Thời gian làm bài: 180 phút !"# $"% Câu 1 !"# !!" #$%&' ()# "*+,- %/,01&2 3%' #45,,6748,9&%&':$;$$<=8>&?,@4A&?8,B4,@ C&+4:>D8C 4+4%&':$;$$%EF45<G<,H,I,J8%K,L8CAM8# Câu 2&*&4+4<EN8C,638@OP " ( ) xx x xx &84( ( 4 "&84 += − +− π "QR +=−++ xxx Câu 3B8,B4<=8P dxx x x ∫ + + 2 &8 " " π Câu 4 .384S<:;4S:(@ @T2#$:,9-U&%+ :;#CS4Q2 2 @C&+4 :;-OV8C,9&;$CS4 ACB∠ >D8C(2 2 W,6X8C,=4Y@,@C&+4:;$@& Z,<[8C ;#$ #4\8C-OV8CCS4-U&%+B8,',B41&4S<,H@ Câu 5 ( " ] ≤ " - ≥ "3C&+,608^8_,4Y@>&'O,I4` ( ) [ ] " xyx yx yx −− ++ !"&'("%)*'+,- ./'" # 0*12#34,,566&7"% 8'9 !": 7;#< : =7# 1>"%6&?" # $@" A$B8)*'+,-68CZ,<[8C,X@%K$4%Ea8C,6b8 #P R "c 2x y x y+ − − + = - @&%&': )"#$; ()"#X&$W@&%&',OK4 #@4:;WK,38>388 &G,<EN8C,638%Ea8C,[8C A$C8)*'+,-68C1V8CC&@8-U&?,X@%Kd$44+4%&': "))(#$; )2)"#-%Ea8C,[8C AP Q " " ( x y z− − − = = e+4%084+4%&'$@4:;W38,&>&G,6D8C8D,6f8A A$D8)*'+,# " $z z W4+48C&?<I44Y@<EN8C,638 "" 2z z− + = B8C&+,604Y@ >&'O,I4 " 2" " # z z M z z + = + < =7# 1>"%6&?" "A"%#87 A$BE)*'+,-68CZ,<[8C-U&?,X@%K$4%Ea8C,6b8 #P c Q " 2x y x y+ − + + = -%Ea8C,[8CAP " 2x y+ − = e+4%08,X@%K4+4%g84Y@38-OV8C:;8C9&,&G<%Ea8C ,6b8 #>&G,%&':,OK4A A$CE)*'+,#68C1V8CC&@8-U&?,X@%Kd$4Z,<[8C `#4I@%Ea8C,[8C AP " " " x y z− = = − − ,9-U&Z,<[8C h#P " 2x y z− − + = CS4 2 Q2 3,X@%KC&@%&'i 4Y@Z,<[8C `#-U&,674d A$DE)*'+,-'F' G9 1>"%6&?" ( ( WC WC # # y x y x x xy y x y − = − − + + = jklmnm =O mK&AO8C &' "" "%&' " ePo ∞+= +∞→ y x W& $ ∞+= −∞→ y x W& p ( 2 ⇔ 2$" ;*8C>&G8,&f8 ∞ "2"! ∞ p 2!22! ! ∞ ! ∞ " 2 2 j%/8C>&G8,6f84+41*8C ")2#) ")! ∞ #$ j8C04>&G8,6f84+41*8C ∞ )"#) 2)"# j%9,4J4%9&,9&2$ 4% " j%9,4E4,&'O,9&"$"$ 4, 2 /,0P45,,6748,9& ")2#) ")2# 5,,674,O8C,9& 2)"# mq8W,674%&I8C " "2" `EN8C,6388%KC&@%&'P !"# !!"2 %Z, , ≥ 2<EN8C,638,6r,8P, !"#,!!"2 "# %'%/,045,,6748,9&%&'<=8>&?,,3<EN8C,638 "#4S@& 8C&?AEN8C<=8>&?, ⇔ ( ) >+= >+=+ >=∆ 2" 2" 2 " " s mtt mtt m −> −> ≠ ⇔ " " 2 m m m ⇔ −> ≠ " 2 m m t# U&%&uO1&?8 t#<EN8C,638 "#4S@&8C&?2], " ], $ Wv4%S%/,045,,6748 ,9&%&'<=8>&?,: t )2#); " t )2#) " t )2#) t )2# &?8,B4,@C&+4:W " :A ):# # 68C%SA ):#w w$: " t ! t # ⇔ " " t ! t # ⇔ , " !, ! " tt "Q ⇔ !"#! " +m "Q 2$x 2x 2x 2x 2x 2x `M86&f8C =O Q@ "%&' @4S #P " R "2 x y − + − = ÷ ÷ 8f8 #4S,= " R ) ÷ -o "2 AB ")#$:; x Ea8C,[8C8C8C-U&:;8f84S<EN8C,638 A98C 2x y m− + = *8C4+4,y%G8W z ) x m CD R h − = − @4S:;8f8 Q x z# x z# x " 2 m m m m = − − = ⇔ − = ⇔ = q4S<EN8C,638 Q 2x y− + = L4!"2 2$x 2$x 2$x 2$x =O z@ "%&' A4S-,4< )")(#u = r -4S`,, Q " ( x t y t z t = + = + = + @,_%&'; ∈ A1G,F<-U&C&*,&G, ∈ A8f8,=4Y@38,&4{8C ,OK4A:;W38,&8f8: ⊥ ;$@W384&GO4Y@:,6f8 X& Q!,)"!,)!(,# ∈ A&%S x ) ( )z ( #AI t t t= + − + + uur 2 x # ( # ( z ( # 2 AI u t t t t= ⇔ + + − + + + = ⇔ = uur r @ )")# -WM8WEN,%&I8C-U&:-;-|O@8f8 ()Q)"#- 2))x# 2$x 2$x 2$x 2$x =O c@ "%&' *&`EN8C,638P "" 2z z− + = ,@%EF48C&?P " ( " z i= − ) ( " z i= + O6@P " z z= = ) " z z+ = %SPi 2" 2" "" "" "" + = 2$x 2$x 2$x `M8; =OQ> "%&' Ea8C,6b8 #P ( ) ( ) ( x y− + + = = )(#);+81B8o X&%&': @)"@# ∈ Ai$mWM8WEF,W,6O8C%&':;-::;W j38-OV8C8C9&,&G< #8f8 : Q Q) x# # c c " 2 ) "# a A a a a a A = ⇒ − ⇔ − = ⇔ − + = ⇔ = ⇒ − W,=%Ea8C,6b84{8CW,=38-OV8C8f8: Q)x#,3 )"#Z4 8CEF4W9& 9838-OV8C>D8Co X& )#@4SP 2AD DC = uuur uuur -: Q# # x# " # 2 z Q# x# "Q Q x 2 z Q) " ") x ) x x x y y x y x y y y x y x y y y x y − − − + + = = + ⇒ ⇔ − + + = + + = = + = = − ⇔ ⇒ = − = − = = − j@ Q)"#,3; )x# 2$x 2$x 2$x 2$x q>8%&838-OV8CWP: Q)x#; )x# )"#) Q)"# =Oz> Ea8C,[8CA%&|O@%&': "$2$2#-4S-,4< ") ") #u − − r iZ,<[8C h#4S-}4,N<+<,Of8W ) ) "#n = − − r &@%&'i 2)2)# ∈ d) ")2) #AM m= − uuuur iZ,<[8C `#4S-,<,WP n ~ AB $ u • ))"# Q2 2 ( ) ( ) "R "" +−+ −−− mm mm " x " +− mm ⇔ x +− mm ⇔ !"2 ⇔ − Z4 + q,X@%K%&'i 2)2) − #)i 2)2) + # 2$x 2$x 2$x 2$x =Oc> "%&' P 2) 2x y> > @4SP ( 2$ ) 2 y x xy y x y x y − + = − + > ∀ > ÷ e},T ( ( "# 2 WC WC "# "# 2 VT x y VP > ⇒ < ⇒ ⇒ < -V8C&f8f8?-V8C&? e},] ( ( "# 2 WC WC "# "# 2 VT x y VT < ⇒ > ⇒ ⇒ > -V8C&?8f8?-V8C&? %S,@-?,@4S 2 2 x y x x = ⇔ = = + = q8C&?4Y@?W )# ) # 2$x 2$x 2$x 2$x EO€P+44+4C&*&%v8C%uO4%&',&%@ . t t t= ⇔ + + − + + + = ⇔ = uur r @ )")# - WM8WEN,%&I8C-U&: - ; - |O@8f8 ()Q)"# - 2))x# 2$x 2$x 2$x 2$x =O c@ "%&' *&`EN8C,638P . ⇒ < -V8C&f8f8?-V8C&? e},] ( ( "# 2 WC WC "# "# 2 VT x y VT < ⇒ > ⇒ ⇒ > -V8C&?8f8?-V8C&? %S,@ - ?,@4S . )x# 2$x 2$x 2$x 2$x q>8%&838-OV8CWP: Q)x#; )x# )"#) Q)"# =Oz> Ea8C,[8CA%&|O@%&': "$2$2# - 4S -, 4< ") ") #u − − r iZ,<[8C h#4S -} 4,N<+<,Of8W