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SƠ ̉ GIA ́ O DU ̣ C – ĐA ̀ O TA ̣ O CÔ ̣ NG HO ̀ A XA ̃ HÔ ̣ I CHU ̉ NGHI ̃ A VIÊ ̣ T NAM VI ̃ NH LONG Đô ̣ c lâ ̣ p – Tư ̣ do – Ha ̣ nh Phu ́ c ------------------ ------------------------------------------ Năm ho ̣ c 2008 – 2009 Môn thi : TOA ́ N Thơ ̀ i gian la ̀ m ba ̀ i : 180 phu ́ t ! " !# $% " &'' " ! (#) !* " *# +,(+#* - ( ./ ( ( ) ( ) ( ) f x y f x f y , x, y R+ = + ∀ ∈ 0 #*1 - 2$% " ( ) n u ' " ! (#34 0 1 n 1 n 2 n u 1 ; u 2 u u u ;n 2,3, . 2 − − = = + = = $% " # (5+% (56. " +!. 1 - 2$% " ( ) n u ) + " (# n n lim u →+∞ 77 #8 " (5(#,9 (5 " .(: $% " +8 (#(!#9 - () : $% " +#8 !:4 " (#4(7+# ;#84(5 +, (# ( ) ( ) n 2 n 1 n 2 n 1 x 3 n 2 x a 0 + + + + − + + = )%(5# 7 ,*(5$% " <#* !$(#!* " 7#* !$(#5* =>#* !$(#/# " ) ?#* !$(#+,.(53 (# @* " 3*(#.! " !#!#$% " #* !$(#* " +# (#0+% =% - +% ?#* !$(#$*!#*4 % - +% .!* " #* ! $(#5* ) " +(#A " +0#* !$(#/# " @ >7 #*+5 " !B).%(5+ !* " BC) D: #84 (5+,.(5+.2 " (@E9 +BCF =DF(@* ,: 3 " (/ " (#84 (5+,* ((% + " ;+5 " !B@#8 " (5(#,9 (5 2 2 2 r 1 m n 20 < + >7 % " (84 (5+#9 (5 1 2 3 4 d ,d ,d ,d %% +$*(5$*(5) /#%(5!* " 384 (5+#9 (5( * (9 +,(!. (5% +9 +;#9 (5@G% +9 +;#9 (5!9 " +!#. " (5+#H*+#8 " +8 + B===I@G% +9 + ;#9 (5 J !9 " +!#. " (5+#H*+#8 " +8 + / / / / A ,B ,C ,D @#8 " (5(#,9 (5#/#% " +8 " 1 (I J B) / / / DA B C !* " +# + " !#39 (5(#.@ KKKKKKKKKKKKKKKKKKKKKK " KKKKKKKKKKKKKKKKKKKKKK 9#* !0LL?M0LLN EB " B " GB " B I E G @L OA (:84 +:A " 2 *# #) " !. +#H*3 " (') 2=+84 ! ( ) ( ) / / f x y f x , x, y R+ = ∀ ∈ 0 ( ) ( ) / / f x y f y , x, y R+ = ∀ ∈ 7 @> 0M7 ( ) ( ) / / f x f y , x, y R= ∀ ∈ ( ) ( ) / f x const f x ax b ⇒ = ⇒ = + 1.5 #2 ( ) f x ax b= + ) *+84 !3FL PA 2&'F'= x R∀ ∈ =: $% " +#8 !+. 22 " 1.0 0 4.0 8 n n 1 n 1 u u u ; n 1,2,3, 2 − + + = = +!* " n 1 n n 1 2u u u + − = + ( ) ( ) n 1 n n n 1 2 u u u u + − ⇒ − = − − ( ) n 1 n n n 1 1 u u u u 2 + − ⇒ − = − − 1.5 QH " +1 - 2$% " ( ) n v ' " ! (#34 n n n 1 v u u ,n 1,2,3, − = − = +!* " n 1 n 1 v v 2 + = − I** " ( ) n v : % +!A " ;$% " (#A()4 " 1 1 v 1 , q 2 = = − 1.0 ( ) ( ) ( ) n n n 1 n 1 n 2 1 0 0 u u u u u u u u − − − = − + − + + − + n 1 n n n 1 1 0 0 1 v 1 2 2 1 v v . v u u 1 1 1 3 2 1 2 − − − ÷ ÷ ÷ = + + + + = + = − − + ÷ ÷ ÷ − − ÷ 1.0 n n 5 lim u 3 →+∞ = 0.5 7 3.0 QH " +# $% " ( ) ( ) n 2 n 1 n 2 y n 1 x 3 n 2 x a + + + = + − + + =)4 " (: $% " +8 (#(!#9 - () : $% " +#8 !:4 " (#4(7=+!* " ( ) ( ) ( ) ( ) ( ) ( ) ( ) / n 1 n n y n 1 n 2 x 3 n 2 n 1 x n 1 n 2 x x 3 + = + + − + + = + + − 1.0 ( ) ( ) n 2 / n 2 n 2 x 0 y a y 0 x 3 y a 3 + + + = = = ⇔ = = − (53 " (+#( @L 8 =+!* " n 3 n 2 CT y y a 3 0 , x R + + ≥ = − > ∀ ∈ ) R7 .2,2RL= x R∀ ∈ I** " ;#84(5+, (# ( ) ( ) n 2 n 1 n 2 n 1 x 3 n 2 x a 0 + + + + − + + = )%(5# +,( 7@L !#* (?#* !$(#+#* 2.!A . 3 ) *+% =?#* !$(#!* (: + *+# (# +% 0@ #* (5* =0/# " =>+,.(53 (#!* " 1 2 5 3 5 8 C C C ! " !# #* (5* =7/# " =+,.(53 (#!* " 1 3 4 3 5 8 C C C ! " !# #* (05* =0/# " =+,.(53 (#!* " 2 2 4 3 5 8 C C C ! " !# #* (05* =7/# " =7+,.(53 (#!* " 2 3 3 3 5 8 C C C ! " !# 2.0 PA 2!* " 1 2 5 1 3 4 2 2 4 2 3 3 3 5 8 3 5 8 3 5 8 3 5 8 C C C C C C C C C C C C 7560+ + + = ! " !# @L > 7@L E9 +F=BF3=BF!=+!* " 2 2 2 2 a AE m b 4 = = + ) 2 2 2 2 b BF n a 4 = = + .2, 2 2 2 5c m n 4 + = 2 2 2 1 4 m n 5c ⇒ = + 0.75 ABC 1 a b c S pr ab r 2 2 ∆ + + = ⇔ = 2 2 ab ab r a b c a b a b ⇔ = = + + + + + 0.75 !* " ( ) 2 2 2 a b a b+ > + 2 2 2 2 2 2 a b a b a b a b 2 a b ⇒ + > + ⇒ + + + > + 2 2 2 2 1 1 a b a b 2 a b ⇒ < + + + + 0.75 G9 +/# " ! 2 2 2 2 2 2 2 2 a b ab a b c ab r 2 4 a b a b 4 a b + + ≤ ⇒ = < = + + + + .2, 2 2 c r 16 < 0 8 ) 0+!* " 2 2 2 2 2 r c 4 1 . m n 16 5c 20 < = + 0.75 < 7@L * FB I I= / / / / / O A C B D= I I*II J JJ J (( ( ) ( ) ( ) ( ) / / / / d D , ABC DD OO d O , ABC = ) ( ) ( ) ( ) ( ) / / / / / / / / d D, A B C DD OO d O, A B C = .2, / / / / D ABC O .ABC DD V V OO = ) / / / / / / / / D.A B C O.A B C DD V V OO = 1.0 E9 + ( ) ( ) / / / h d BB , ACC A= !* " ( ) ( ) / / h d B, ACC A= = ( ) ( ) / / / d B , ACC A / / / O .ABC B.O AC O AC 1 V V h.S 3 ∆ = = 0 / / / / / / / / O.A B C B .OA C OA C 1 V V h.S 3 ∆ = = 7 1.0 E9 +1FBB J = J +# / / / / O AC OA C 1 S S OO .d 2 ∆ ∆ = = 8 =0=7=$.2, .;# !#8 " (5(# 1.0 . SƠ ̉ GIA ́ O DU ̣ C – ĐA ̀ O TA ̣ O CÔ ̣ NG HO ̀ A XA ̃ HÔ ̣ I CHU ̉ NGHI ̃ A VIÊ ̣ T NAM VI ̃ NH LONG Đ ̣ c lâ ̣ p – Tư ̣ do – Ha ̣ nh Phu. Năm ho ̣ c 2008 – 2009 Môn thi : TOA ́ N Thơ ̀ i gian la ̀ m ba ̀ i : 180 phu ́ t
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