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Toan pt.de075.2012

  • 1. ! " # = − + !"# $ % &' ( )* &+ ( , ( - !. / # 0 % 1 2 3 4 5 6 76 # ! ( ! 8# 9 : ; ) &+ ( )< &+ ( => 7 $% & ? % &' ( )* 5 5 ! ! ! − − + = ? % &' ( )* 55 5 5 + − + − = − + + − ∈ $% @> >! % 1 A A + + = +∫ $% ' AB ( )C D ( 37 3E7E E !F 37 A # ( ! !1 G 4 &+ ( , ( 7 E / H I % , ( 377E3E (F! J KJ 37 L 33E L # ?8 M6 N6 O AP A&Q A )R ( 0 !"# 77E6 E6 7 S A 9 0 ) !/ 37 # ! 7S L 5 @> T # 0 >! = AB ( )C 37 3E7E E ! D ( ); ( M3 NOS⊥ $% ' # ! -&' ( U# V L D ( ); ( 5 + + ≥ + + + ( ) !" # $ % $ % & "' ( $% ' &* @) ( I % , ( / 9 ) * 6 ! * * :37 !F - 2 >! ; ( 5 7 3 W 4 ( # 0 X !"# # &+ ( ! Y ; ) &+ ( , ( L W @* 8# 9 G 7 @) ( = Z ( ( # H 2 8# 9 : [6 ! I % , ( O J* +− + − = ! ! &+ ( , ( * +− − = = − 6 5 * +− + = = @* ! ! 0 3 ) 7 ) # ! 37 ( ( H I % , ( O 37 ! ! O 9 = ( ; ( $% ' &* @* / ( = Z ( ! D# ) ( = # ) 0 , + = + 6 A (R -&' ( U# V + = ! " $% ' & + & @) ( I % , ( 8# 9 ) * ! & - . / &+ ( , ( 0 1 * 1 / 2 ]# 0 ( 3 - 9 ( ) # ! / (3 ARZ !F 9 - ; ( @* ( 3 # ! ! R # ( ! &(3 A U ^ @) ( = Z ( ( # H 2 / 9 : [6 ! * RZ ( 37 _ H 3 4 4 J 4 4 4 W5 G 7 ; ) I % , ( S J=−++ +* @* / 9 !"# G _ $% ' &+ @* (R -&' ( U# J ` ` 3 3 3 3 + + + + + = + J& = &&&&&&&&&&&&&&& ,- &&&&&&&&&&&&&&&& 4 5 # 6 7 # 89: 3; " 4 5 # # < #= > : ?@ > AAAAAAAAAAAAA:BC ;" AAAAAAA Thi thử Đại học www.toanpt.net
  • 2. = − = = ⇔  = − ! ( )−∞ − " ( )+∞ #$ ! ( )− % & $ $ '( & ) *+ ,- . % & $ $ & & ) /*+ ,- ,0/*1 2 3 4 & →+∞ = +∞ + →−∞ = −∞ 5! ) /∞∞∞∞ /* * %∞∞∞∞ ,6 % . / . % , 2 /∞∞∞∞ . %∞∞∞∞ 7 # % 3 "4 8$ 9, 0.+ *1 % 3 "4 8$ 9) 0*+ .1 0/:+ .1 ; <= > <? @ A B( ' $C D C$ E ( )!= − + F ' $G $G <? @ A " # 0-1 E D $G H <= > ( ) ( )( )" ! "! ! ! ! !− + = − + ⇔ − + + − = ! ! ! − = ⇔  + + − = <? @ A $I # 0-1 & ' H J D > H <= > $C D H J D K$ : # # > >  ⇔ ⇔  − ≠ ≠  L C M F 50)*+,*1+ -0):+,: + = −  = − = − + = − + ' 9 N <? O <? P 5- " $ Q $ = " # %− + − = ⇔ = &'() * +, - . / !0 $ $ 1. π≠ ∈» +2 1 &34 '56 7 &38 ' 9* :'; &56 7 956 7
  • 3. <2 . + = − − ⇔ − = − − − = − − ⇔ = − ⇔ − − = :;= :;= =   =  π π π  = ⇔  = ± + ∈ > :' ? <2 9 @ A &) 95B: 7' A :C) '56 7 &38 ' DE π π= ± + ∈ » 0 9 @ A ≤ ≤ F&  = ≥ ⇒ + = = − ≥ 0 '56 7 &38 ' &3G &'E ' " " + + = + + ⇔ − + + − = 8$$$$$ = ⇔ + =  + = 0 +2 ) / H = − ⇔ = 0 +2 )0H/ &) :I 'A  + = + = + = =+ =   ⇔ ⇔ ⇔=    + = + =+ − − =     =  = = ⇔  = +, '56 7 &38 ' :I " 7' A !/ !/ = $ D " D D D D D D + + + + + + = = = + + + +∫ ∫ ∫ ∫ = = = −∫
  • 4. " D D + = +∫ D D= + ⇒ = + D D + + = = = +∫ D= + = + + − + J DE &3 7 9 KLK &'8 M M M M M M M M ⊥  ⇒ ⊥ ⊥  = 3) 7I: 7 N) L K <E LLK K :'O ' DE 7I: M $ P 3) M Q= $ M $&) M= = I M M M $ M M$ M - -= = " $ M M M M M M $$ $M$ M $ M M= = = 9<&& 0 R R M R R M R R M  ⇒  0 M M M # L = − − = + = ⇒ ⊥ $ F& ' : &'S; :'T 7 ' &34 K ⊥ 4 ⊥ M P 3) ⊥ M U <E = 3) V⊥ + $W; )H 0 H: 0 :) / " 4 + XXX / " " " + + + + + + + + + + + / " " " + + + + + + + +
  • 5. 'S; L Y = &) :I " " Z Z + + + + ≥ + + " Z − − ⇒ ≥ + + ;E &;E &56 7 &[ &) :'T 7 ' 95B:. " Z − − ≥ + + " Z − − ≥ + + " 7 <? <2 <? :C) " &) 95B: XXX + + ≥ F& ' : &) -] -E 7 :'T 7 ' 95B: . ) 0 H 0 : ^ " + + / "$ _ 7 &'T: !` 3) ' ) / H / : / : + ) ) :I '56 7 &38 ' 95a 7 &'_ 7 b . !0 / $ 7J ' DE ';` 7 : :' &U &2 L$ = = ⇒ = $ $⇔ = ⇔ = J &;c 9 - DE ( ) &) :I 'A " "  + = = =  + =  ⇔ ⇔ − −   = − = = = −  W; DE &3 7 9 bL <E 4 0 +2 = 3) L <E " d 0 +2 " − " − = 3) Z " " − −      <E " " −      +, :I ') :F L &';` * L <E " d ';F: Z " " − −      <E " " −      ) :I " . " . = + = +    = + =   = − = − +  <S:&6 ' & ? :C) DE ! − "∈ ⇒ + + − "∈ ⇒ + − " "= − + − − + − $ "! = ⇔ Q + + = ( )R " R R " " + − − − − + ⇒ = = = = − ⇔  =
  • 6. +2 Z # % " " " −  = − ⇒ = ⇒ − −     % " " " " − − −  = ⇒ = ⇒ −     $ +, eeee + ) . ∈ ^ "$ + = ⇔ + = − − 0 ⇔ f f 0 f / Q ⇔ f f / ⇔ =  = − +, / $ 0 +2 / &) :I " " " − + = = + = ∑ 0 'S; HE 3) &) :I d 0" / / $ +, => 'c 7 'Y 7 :'T) ! &3; 7 ') &3 DE " #= + H$ J # DE 95a 7 &'_ 7 g ) <E RR $$%&$ # :I &. ' $($) $*$+$%$,- J ./ $0$ 1 &34 $ # =); :'; .$%$2$ ) :I. ( ) ( )Q K f f $ " " " " . . . . .+ ⇒ = − − = ⇒ ) :I :' < &) 7 : $ 34$ $*$ $*$ $%$ $*$ $*$2 /h :' < &) 7 : '( 'i& ' $*$ '( 'i&$ jk& &T 7 : .- W] :I . DE '8 ' H8 ' 'E ' %&$ $*$ $%$ $*$ . J # 9> !T 7 <2 g ) $%&$ $%$ # $%&$ $*$ .$%$ # $*$ .- $*$ '( 'i& ' <E :'l ' # $*$ . '( 'i& ') " 9 #5$ 5$. &'_ 7 'E 7$ W; # 9> !T 7 <2 g ) 4 &8 95B: #. ) $*$' $($66 / &) :I$ ( )M K # f $7 7= ∩ ⇒ − ⇒ $ /h KW. + $*$ $($6'$%$,$ &) :I " M.= ∩ ⇒ $ W; % ".= ⇒ − $ W] &'i ' K W &'_ 7 'E 7 &'8 K L WK :m 7 &'_ 7 'E 7 $ +, ') 9 :n &8 DE. % "− <E " $ 0 J DE &3 7 9 :C) /h " − J L ) H : /h "− − − − + ) :I "∈ ⇒ + + − =
  • 7. Q 0 +8 L W DE '8 ' < Y 7 &) :I " " = + − =  ⇔  ⊥ − − + − − + + =  0 U <E &) :I # # = +  = − − &') <E; " &) 95B: % % Q % = − + + = ⇔ − =  +2 : / d /h L " d -; &3 7 9 LW 4 W d $ 0 +2 Q % − = /h % " % Q % % % − − -; &3 7 9 LW 4 "%Z Z % % % % . − +, :I 9 &'() * W d "%Z Z % % % % . − . " E! !≥ ∈ " " Z! ! ! ! ! ! ! != ⇔ − − = ⇔ − − = ⇔ / Q <E / f " D;c 1' 9I. % Q Q Q Q % $ $ $$$$ % % + + + = ) :I . Q " " Q Q Q Q Q Q Q Q Q+ = + + + + + + $ oi &O:' ' ') <? Q " " Q Q Q Q Q Q Q Q Q+ = + + + + + +∫ ∫ ⇔ [ ] % % % Q Q Q Q Q Q Q Q$$$ $ $ $$$$ % % %      + = + + + = + + +            + H ⇔ % % % %% Z % % % + − = ⇒ + = ⇒ + = ⇔ = +, / Q ) /