Đề&HD TS ĐH Toán 2010 số 31

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X x y z d − − = = $ &9 3 Z+M+M])  &Q  ' 8 Q 8 #Q 3 &" #$%&'<  Q 8 #Q 3 &  #789;? 2#$%&'<  9 ! ! ! !:  !:  !:  @& @& x x x x x Log x x x + + + + =  0<0=>  0$7? #789;A ;'&Q 8 #Q 3 & 8  8 RS*$%  &'   ! !   9 C x y+ = +$%  &Q 3 &   9 7d x y m+ + = ;<   m  3  C Q   d  8 C  DM 8 < & CDR@% >  #789;A ;'&,&&%  8  8  8 RS*Y+G#J&9 ^9!S_*OYO?7+`9S_*O!YO6?7+a9SO!*_6YO?7 $T&J&  ∆ 9 ! ! − − x ?   + y ? 6 z 2U ! ∆ @&)*^` "#$%&'($T&J&M)&&AFab$T&J&  ∆ + ! ∆  #789;A 2c#$%&'(9@& S @& 6 d S _4! ≤  [[[[[[[[[[I [[[[[[[[[[ BB$9C $6D& #78EF $8 GH  e;f#S9 { } g D = ¡ e;= !  \ 7   y x D x − = < ∀ ∈ − Ih&',&  0−∞  0 +∞ eIh,&A' e2FE x Limy + → = +∞  x Limy − → = −∞ ! x Lim y →+∞ =  ! x Lim y →−∞ = iAjfP&9S?+jf&&*?! eD& S −∞  +∞ *] [[ * e" 7!X 7!X 7!X 7!X ! e;#)*E. 7 7  0    M x f x C∈ A#$%&'(  7 7 7 \    y f x x x f x= − + I* ! ! 7 7 7   ! !  7x x y x x+ − − + − = e e&-./0!#)*e1& !  7 : 7 ! ! !    x x − ⇔ = + −  &$W&j 7 7x =  7 !x = e#)*k(9  7x y+ − =  X 7x y+ − = 7!X 7!X 7!X 7!X ! eDl#$%&'(m$%&$%&F  ! 6  ! 7   5 7 5 c x x c x π − + + + =  !  X   6 7 6 5 c x c x π π ⇔ + + + + =  ! !    X   ! 7 5 5 c x c x π π ⇔ + + + + = 2$W    5 ! c x π + = −    ! 5 c x π + = − @E e2    5 ! c x π + = − $W&j ! ! x k π π = +  X ! 5 x k π π = − + 7!X 7!X 7!X 7!X !! eDlj$%&$%&F ! ! 6 6 !       x xy x y x y x xy  − = −   − − = −   eiGn#o ! 6 x xy u x y v  − =   =   +$Wj !   u v v u  = −  − = −  e2j'$W&j)0@07[!0[6 e;-A&$W&jS0*@07[07 7!X 7!X 7!X 7!X 6 eiG?S ;=M?[SMS+lfS?7(?+ : x π = (  ! t = ;-A   ! ! !   ! @ @t t I dt dt t t = − = ∫ ∫ eiG !  @ 0u t dv dt t = =    0du dt v t t ⇒ = = − B)*'  !  !     !  @ @ !   ! ! ! I t dt t t t = − + = − − ∫ ep) ! !  @ ! ! I = − −  7!X 7!X 7!X 7!X : e"( e2UI@')&.D+P&  SH ABC⊥ eqr&&A&LG#J&BCD+BCFG*@  7 57SEH SFH= = es HK SB⊥ +@f#@)f)*'&A&LG#J&BCDBD 1& HK A  etf#@)f=$WC?CD?+ ! ! a HA = + 7 6  57 ! a SH HF= = e;&BI)&EIA ! ! !    6 7 KH a HK HS HB = + ⇒ = e;&CI)&EIA ! !7 !  6 6 7 a AH AK H KH a = = =  6  !6 AK H⇒ =  7!X 7!X 7!X 7!X X eDl       a b c c ab c ab b a a b + − − = = + + − − − − 7!X e;-A             c b a VT a b c a c b − − − = + + − − − − − − u++M$%&OO?++)V,&70?v[+[+[ M$%& e#Mo&cJ&PhM$%&$W 6    6            c b a VT a b c a c b − − − ≥ − − − − − − ?6# iJ&PS*',H,  6 a b c= = = 7!X 7!X 7!X 5 e ∆ A#$%&'(h  6 ! ! x t y t = −   = − +  A#  60!u = − ur eC)V ∆   6 0 ! ! A t t⇒ − − +  e;ACD0 ∆ ?:X 7    0  ! c AB u⇔ = uuuur ur    !  AB u AB u ⇔ = uuuur ur ur  ! X 6 5d X5 :X 7 6 6 t t t t⇔ − − = ⇔ = ∨ = − e.k(@  ! 6! : !! 6!  0 +  0  6 6 6 6 A A− − 7!X 7!X 7!X 7!X 4 eMp)  70 07M − A#  0 !0 6u = − − uur M]p) ! 700:M A# ! 0!0Xu = uur e;A  ! 0  :0 w0:u u O   = − − ≠   uur uur ur +  ! 70!0:M M = uuuuuuur qx  !  ! 0  5 : 7u u M M   = − + =   uur uur uuuuuuur  MM]&#J& e2U^@G#J&PMM]?v^A# 0!0 n = − ur  p)Z  A#$%&'( ! ! 7x y z+ − + = euyc*.Z0[0)Vz^+-AA# 7!X 7!X 7!X 7!X w ei{),j9Sv7 e;I9SxS?@&j e;I!9Sx x ≠ +l#$%&'($%&$%&F   !   !@& !:  ! @& !:  @& !:  x x x x x x + = + + + + + iG @&   x x t+ = +$W#$%&'(   !   ! !t t t + = + + &$W??[!|6 e"F? @&    x x⇒ + = #$%&'(*&j e"F?[!|6 ! @&   6 x x⇒ + = −   ! 6 !:  x x⇔ + = e }fc*  w x = @&je })  w x > (";ev 7!X 7!X 7!X 7!X })  w x < (";e~+f*eA&jM)*c  w x = e@)f9&j#$%&'(m@S?  w x = 5 eA>R707+,=a? eMbE.#>j  0  d O d⇔ < e;A       ! ! ! OAB S OAOB AOB AOB= = ≤ ;-AMj=&CRD@Fc,H, 7 d7AOB =    0  ! d I d⇔ =  m ⇔ = ± 7!X 7!X 7!X 7!X 4 e  ∆ A#$%&'(h ! !  6 x t y t z t = −   = − +   =  e ! ∆ A#$%&'(h ! X 6 x s y s z s = +   = +   =  e2•  ! 0d A d B∩ ∆ = ∩ ∆ = ! ! 0  06 D!O0XO60A t t t⇒ − − + e  ! 06 50 6 AB s t s t s t= + − + − uuuur +zaA# 0!0 6n = − ur e   €d R AB n⊥ ⇔ uuuur ur K&#$%&  ! 6 5 6  ! 6 s t s t s t+ − + − ⇔ = = −  !6 !: t⇒ = eMp)   !6  0 0  ! ! w A A# 0!0 6n = − ur ?vMA#$%&'( !6   w ! !  ! 6 z x y − − − = = − 7!X 7!X 7!X 7!X w ei{),j9 6 7 @& d 4! 7 d 4! 7 x x x >   − >   − >  &$W d @& 46x > "( d @& 46x > v#m$%&$%&F  6 @& d 4! x x− ≤  d 4! 6 x x ⇔ − ≤  6 w 6 d x x  ≥ −  ⇔  ≤    !x ⇔ ≤ e@)ff#&j9 d @& 4!0!•T = 7!X 7!X 7!X 7!X t$)‚9})=@,r&(&,cƒ$F@A