{|3Åz{|WXÆÇ⚪.ÈᙠÊe/?.%e/(%i)<஺(᝕)ᡂÏ+ÁX:%eR,xe(-l,+oo),22/(-I)=--+-+e2=g2-g(x)————2x1+a=—(x+1)2+a,.ᦪg(x)ᙠxG(1,+8)Üᓫ¾⌴ßᙠãE(-8,-1)ᓫ¾⌴Þ•••g(x)251111-'-a+b=èØ+éØ=l°g2+kg65=log6(2x5)=log^lO=2.(î)ï=(log3+|log3)(log24-ilog2)=^log3-|log2=2.223323ூL᪆௃(ð)ᐜᢣᦪᓄᦪpᑭᵨᦪḄyzឋnL.()ᑭᵨᦪḄyzឋnL.B⚪⌕ὃEvᢣᦪᓄᦪὃEvᦪḄyzឋWX~Ạ⚪.17.ூ?ᫀ௃L(ð)•..ᦪ/(x)=ax2+(6-2)x+3(a*0),)+f(x)>0ḄLd(1,1),.•.஺/+(ᓃ-2²+3=0Ḅ'᪷1,1,f--=-1+1=0•••La,La=-3,b=2.[-=(-l)xl=-l(0)(i)/(/)=a+b—2+3=2,•-a+b=1,8⚓ᐳ10⚓

8va>0,b>0,V+õö+Ò(a+b)="^+5N2j^+5=9,£úû£³=£ᓽ஺=õ,ᓃ=᪛+0ab33.•+Ḅᨬ°9;ab(ii),.)+/"(x)<1ᙠRÜḄLdþda/+ÿ_2)x+3<1,ᓽa/+(ᓃ-2)+2<0ᙠRḄ,(a>0(4=(6-2)2-8a<0,••Q+b=1,ᐭ!"(a+I)2-8Q<0,a2-6a+1<0,"3-2ᡈ?@ᳮBCD.(E)ᵫᩩGDHa+b=1,஺)ᑭᵨJKLM!DH5+OḄᨬQ+R(S)ᵫ஺T2+(ᓃ-2)%+3<1,"ax2+(b-2)x+2<0,ᵫLM!ᙠR.0,ᑡLM!VWXDH(ᦪ”Ḅ*+-.K⚪ὃ\8ᐗ^_LM!Ḅឋabcஹ>?@ᳮஹJKLM!ஹ᪷Ḅᑨf!MJẠ6hWὃ\ijDXkW.l᫏⚪.18.ூnᫀ௃O(p)q஺=rsW/(X)=lnx-ix,x€(0,+8),ᡠz/W(%)=ORMW{/'(x)=0,"x=2,X(0.2)2(2,+oo)f(x)+0-f.ᓫ⌴ln2-1ᓫ⌴ᡠz/(%)Ḅ᩽ᜧ+ln2—l,᩽Q+.(3)ᵫ⚪"g(x)=Inx-(a+2)x+1<0ᙠ(0,+8)ឤᡂ,T>0,ᡠzQ+2ᗸᙠ(0,+QO)ឤᡂ.-Inx(%)=%(%>0),ᑣ'(%)={'(x)=0,"x=1,q00,ᦪ(x)ᓫ⌴;qx>1Wh,'(x)<0,ᦪ(x)ᓫ⌴./i(x)min=hপ=1-ᡠza+2>1,ᓽa>-1.ᡠz(ᦪ஺ḄᨬQ+-1.(p):ᵫ/'(x)=X2ᓽ1nx—ax=/"M—x—a=0,

9{m(%)=M—x-a(x>0),ᑣ7n'(x)=1-lnxl-x2-lnx-1=x2t(x)=1—x2—In%,ᑣ£'(%)=-2x—x>0,ᡠzt'(x)<0ឤᡂWᦪ£(%)ᙠ(0,+8)ᓫ⌴W¤£(1)=0,ᦑᙠ(0,1)t(%)>0,m^x)>0,m(%)ᓫ⌴,ᙠ(L+8)£(%)V0,mr(x)<0,m(%)ᓫ⌴,ᡠz7H(X)max=7n(1)=818Q.ᦑ¨©/(%)=/ាᨵ:¬®Ḅ(᪷¯◤—1—஺>0.ᡠz(ᦪaḄ*+-.(-ᓅ-1).²OXX>1WL³´<%2Wᑣ0<%1<1<%2W0<—<1,r2X2ᡠz>1=>£=m(%i)>?n(;q)=m(x)=0,2ᡠzm(%i)-m(7-)=m(x)-m(2)=(M-x-a)-(·8ᓝ8஺)22x?%2x2—%2=M8T2-3+¹=º-T2+xinx+}=(O+x)lnx-Q+¼W2222ᐔ2—<*2ᐭ2"2ᐔ2ᐔ2x2{W(x)=(O+x)lnx-%+i(x>1),ᑣ"(x)=(1-Á)lnx>0,ᡠz0஺)ᙠ(1,+8)ᓫ⌴Wᡠzq4>1Ww(x)>3প=0,ᓽ(¼+%2)1nx2-T2+ஹ>஺WᡠzmQi)>ᡠzXi©>1-ூ᪆௃(3)✌ᐜDHᦪḄÆᦪWᓽÇ"ᑮXஹÉ(Ê´f஺)ḄᐵÌWͤDHᦪḄ᩽+R(3)Î⚪ÏÐᑖÒᓽÇ"ᑮa+22*ᙠ(0,+8)ឤᡂW{Óx)=*஺>0),ᑭᵨÆᦪÔᦪḄᓫឋWDHᦪḄᨬQ+WᓽÇDHÏᦪḄ*+-R(3)ᵫ/(%)=%2,ᓽÇ"ᑮM-x-a=0,{Õn(x)=Ö8×8a(x>0),ᑭᵨÆᦪÔᦪḄᓫឋWᓽÇDHᦪḄᨬQ+WÎ⚪Ç"-1-a>0,ᓽÇDHÏᦪ஺Ḅ*+-R/1=>"=m(%1)>Ø(})WᑣØ(%1)8=(~+x2)lnx2~x2+7-)Ú{9(x)=C+x)lnx-X+O(X>1),ᑭᵨÆᦪÔᦪḄᓫឋWDHᦪḄᨬQ+WᓽÇ"RK⚪ὃ\ÝᑭᵨÆᦪẆßᦪḄᓫឋ´᩽+WLM!ឤᡂà⚪W᪷ᨩḄ(᪷DÏᦪḄ*+-âLM!ḄWὃ\ݨ©ãäâåᓄãäWçl᫏⚪.è10⚓Wᐳ10⚓