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Toan pt.de023.2012

B畉O H鱈
B畉O H鱈
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I.PH畉NCHUNGCHOT畉TC畉CCTHSINH(7,0 i畛m) C但uI(2,0i畛m) Chohms畛y=x4 - 2mx2 +m(1),mlthams畛 1.Kh畉os叩ts畛餌bi畉nthi棚nvv畉渋畛th畛hms畛khim=1. 2. Bi畉tAli畛mthu畛c畛th畛hms畛(1)c坦honh畛b畉ng1.T狸mm畛kho畉ngc叩cht畛i畛m 3 余1 4 B 脱 旦 = 巽 歎 竪 淡 畉nti畉ptuy畉nc畛a畛th畛hms畛(1)t畉iAl畛nnh畉t. C但uII(2,0i畛m) 1. Gi畉iph動董ngtr狸nh 5 2.cos5 sin( 2 ) sin 2 .cot3 . 2 x x x x p p 脱 旦 - + = +巽 歎 竪 淡 2.Gi畉i h畛ph動董ngtr狸nh 2 2 4 2 2 2 3 15 0 2 4 5 0 x y x y x y x y 狸 + + - =誰 鱈 + - - - =誰樽 C但uIII(1,0i畛m) T鱈nh 2 3 9 1 x I dx x x = + - 嘆 C但uIV(1,0i畛m) Choh狸nhch坦pS.ABCDc坦叩yABCDlh狸nhthoic畉nha,h狸nhchi畉uvu担ngg坦cc畛a 畛nhStr棚n(ABCD)ltrungi畛mHc畛aAB,動畛ngtrungtuy畉nAMc畛a D ACDc坦畛di 3 2 a ,g坦cgi畛a (SCD)v(ABCD)b畉ng300 .T鱈nhth畛t鱈chkh畛ich坦pS.ABCDvt鱈nhdi畛nt鱈chm畉tc畉ungo畉iti畉ph狸nhch坦p S.ABC. C但uV(1,0i畛m) Cho , ,x y zlc叩cs畛th畛cd動董ngtho畉Ｂm達n x y z続 続 v 3x y z+ + = . T狸mgi叩tr畛nh畛nh畉tc畛abi畛uth畛c: 3 x z P y z y = + + II.PH畉NRING(3i畛m) Th鱈sinhch畛ch畛nm畛ttronghaiph畉n(ph畉nAho畉cph畉nB) A.Theoch動董ngtr狸nhchu畉n C但uVI.a(2,0i畛m) 1. Trongm畉tph畉ngt畛a畛Oxychoh狸nhthoiABCDbi畉tph動董ngtr狸nhc畛am畛t動畛ngch辿ol:3 7 0x y+ - = , i畛mB(0余足3).T狸mt畛a畛c叩c畛nhc嘆nl畉ic畛ah狸nhthoibi畉tdi畛nt鱈chh狸nhthoib畉ng20. 2. Gi畉iph動董ngtr狸nh: .25log)20.155.10log( +=+ xxx C但uVII.a(1,0i畛m) Chokhaitri畛n(1+2x)10 (x2 +x+1)2 = a0+a1x+a2x2 +β+a14x14 . H達yt狸mgi叩tr畛 c畛a a6. B.Theoch動董ngtr狸nhn但ngcao C但uVI.b(2,0 i畛m) 1. Choh狸nhthangvu担ngABCDvu担ngt畉iAvDc坦叩yl畛nlCD,動畛ngth畉ngADc坦ph動董ngtr狸nh 3x y =0,動畛ngth畉ngBDc坦ph動董ngtr狸nhx足2y=0,g坦ct畉ob畛ihai 動畛ngth畉ngBCvABb畉ng450 . Vi畉tph動董ngtr狸nh 動畛ngth畉ngBCbi畉tdi畛nt鱈chh狸nhthangb畉ng24vi畛mBc坦honh畛d動董ng. 2. Gi畉ib畉tph動董ngtr狸nh 2 2 2 1 log log ( 2) log (6 )x x x+ + + > - C但uVII.b(1,0i畛m)Cho * Nnﾂ Ch畛ngminhr畉ng 0 1 2 3 2 2 2 2 2 22 3 4 ... (2 1) 0n n n n n nC C C C n C- + - + + + = 足足足足足足足足足足足足足足足足H畉t足足足足足足足足足足足足足足足足足足足足 Th鱈sinhkh担ng動畛cs畛d畛ngtili畛u.C叩nb畛coithikh担nggi畉ith鱈chg狸th棚m H畛vt棚nth鱈sinh..............................................................S畛 b叩odanh............................... S畛GD&THT懲NH TR働畛NGTHPT畛CTH畛 畛THITH畛畉IH畛C,CAO畉NGL畉NI,NM2012 M担n:TON余Kh畛iA,B, D Th畛igianlmbi:180ph炭t(Kh担ngk畛th畛igianph叩t畛) Thi th畛 畉i h畛c www.toanpt.net
C但u 箪 N畛idung i畛m V畛im=1hms畛l: 4 2 2 1y x x= - + +)TX:D=R +)Gi畛ih畉n,畉ohm: lim 余lim x x y y 速+促 速-促 = = +促+促 . 3 0 ' 4 4 余 ' 0 1 x y x x y x =辿 = - = 棚 = 賊谷 0.25 +)Hms畛畛ngbi畉ntr棚nc叩ckho畉ng(足1余0),(1余+促 ) ngh畛chbi畉ntr棚nc叩ckho畉ng(足促 余足1),(0余1) +)Hm畉tc畛c畉it畉ix=0,yC=1,c畛cti畛ut畉ix= 賊 1,yCT=0 0.25 +)BBT: x 足 促 足1 01+促 y' 足 0+0 足 0+ y +促 1+促 0 0 0.25 1 +)畛th畛 10 8 6 4 2 足2 足4 足6 足8 足10 足15 足10 足5 5 10 15 0.25 +)A ( )Cmﾂ n棚nA(1余1足m) 0.25 +) 3 ' 4 4 '(1) 4 4y x mx y m= - = - Ph動董ngtr狸nhti畉ptuy畉nc畛a(Cm)t畉iAc坦ph動董ngtr狸nh y(1- m)=y(1).(x1) Hay(44m).xy 3(1 m)=0 0.25 Khi坦 2 1 ( 余 ) 1 16(1 ) 1 d B m - D = 贈 - + ,D畉u=x畉yrakhivch畛khim=1 0.25 S畛GD&THT懲NH TR働畛NGTHPT畛CTH畛 PN&THANGI畛M 畛THITH畛畉IH畛C,CAO畉NGL畉NI,NM2012 M担n:TON余Kh畛iA,B,D (叩p叩ng畛m04trang)
Do坦 ( 余 )d B D l畛nnh畉tb畉ng1khivch畛khim=1 0.25 K: sin3 0x 孫 pt 2cos5 sin 2 cos2 .cot3x x x x+ = 0.25 2cos5 sin3 sin 2 cos3 cos2 .cos3x x x x x x+ = 2cos5 sin3 cos5 0x x x- = cos5 ( 2 sin 3 1) 0x x - = 0.25 +) 1 sin3 0 2 x = 孫 (t/mk) 2 12 3 2 4 3 k x k x p p p p 辿 = +棚 棚 棚 = + 棚谷 0.25 1 +)cos5 0x = 10 5 k x p p = + t/mk KL:β 0.25 H畛pt 2 2 2 2 2 ( 1)( 2) 4( 1) 4( 2) 5 ( 1) ( 2) 10 x y x y x y 狸 - - + - + - =誰 鱈 - + - =誰樽 .畉t 2 1 2 u x v y 狸 = - 鱈 = -樽 Tac坦hpt 2 2 2 10 ( ) 2 10 4( ) 5 4( ) 5 u v u v uv uv u v uv u v 狸 狸+ = + - = 鱈 鱈 + + = + + =樽 樽 0.25 10 45 u v uv + = -狸 鱈 =樽 (v担nghi畛m)ho畉c 2 3 u v uv + =狸 鱈 = -樽 3 1 u v =狸 鱈 = -樽 ho畉c 1 3 u v = -狸 鱈 =樽 0.25 +) 3 1 u v =狸 鱈 = -樽 T狸m 動畛c2nghi畛m( 余 ) (2余1)x y = v( 余 ) ( 2余1)x y = - 0.25 II 2 +) 1 3 u v = -狸 鱈 =樽 T狸m 動畛cnghi畛m ( 余 ) (0余5)x y = K畉tlu畉n:H畛ph動董ngtr狸nhc坦3nghi畛m:(2余1),(足2余1),(0余5) 0.25 2 2 2 2 (3 9 1) 3 9 1 3 9 1 x I dx x x x dx x dx x x dx x x = = - - = - - + - 嘆 嘆 嘆 嘆 0.25 +) 2 3 1 13I x dx x C= = +嘆 0.25 +) 2 2 9 1I x x dx= -嘆 3 2 2 2 2 2 1 1 9 1 (9 1) (9 1) 18 27 x d x x C= - - = - +嘆 0.25 III V畉y 3 2 32 1 (9 1) 27 I x x C= - + + 0.25
+)T鱈nhth畛t鱈chkh畛ich坦p Tac坦cos 0 60=ACD suyra ACDD 畛u. 3 2 a HC AM= = v ( )HC CD CD SHC^ ^ .Suyrag坦cgi畛a(SCD)v(ABCD)lSHC=300 0,25 0 .tan 30 2 a SH HC= = , 2 3 3 1 3 . . 2 3 12 ABCD SABCD ABCD a a S AB CH V S SH= = = = 0,25 IV +)G畛iGltr畛ngt但mtamgi叩cABC.Tac坦 3 a GA GB GC= = = .Do 2 a HS HB HA= = = n棚nc叩ctamgi叩cGHA,GHB,GHSlc叩ctamgi叩cvu担ng b畉ngnhaun棚nGA=GB=GS.SuyraGt但mm畉tc畉ungo畉iti畉ph狸nhch坦pvb叩n k鱈nh 3 a R GC= = . Di畛nt鱈chm畉tc畉u 3 4 4 2 2 a RS p p == 0.5 S畛d畛ngbtAM足GM,tac坦 2 , 2 x z xz x yz z z y + 続 + 続 0.25 T畛坦suyra 3 2 2 3 x z P y x xz z yz y z y = + + 続 - + - + 2 2( ) ( ) 2( ) ( ) x z y x y z xz yz x z y x y z = + + + + - - = + + + - 0.25 V Do 0x > v y z続 n棚n ( ) 0x y z- 続 .T畛但yk畉th畛pv畛itr棚nta動畛c 2 2 2 3 2( ) 2(3 ) ( 1) 5 5 x z P y x z y y y y z y = + + 続 + + = - + = - + 続 . V畉ygi叩tr畛nh畛nh畉tc畛aPb畉ng5畉tkhi x=y=z=1 0.5 Ph動董ngtr狸nhBD 3 9 0x y- - = .T畛a畛 I AC BD= (3余 2)I - 0.25 DoIltrungi畛mBDn棚n (6余 1)D - . G畛i ( 余7 3 )A a a AC- ﾂ tac坦 2 10BD = 0.25 1 dt(ABCD)=2.dt(ABD) 2 2 3(7 3 ) 91 .2 10 10 2 1 3 a a- - - = + 0.25 S B C M D H A
2 4 a a =辿 棚 =谷 dov畉y 1 1 2 2 (2余1)余 (4余 5) (4余 5)余 (2余1) A C A C -辿 棚 -谷 0.25 PT ( ) ( )xxx 10.25log20.155.10log =+ xxx 10.2520.155.10 =+ 0102.254.15 =+- xx (chiahaiv畉紳c畛aph動董ngtr狸nhcho x 5 ) 0.25 畉t )0(2 >= tt x ,Tac坦pt :15t2 足25t+10=0 棚 棚 谷 辿 = = )( 3 2 )(1 tmt tmt 0.25 VI.a 2 V畛i 1=t 012 == xx V畛i 歎 淡 旦 巽 竪 脱 === 3 2 log 3 2 2 3 2 2xt x V畉yph動董ngtr狸nh達choc坦hainghi畛ml 0=x v 歎 淡 旦 巽 竪 脱 = 3 2 log2x . 0.5 Tac坦 ( )奪= =+ 10 0 10 10 2.)21( k kk xCx v 2 2 4 2 3 ( 1) ( 3 1 2 2 )x x x x x x+ + = + + + + 0.25 ( ) 10 10 2 2 4 2 3 10 0 (1 2 ) ( 1) ( 3 1 2 2 ). . 2 kk k x x x x x x x C x = + + + = + + + + 奪 0.25VII.a ( ) ( ) ( ) ( ) ( ) 417482..22..22.2..32. 55 10 33 10 66 10 44 10 22 106 =++++= CCCCCa 0.5 T畛a畛i畛mDl: 3 0 0 2 0 0 x y x x y y - = =狸 狸 鱈 鱈 - = =樽 樽 =>D(0余0) 尊O Vectoph叩ptuy畉nc畛a動畛ngth畉ngADvBDl畉nl動畛tl ( ) ( )1 23余 1 , 1余 2n n- - ur uur => cosADB= 2 1 =>ADB=450 =>AD=AB(1) 0.25 V狸g坦cgi畛a動畛ngth畉ngBCvABb畉ng450 =>BCD=450 => D BCDvu担ng c但nt畉iB=>DC=2AB.Theobiratac坦: ( ) 2 1 3. 24 2 2 ABCD AB S AB CD AD= + = = =>AB=4=>BD= 4 2 0.25 G畛it畛a畛i畛m 余 2 B B x B x 脱 旦 巽 歎 竪 淡 ,i畛uki畛nxB>0 => 2 2 8 10 ( ) 5 4 2 2 8 10 ( ) 5 B B B B x loai x BD x x tm 辿 = -棚 脱 旦 棚= + = 巽 歎 棚竪 淡 =棚 谷 uuur T畛a畛i畛m 8 10 4 10 余 5 5 B 脱 旦 巽 歎巽 歎 竪 淡 0.25 1 Vect董ph叩ptuy畉nc畛aBCl ( )2余1BCn = uuur =>ph動董ngtr狸nh動畛ngth畉ngBCl: 2 4 10 0x y+ - = 0.25 k:0<x<6.BPT 2 2 2 2log (2 4 ) log (6 )x x x+ > - 0.25 BPT 2 2 2 2 4 (6 ) 16 36 0x x x x x+ > - + - > 0.25 x< 足18ho畉c x >2 0.25 VI.b 2 K畉th畛pktac坦t畉pnghi畛mBPTlS=(2余6) 0.25 X辿thms畛 2 2 2 1 ( ) (1 ) '( ) (1 ) 2 (1 )n n n f x x x f x x nx x - = + = + + + (1) 0,25
Theoc担ngth畛ckhaitri畛nnh畛th動cnewtontac坦: 0 1 2 2 2 2 2 2 2 2( ) ( ... )n n n n n nf x x C C x C x C x= + + + + 0,25 0 1 2 2 2 2 2 2 2 2'( ) 2 3 ... (2 1) n n n n n nf x C C x C x n C x= + + + + + (2) 0,25 VII.b Thayx=足1vo(1)v(2)ta動畛c畉ngth畛cc畉nch畛ngminh 0,25 C叩cc叩chgi畉ikh叩c炭ngchoi畛mt動董ng動董ng

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Toan pt.de023.2012

  • 1. I.PH畉NCHUNGCHOT畉TC畉CCTHSINH(7,0 i畛m) C但uI(2,0i畛m) Chohms畛y=x4 - 2mx2 +m(1),mlthams畛 1.Kh畉os叩ts畛餌bi畉nthi棚nvv畉渋畛th畛hms畛khim=1. 2. Bi畉tAli畛mthu畛c畛th畛hms畛(1)c坦honh畛b畉ng1.T狸mm畛kho畉ngc叩cht畛i畛m 3 余1 4 B 脱 旦 = 巽 歎 竪 淡 畉nti畉ptuy畉nc畛a畛th畛hms畛(1)t畉iAl畛nnh畉t. C但uII(2,0i畛m) 1. Gi畉iph動董ngtr狸nh 5 2.cos5 sin( 2 ) sin 2 .cot3 . 2 x x x x p p 脱 旦 - + = +巽 歎 竪 淡 2.Gi畉i h畛ph動董ngtr狸nh 2 2 4 2 2 2 3 15 0 2 4 5 0 x y x y x y x y 狸 + + - =誰 鱈 + - - - =誰樽 C但uIII(1,0i畛m) T鱈nh 2 3 9 1 x I dx x x = + - 嘆 C但uIV(1,0i畛m) Choh狸nhch坦pS.ABCDc坦叩yABCDlh狸nhthoic畉nha,h狸nhchi畉uvu担ngg坦cc畛a 畛nhStr棚n(ABCD)ltrungi畛mHc畛aAB,動畛ngtrungtuy畉nAMc畛a D ACDc坦畛di 3 2 a ,g坦cgi畛a (SCD)v(ABCD)b畉ng300 .T鱈nhth畛t鱈chkh畛ich坦pS.ABCDvt鱈nhdi畛nt鱈chm畉tc畉ungo畉iti畉ph狸nhch坦p S.ABC. C但uV(1,0i畛m) Cho , ,x y zlc叩cs畛th畛cd動董ngtho畉Ｂm達n x y z続 続 v 3x y z+ + = . T狸mgi叩tr畛nh畛nh畉tc畛abi畛uth畛c: 3 x z P y z y = + + II.PH畉NRING(3i畛m) Th鱈sinhch畛ch畛nm畛ttronghaiph畉n(ph畉nAho畉cph畉nB) A.Theoch動董ngtr狸nhchu畉n C但uVI.a(2,0i畛m) 1. Trongm畉tph畉ngt畛a畛Oxychoh狸nhthoiABCDbi畉tph動董ngtr狸nhc畛am畛t動畛ngch辿ol:3 7 0x y+ - = , i畛mB(0余足3).T狸mt畛a畛c叩c畛nhc嘆nl畉ic畛ah狸nhthoibi畉tdi畛nt鱈chh狸nhthoib畉ng20. 2. Gi畉iph動董ngtr狸nh: .25log)20.155.10log( +=+ xxx C但uVII.a(1,0i畛m) Chokhaitri畛n(1+2x)10 (x2 +x+1)2 = a0+a1x+a2x2 +β+a14x14 . H達yt狸mgi叩tr畛 c畛a a6. B.Theoch動董ngtr狸nhn但ngcao C但uVI.b(2,0 i畛m) 1. Choh狸nhthangvu担ngABCDvu担ngt畉iAvDc坦叩yl畛nlCD,動畛ngth畉ngADc坦ph動董ngtr狸nh 3x y =0,動畛ngth畉ngBDc坦ph動董ngtr狸nhx足2y=0,g坦ct畉ob畛ihai 動畛ngth畉ngBCvABb畉ng450 . Vi畉tph動董ngtr狸nh 動畛ngth畉ngBCbi畉tdi畛nt鱈chh狸nhthangb畉ng24vi畛mBc坦honh畛d動董ng. 2. Gi畉ib畉tph動董ngtr狸nh 2 2 2 1 log log ( 2) log (6 )x x x+ + + > - C但uVII.b(1,0i畛m)Cho * Nnﾂ Ch畛ngminhr畉ng 0 1 2 3 2 2 2 2 2 22 3 4 ... (2 1) 0n n n n n nC C C C n C- + - + + + = 足足足足足足足足足足足足足足足足H畉t足足足足足足足足足足足足足足足足足足足足 Th鱈sinhkh担ng動畛cs畛d畛ngtili畛u.C叩nb畛coithikh担nggi畉ith鱈chg狸th棚m H畛vt棚nth鱈sinh..............................................................S畛 b叩odanh............................... S畛GD&THT懲NH TR働畛NGTHPT畛CTH畛 畛THITH畛畉IH畛C,CAO畉NGL畉NI,NM2012 M担n:TON余Kh畛iA,B, D Th畛igianlmbi:180ph炭t(Kh担ngk畛th畛igianph叩t畛) Thi th畛 畉i h畛c www.toanpt.net
  • 2. C但u 箪 N畛idung i畛m V畛im=1hms畛l: 4 2 2 1y x x= - + +)TX:D=R +)Gi畛ih畉n,畉ohm: lim 余lim x x y y 速+促 速-促 = = +促+促 . 3 0 ' 4 4 余 ' 0 1 x y x x y x =辿 = - = 棚 = 賊谷 0.25 +)Hms畛畛ngbi畉ntr棚nc叩ckho畉ng(足1余0),(1余+促 ) ngh畛chbi畉ntr棚nc叩ckho畉ng(足促 余足1),(0余1) +)Hm畉tc畛c畉it畉ix=0,yC=1,c畛cti畛ut畉ix= 賊 1,yCT=0 0.25 +)BBT: x 足 促 足1 01+促 y' 足 0+0 足 0+ y +促 1+促 0 0 0.25 1 +)畛th畛 10 8 6 4 2 足2 足4 足6 足8 足10 足15 足10 足5 5 10 15 0.25 +)A ( )Cmﾂ n棚nA(1余1足m) 0.25 +) 3 ' 4 4 '(1) 4 4y x mx y m= - = - Ph動董ngtr狸nhti畉ptuy畉nc畛a(Cm)t畉iAc坦ph動董ngtr狸nh y(1- m)=y(1).(x1) Hay(44m).xy 3(1 m)=0 0.25 Khi坦 2 1 ( 余 ) 1 16(1 ) 1 d B m - D = 贈 - + ,D畉u=x畉yrakhivch畛khim=1 0.25 S畛GD&THT懲NH TR働畛NGTHPT畛CTH畛 PN&THANGI畛M 畛THITH畛畉IH畛C,CAO畉NGL畉NI,NM2012 M担n:TON余Kh畛iA,B,D (叩p叩ng畛m04trang)
  • 3. Do坦 ( 余 )d B D l畛nnh畉tb畉ng1khivch畛khim=1 0.25 K: sin3 0x 孫 pt 2cos5 sin 2 cos2 .cot3x x x x+ = 0.25 2cos5 sin3 sin 2 cos3 cos2 .cos3x x x x x x+ = 2cos5 sin3 cos5 0x x x- = cos5 ( 2 sin 3 1) 0x x - = 0.25 +) 1 sin3 0 2 x = 孫 (t/mk) 2 12 3 2 4 3 k x k x p p p p 辿 = +棚 棚 棚 = + 棚谷 0.25 1 +)cos5 0x = 10 5 k x p p = + t/mk KL:β 0.25 H畛pt 2 2 2 2 2 ( 1)( 2) 4( 1) 4( 2) 5 ( 1) ( 2) 10 x y x y x y 狸 - - + - + - =誰 鱈 - + - =誰樽 .畉t 2 1 2 u x v y 狸 = - 鱈 = -樽 Tac坦hpt 2 2 2 10 ( ) 2 10 4( ) 5 4( ) 5 u v u v uv uv u v uv u v 狸 狸+ = + - = 鱈 鱈 + + = + + =樽 樽 0.25 10 45 u v uv + = -狸 鱈 =樽 (v担nghi畛m)ho畉c 2 3 u v uv + =狸 鱈 = -樽 3 1 u v =狸 鱈 = -樽 ho畉c 1 3 u v = -狸 鱈 =樽 0.25 +) 3 1 u v =狸 鱈 = -樽 T狸m 動畛c2nghi畛m( 余 ) (2余1)x y = v( 余 ) ( 2余1)x y = - 0.25 II 2 +) 1 3 u v = -狸 鱈 =樽 T狸m 動畛cnghi畛m ( 余 ) (0余5)x y = K畉tlu畉n:H畛ph動董ngtr狸nhc坦3nghi畛m:(2余1),(足2余1),(0余5) 0.25 2 2 2 2 (3 9 1) 3 9 1 3 9 1 x I dx x x x dx x dx x x dx x x = = - - = - - + - 嘆 嘆 嘆 嘆 0.25 +) 2 3 1 13I x dx x C= = +嘆 0.25 +) 2 2 9 1I x x dx= -嘆 3 2 2 2 2 2 1 1 9 1 (9 1) (9 1) 18 27 x d x x C= - - = - +嘆 0.25 III V畉y 3 2 32 1 (9 1) 27 I x x C= - + + 0.25
  • 4. +)T鱈nhth畛t鱈chkh畛ich坦p Tac坦cos 0 60=ACD suyra ACDD 畛u. 3 2 a HC AM= = v ( )HC CD CD SHC^ ^ .Suyrag坦cgi畛a(SCD)v(ABCD)lSHC=300 0,25 0 .tan 30 2 a SH HC= = , 2 3 3 1 3 . . 2 3 12 ABCD SABCD ABCD a a S AB CH V S SH= = = = 0,25 IV +)G畛iGltr畛ngt但mtamgi叩cABC.Tac坦 3 a GA GB GC= = = .Do 2 a HS HB HA= = = n棚nc叩ctamgi叩cGHA,GHB,GHSlc叩ctamgi叩cvu担ng b畉ngnhaun棚nGA=GB=GS.SuyraGt但mm畉tc畉ungo畉iti畉ph狸nhch坦pvb叩n k鱈nh 3 a R GC= = . Di畛nt鱈chm畉tc畉u 3 4 4 2 2 a RS p p == 0.5 S畛d畛ngbtAM足GM,tac坦 2 , 2 x z xz x yz z z y + 続 + 続 0.25 T畛坦suyra 3 2 2 3 x z P y x xz z yz y z y = + + 続 - + - + 2 2( ) ( ) 2( ) ( ) x z y x y z xz yz x z y x y z = + + + + - - = + + + - 0.25 V Do 0x > v y z続 n棚n ( ) 0x y z- 続 .T畛但yk畉th畛pv畛itr棚nta動畛c 2 2 2 3 2( ) 2(3 ) ( 1) 5 5 x z P y x z y y y y z y = + + 続 + + = - + = - + 続 . V畉ygi叩tr畛nh畛nh畉tc畛aPb畉ng5畉tkhi x=y=z=1 0.5 Ph動董ngtr狸nhBD 3 9 0x y- - = .T畛a畛 I AC BD= (3余 2)I - 0.25 DoIltrungi畛mBDn棚n (6余 1)D - . G畛i ( 余7 3 )A a a AC- ﾂ tac坦 2 10BD = 0.25 1 dt(ABCD)=2.dt(ABD) 2 2 3(7 3 ) 91 .2 10 10 2 1 3 a a- - - = + 0.25 S B C M D H A
  • 5. 2 4 a a =辿 棚 =谷 dov畉y 1 1 2 2 (2余1)余 (4余 5) (4余 5)余 (2余1) A C A C -辿 棚 -谷 0.25 PT ( ) ( )xxx 10.25log20.155.10log =+ xxx 10.2520.155.10 =+ 0102.254.15 =+- xx (chiahaiv畉紳c畛aph動董ngtr狸nhcho x 5 ) 0.25 畉t )0(2 >= tt x ,Tac坦pt :15t2 足25t+10=0 棚 棚 谷 辿 = = )( 3 2 )(1 tmt tmt 0.25 VI.a 2 V畛i 1=t 012 == xx V畛i 歎 淡 旦 巽 竪 脱 === 3 2 log 3 2 2 3 2 2xt x V畉yph動董ngtr狸nh達choc坦hainghi畛ml 0=x v 歎 淡 旦 巽 竪 脱 = 3 2 log2x . 0.5 Tac坦 ( )奪= =+ 10 0 10 10 2.)21( k kk xCx v 2 2 4 2 3 ( 1) ( 3 1 2 2 )x x x x x x+ + = + + + + 0.25 ( ) 10 10 2 2 4 2 3 10 0 (1 2 ) ( 1) ( 3 1 2 2 ). . 2 kk k x x x x x x x C x = + + + = + + + + 奪 0.25VII.a ( ) ( ) ( ) ( ) ( ) 417482..22..22.2..32. 55 10 33 10 66 10 44 10 22 106 =++++= CCCCCa 0.5 T畛a畛i畛mDl: 3 0 0 2 0 0 x y x x y y - = =狸 狸 鱈 鱈 - = =樽 樽 =>D(0余0) 尊O Vectoph叩ptuy畉nc畛a動畛ngth畉ngADvBDl畉nl動畛tl ( ) ( )1 23余 1 , 1余 2n n- - ur uur => cosADB= 2 1 =>ADB=450 =>AD=AB(1) 0.25 V狸g坦cgi畛a動畛ngth畉ngBCvABb畉ng450 =>BCD=450 => D BCDvu担ng c但nt畉iB=>DC=2AB.Theobiratac坦: ( ) 2 1 3. 24 2 2 ABCD AB S AB CD AD= + = = =>AB=4=>BD= 4 2 0.25 G畛it畛a畛i畛m 余 2 B B x B x 脱 旦 巽 歎 竪 淡 ,i畛uki畛nxB>0 => 2 2 8 10 ( ) 5 4 2 2 8 10 ( ) 5 B B B B x loai x BD x x tm 辿 = -棚 脱 旦 棚= + = 巽 歎 棚竪 淡 =棚 谷 uuur T畛a畛i畛m 8 10 4 10 余 5 5 B 脱 旦 巽 歎巽 歎 竪 淡 0.25 1 Vect董ph叩ptuy畉nc畛aBCl ( )2余1BCn = uuur =>ph動董ngtr狸nh動畛ngth畉ngBCl: 2 4 10 0x y+ - = 0.25 k:0<x<6.BPT 2 2 2 2log (2 4 ) log (6 )x x x+ > - 0.25 BPT 2 2 2 2 4 (6 ) 16 36 0x x x x x+ > - + - > 0.25 x< 足18ho畉c x >2 0.25 VI.b 2 K畉th畛pktac坦t畉pnghi畛mBPTlS=(2余6) 0.25 X辿thms畛 2 2 2 1 ( ) (1 ) '( ) (1 ) 2 (1 )n n n f x x x f x x nx x - = + = + + + (1) 0,25
  • 6. Theoc担ngth畛ckhaitri畛nnh畛th動cnewtontac坦: 0 1 2 2 2 2 2 2 2 2( ) ( ... )n n n n n nf x x C C x C x C x= + + + + 0,25 0 1 2 2 2 2 2 2 2 2'( ) 2 3 ... (2 1) n n n n n nf x C C x C x n C x= + + + + + (2) 0,25 VII.b Thayx=足1vo(1)v(2)ta動畛c畉ngth畛cc畉nch畛ngminh 0,25 C叩cc叩chgi畉ikh叩c炭ngchoi畛mt動董ng動董ng