                      !"#  $ %  &'( )%  *+*,"-,  ./,  *#&)0  1 23  $45*6  .(78  *1)9  :*")56  0-,  .2);  "<)0"+ =,  *'#$>5*6  .( ,( ),  8:,  1),  .:!   >  ? @ >@ = − + /( 9  ..56  &)A%"+1B9  ") >  @ >@ . − − = <8  /,"+)*6  .&);"/*6  1 =,  *#$5*6  .( *,  *<,  <&)A%"+1B9  "):,0C%  *;  ":!  1)A  < ,( @ ' @ >   '  + + + − = /( ( ) ( ) D D D -8+ >@ '' -8+ @ 4 -8+ '− + − = =,  *>#$5*6  .( )8)9  ")<)8  &7=<8  5,  ?-,  1,.+*,  <56  0<,  "),E<,  ")/6"1,  8C%  *.F  15,  ?.!  1+8  <G  79  ") <)*6  0<0  ,1B6".F  1&)F  "+$=(1B0  "+C%  *1B0"+5*6  .<0  ,<,  ")=7 ,( )A  "+.*")=C0!"++8  <7 /( 9  ")1)H8,1)6  19  <)I)!  *<)8  &7= 23  $>5*6  .(7)9  :*"))8  <<)A%"+1B9  ")",  81)9  -,  .B*6"+<)A%"+1B9  ")58  $I)!"+-,  .<,  ),* &);  "B*6"+( A. CHƯƠNG TRI ̀ NH NÂNG CAO =,  *J7$5*6  .(7 9  .+*,  1B*  -%  "");  1C,  +*,  1B*  ")8  ");  1<0  ,),  .:!    ( )  @ @  ? K @ @ ' + + = = + 1B6"58,  " [ ] L =,  *D7$'5*6  .(7 )A  "+.*")BF  "+5!  1)*  $(<0  ,),  .:!   >  ? @ @ J= − + 1*6  &@0  <C%  *5!  1)*  $ M (<0  ,),  .:!   ? @ 4@ = + + 79  .18  ,5!  1*6  &5*6  .7 =7 CHƯƠNG TRI ̀ NH CHUÂ ̉ N =,  *J=7$'7D5*6  .(7 9  .+*,  1B*  -%  "");  1C,  +*,  1B*  ")8  ");  1<0  ,),  .:!    ( ) J  ? K @ @ @ = = − + 1B6"58,  " [ ] N'L> =,  *D=7$'7D5*6  .(7 9  ") ( ) J  @ ' @ O@+ ∫ $/F  "+<,  <)5F  10P'Q@  C,  O0  "+&)A%"+&),  &5!  */*6  ":!  ( 7    HƯƠ ́ NG DĂ ̃ N CHÂ ́ M MÔN TOA ́ N 12 HO ̣ C KI ́ I NĂM HO ̣ C 2008 – 2009 23   =,  * ;0 !  *O0"+ *6  . ' >7 , 7 RP 7D @ -*. ? →−∞ = −∞ L @ -*. ? →+∞ = +∞ 7D M  M @  ? >@ G@E ?  @  =  = − = ⇔  =  =,  "+/*6  "1)*6" 7D ?5!  "+/*6  "1B6" ( ) ( ) L E L−∞ +∞ C,  "+)*  <)/*6  "1B6" ( ) L 7D $L(E$LN( 7D *6  .5F  </*6  1$N'LN(E$>L(E$'L( 7D !  1)*   7D / '7 21B%  1),  ")# >  @ >@  . − + = + !  "+)*6  .<0  ,&)A%"+1B9  ")/F  "+:!  +*,85*6  .<0  ,5!  1)*  $(# >  ? @ >@ = − + C%  *5A%  "+1)F  "+$O(#?P.Q 7D 2<8  >"+)*6  .&);"/*6  1I)*S.QS J . ⇔ − < < 7D  7 , '7 21B%  1),  ")# @ @ 7 7 ' + − = 7D F  11P @ $1T(721B%  1),  ")1  Q1N'P 7D *,  *B,1,5A%  <#1P'$");  "(E1PND$-8,  *( 7D %  *1P'1,<8  # @ P' ⇔ @P 7D / '7 #@T4 7D 21B%  1),  ")# ( ) ( ) D D -8+ >@ '' @ 4 -8+ '− − = 7D ( ) ( )  >@ ' @ 4 ' >@ @ 4> ⇔ − − = ⇔ − − = 7D *,  *B,1,5A%  <#@P>4$");  "(E@PN$-8,  *( 7D > 7 , '7 8  *-,  1B0"+5*6  .=7)A  "+.*")5A%  < ( ) = ⊥ 7D 0?B,# =  ⊥ 7D / '7  = , >  J ∆ = 7D  >,  71," G  = = 7D > , >   = 7D PHÂ ̀ N RIÊNG CHO CHƯƠNG TRI ̀ NH NÂNG CAO Ba ̀ i Nô ̣ i dung Điê ̉ m 4A 2.0 ( ) ( )  M  @ @ K @ @ ' + = + 0.5 ( ) M @  K @  @  =  = ⇔  = −  0.5 ( ) ( ) ' K  E K  > = = 0.5 [ ] ( ) [ ] ( ) L L ' *" K @ E,@ K @ > = = 0.5 5A 1 RH  1)6   >    @ @ J @ 4@  >@ @ @ 4  − + = + +   − = +   7D >   @ @ 4@ J  >@ J@ 4   − − − =  ⇔  − − =   7D @ '7⇔ = − ;  ?$(1*6  &@0  <C%  *$ M (1,  *$N'L( 0.5 PHÂ ̀ N RIÊNG CHO CHƯƠNG TRI ̀ NH CHUÂ ̉ N Ba ̀ i Nô ̣ i dung Điê ̉ m 4B 1.5 ( ) M > K @ J@ 'G@= − 0.25 ( ) ( ) ( ) ( ) M @  'L> K @  @  'L> @  'L> = ∈ −  = ⇔ = ∈ −   = − ∉ −  7D ( ) ( ) ( ) ( ) K  LK  'JLK ' DLK > ''= = − − = − = 0.5 [ ] ( ) [ ] ( ) 'L> 'L> *" K @ 'JE,@K @ '' − − = − = 0.25 5B 1.5 F  1  ' 0 ' @ @7O@ 7O0  = + ⇒ = 0.5 ( ) ( ) J D  J D  ' ' ' @ ' @ O@ 0 O0 0  ' @   ' ' + = = + = + + ∫ ∫ 1.0