!"# $ % &'( )% *+*,"-, ./, *#&)0 1 23 $45*6 .(78 *1)9 :*")56 0-, .2); "<)0"+ =, *'#$>5*6 .( ,( ), 8:, 1), .:! > ? @ >@ = − + /( 9 ..56 &)A%"+1B9 ") > @ >@ . − − = <8 /,"+)*6 .&);"/*6 1 =, *#$5*6 .( *, *<, <&)A%"+1B9 "):,0C% *; ":! 1)A < ,( @ ' @ > ' + + + − = /( ( ) ( ) D D D -8+ >@ '' -8+ @ 4 -8+ '− + − = =, *>#$5*6 .( )8)9 ")<)8 &7=<8 5, ?-, 1,.+*, <56 0<, "),E<, ")/6"1, 8C% *.F 15, ?.! 1+8 <G 79 ") <)*6 0<0 ,1B6".F 1&)F "+$=(1B0 "+C% *1B0"+5*6 .<0 ,<, ")=7 ,( )A "+.*")=C0!"++8 <7 /( 9 ")1)H8,1)6 19 <)I)! *<)8 &7= 23 $>5*6 .(7)9 :*"))8 <<)A%"+1B9 ")", 81)9 -, .B*6"+<)A%"+1B9 ")58 $I)!"+-, .<, ),* &); "B*6"+( A. CHƯƠNG TRI ̀ NH NÂNG CAO =, *J7$5*6 .(7 9 .+*, 1B* -% ""); 1C, +*, 1B* ")8 "); 1<0 ,), .:! ( ) @ @ ? K @ @ ' + + = = + 1B6"58, " [ ] L =, *D7$'5*6 .(7 )A "+.*")BF "+5! 1)* $(<0 ,), .:! > ? @ @ J= − + 1*6 &@0 <C% *5! 1)* $ M (<0 ,), .:! ? @ 4@ = + + 79 .18 ,5! 1*6 &5*6 .7 =7 CHƯƠNG TRI ̀ NH CHUÂ ̉ N =, *J=7$'7D5*6 .(7 9 .+*, 1B* -% ""); 1C, +*, 1B* ")8 "); 1<0 ,), .:! ( ) J ? K @ @ @ = = − + 1B6"58, " [ ] N'L> =, *D=7$'7D5*6 .(7 9 ") ( ) J @ ' @ O@+ ∫ $/F "+<, <)5F 10P'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 23 =, * ;0 ! *O0"+ *6 . ' >7 , 7 RP 7D @ -*. ? →−∞ = −∞ L @ -*. ? →+∞ = +∞ 7D M M @ ? >@ G@E ? @ = = − = ⇔ = =, "+/*6 "1)*6" 7D ?5! "+/*6 "1B6" ( ) ( ) L E L−∞ +∞ C, "+)* <)/*6 "1B6" ( ) L 7D $L(E$LN( 7D *6 .5F </*6 1$N'LN(E$>L(E$'L( 7D ! 1)* 7D / '7 21B% 1), ")# > @ >@ . − + = + ! "+)*6 .<0 ,&)A%"+1B9 ")/F "+:! +*,85*6 .<0 ,5! 1)* $(# > ? @ >@ = − + C% *5A% "+1)F "+$O(#?P.Q 7D 2<8 >"+)*6 .&);"/*6 1I)*S.QS J . ⇔ − < < 7D 7 , '7 21B% 1), ")# @ @ 7 7 ' + − = 7D F 11P @ $1T(721B% 1), ")1 Q1N'P 7D *, *B,1,5A% <#1P'$"); "(E1PND$-8, *( 7D % *1P'1,<8 # @ P' ⇔ @P 7D / '7 #@T4 7D 21B% 1), ")# ( ) ( ) D D -8+ >@ '' @ 4 -8+ '− − = 7D ( ) ( ) >@ ' @ 4 ' >@ @ 4> ⇔ − − = ⇔ − − = 7D *, *B,1,5A% <#@P>4$"); "(E@PN$-8, *( 7D > 7 , '7 8 *-, 1B0"+5*6 .=7)A "+.*")5A% < ( ) = ⊥ 7D 0?B,# = ⊥ 7D / '7 = , > J ∆ = 7D >, 71," G = = 7D > , > = 7D PHÂ ̀ N RIÊNG CHO CHƯƠNG TRI ̀ NH NÂNG CAO Ba ̀ i Nô ̣ i dung Điê ̉ m 4A 2.0 ( ) ( ) M @ @ K @ @ ' + = + 0.5 ( ) M @ K @ @ = = ⇔ = − 0.5 ( ) ( ) ' K E K > = = 0.5 [ ] ( ) [ ] ( ) L L ' *" K @ E,@ K @ > = = 0.5 5A 1 RH 1)6 > @ @ J @ 4@ >@ @ @ 4 − + = + + − = + 7D > @ @ 4@ J >@ J@ 4 − − − = ⇔ − − = 7D @ '7⇔ = − ; ?$(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