Để biết thêm chi tiết liên hệ tại Văn phòng Trung Tâm BDVH 60 An Sương – ĐT: 08. 3719 4559 – 0932. 178517)Câu 1 (2,0 điểm). Cho hàm số: (1) có đồ thị ), với m là tham số .a) Khảo sát và vẽ đồ thị (C) của hàm số (1) khi .b) Tìm m để đường thẳng (d): y = x + 1 cắt đồ thị ) tại 3 điểm phân biệt P(0;1), M, N sao cho bán kính đường tròn ngoại tiếp tam giác OMN bằng với O(0;0).Câu 2 (1,0 điểm). Giải phương trình: .Câu 3 (1,0 điểm). Tính tích phân:
!"#$%&'() (hc ca ti: 18h00 20h15 21h00) *)((*(((+,-.%/01 !!"! !#$!% !"#$%&'()2(3*/456))5 (5/'*43)4 78'9(*+&"'( )*)+, -, +++−= xmxxy +)*./!0 m C+ *12"#!3"'( 3*4&'5!6/!0+*73"'(+)*8 )−=m *9"":;!<+=*>?@)A!/!0 m C+ *!%,"B$!+CD)*11E'3&&58 :;!FG&%! !3"5HEI - -J 2H+CDC* 78'9(*+:K!F9 xxxxxx &',',L)L&'M'L-&' &'- - +=++− 78/9(*+!B ∫ − −++ = C - ) - -,*)+ xxx dx I 7869(*+ 3*:K!F9 C-N),MOP,P)M ) -M )) ), =+− − − −− − x x x x x x *F&"!8Q-R1J!FAO+5S853T" 'A*UVL1!9"?5'U!L#UF38W.73" 78)9(*+F&8W3Hxyz, &,"X+LDYLD,*1Z+)D,DY)*1+Y-DCDY)*[ !:K!F9 "\!+]*^35"X1Z1A!3"\!< + * - Cx y z α + + + = CL*+ =−−− zyx β !_&33&! #3:;!FG.58I3 78:9(*+&9#`!Fa!3"5XZXbZbb.%I315XbZbb#!3"5T %I319 W.73SZ#+XbZbb*#!F"73%XbZbc#!F "73%X!!738(!d=$cZbb8&5!e"Z "\!< +XbXb* 7849(*+F&"\!<!3Hxy1&9fg!XZh3"Z!!Fa! :K!F9:;i&X,?@Lj)M>Ck50!35S739fg!l&1 ! FI58:;!FG! !3"5XhI) !"#$%&'()*++, /+0.#$1./!2 "345$67886 9:":*;<=& >>>:?*;?;&@>>>A*B?;&@>>>A*B 7839(*+$:K!F9 −+=++− −+=−−− , , -), -), yxyxyyxy xxyyxxyx + Ryx ∈1 * 7859(*+ki!3'(!Q?1!R3"lT8$ -L*+ , ≥++ xyyx 9"EE73 !d -C)J*L,+*+-*+, +−−+−+= xyxyyxyxP m ;<= 78*>*:K!F9&3&"73 m C+ *+=* ))*)+, -, +=+++− xxmxx =+− ⇒=⇒= ⇔=+−⇔ *-+C, *)DC+)C C*,+ - - mxx Pyx mxxx m C+ *A!+=*!%,"B$! ⇔ +-*.-$"B$!85C < ≠ ⇔ L P C m m 'n *)D+ )) +xxM 1 *)D+ +xxN 8. -) D xx #$"73!+-* 3. R MNONOM dOdMNS OMN L **+D+ - ) == 2o#58:;!FG&%! !3"5HE **+D+-J**+D+- L **+D+ - ) dOddOdRONOM R MNONOM dOdMN ==⇔= +,* *) *+) + ) - )) - ) ++++= xxxxONOM [2 -J)-L,D, - - - -) - ) ++=⇒−=−= mmONOMmxxmxx - - - ) **+D+ ==dOd 4.! &+,*!3:p −= = ⇔==++ , C J - - -J-J)-L - m m mm !R3TS. , −= m 78'*! ⇔ xxxxxx &',',L-'-M'L-&' &'- +=+− xxxxxx &',', 'M' &'-&' +=+−⇔ xxxxxx &',',-M' &'-'-&' =+−−⇔ xxxxx &',',-M' &'L&' =+−⇔ xxxxxx &',',-,&','L','- =+−⇔ =+ = ⇔=+−−⇔ xxx x xxxx ,&'-&',' C,' C*&',,&'-+','- q *+ , C,' Ζ∈=⇔= kkxx π !"#$%&'()*++, /+0.#$1./!2 "345$67886 9:":*;<=& >>>:?*;?;&@>>>A*B?;&@>>>A*B q += +−= ⇔= −⇔=+ L )- ,&' M &',&'-&',' ππ π π π k x kx xxxxx *+ Ζ∈k [g$"73:K!F9# π π kx +−= )- 1 L ππ k x += 1 , π k x = *+ Ζ∈k 78/* ∫ − −++ = C - ) - -,*)+ xxx dx I = dx xxx ∫ − +−++ C - ) *,*+)+*)+ ) > dx x x x ∫ − + +− + C - ) - ) , *)+ ) \! ) , ) , - + +− =⇒ + +− = x x t x x t dx x tdt - *)+ L - + − =⇒ *,O+ - ) - ) , O −=−=⇒ ∫ dtI 786* 3*T8$ ) ≠ x :3:K!F9T=% CN) - , M OP, L P )M ) ), ) ), =+ − − − − − x x x x 1F/\! ) ), - , − − = x x t 5'( -D - ) == xx *](5#ULU!8r# )CC) L )L =C 5 3 "'(5#UL.7" @))1)1-[. - O ) J ) - CCC 5 @-)1-1)[. ) O - J ) - CCC 5 @,-1)1)[. ) O ) J - - CCC 5 [g'(5#UL.7,"# - O ) J ) - CCC @ ) O - J ) - CCC @ ) O ) J - - CCC >,NJ5 k5'U!#UL8W7,"# ), N )CC) M)M )CC) ,NJ)CC) == − =P 78)*s+3DD*#!B"73"\!+]* [9+]*^35"X1Z1A!3"\!< C-*+ =+++ zyx α CL*+ =−−− zyx β !_& 33&! #3:;!FG.58I3!3.$ −−−=+++ =+− =+− ⇔ = = = L- P , )JLO, **+1+**+1+ cbacba cba cba IdId ICIA IBIA βα $!3:p = = = , C ) c b a &\ −= −= = OP O)- O)P c b a !"#$%&'()*++, /+0.#$1./!2 "345$67886 9:":*;<=& >>>:?*;?;&@>>>A*B?;&@>>>A*B [2 = = = , C ) c b a 1 !:p:K!F9"\! -J*,+*)+ =−++− zyx [2 −= −= = OP O)- O)P c b a 1"\!.:K!F9 LP )-,O O P O )- O )P = ++ ++ − zyx 78:* *tttuu+ CBABE =+c1+XbZbb*>Zb 3"5ZbbW!%Zb> - , tt a HBBB =− - tt -C ttt N , L , MC'tttt - ) aSaCBBAS CHBCBA =⇒==⇒ )MN , - , , ) t , ) ,- tttt aaa SHBV CHBCEHB ===⇒ tt tt , **tt+1+ AACC AACCB S V AACCBd = D LNN , ,,, tttttttt aaa VVV CBABCBAABCAACCB =−=−= ACJASACJAACIJABIA AACC t1t1t tt =⊥⇒⊥⊥ J )J L )J L , **tt+1+ L )J tt , a a a a AACCBd a IJAAJA ==⇒=−= 784*3.#3&"73!Fa!:;!<X+CDL* [958:;!FG! !3"5XhI)58:;!FG! !3"5XZ I) [9ZI"!F!Fa!Z+CD*:;!<XZ^3ZW.2Z C =≡ xOy XZ > [9X#3&"73XZX − b b A D , L)M F#58:;!FG! !3"5XZ3. L , J L , L L L , L , L)M *L+ , L)M L , L)M L - - - - −+−+− − = − +−+ − +− − − = ++ = bbb b b b b b b b CABCAB S r ABC L , ) −= b _&! !F>)!3.>)&\>O [2>)!3.X+LD)*1Z+CD)*]F3h+LDL* [2>O!3.X+YLDO*1Z+CDYO*]F3h+YLDL* 783*$:K!F9 −+=++− −+=−−− *-+-), *)+-), , , yxyxyyxy xxyyxxyx e+)*+-*!3. iyxyxxxyyiyyxyxxyx *-+-*),+), ,-, −+−−+=++−−−−− *)+*)+-*)+)*+,, ,, , ixixyyiiyixiyixyyixx +−−++=−−+−+++⇔ *-*+)+)*+*+ , xixyiyiiyixyix +−+=−−+−+⇔ !"#$%&'()*++, /+0.#$1./!2 "345$67886 9:":*;<=& >>>:?*;?;&@>>>A*B?;&@>>>A*B -, **+)+)*+*+ ixyiiyixyix −+=−−+−+⇔ C*)+*)+ -, =+−−++⇔ izziz izzz −−=−==⇔ )D)D) h&.+?D*>+)DC*D+Y)DC*D+Y)DY)* 785*[2"'(!Q?1!3#W. xyyx L*+ - ≥+ 1!eT8$'F3 )C-*+*+-L*+*+*+ -,,-, ≥+⇒≥−+++⇒≥++≥+++ yxyxyxxyyxyxyx 3 v:'3 -C)J*L,+*-+-*+ - , *+ - , +−−++−+++= xyxyxyyxyxyxP -C)J*+-*+ - , *+ - , LL ++−+++= yxyxyx +,* h& - *+ LL yx yx + ≥+ !e+,*'F3 -C)J*+-*+ L P ++−+≥ yxyxP \! tyx =+ !9 - ) ≥t +=& *)≥+ yx ki!"'( -C)J- L P *+ - +−= tttf 2 - ) ≥t 1. C- - P *+t >−= ttf 12 - ) ≥t "'(w+!*/ !F +∞D - ) ]F3 )M , ,, - ) *+" D - ) = = +∞∈ ftf t h&.EE73I )M , ,, 1%!:p8S8 - ) == yx qxxx#_!=3&_=qxxx8!^&3_= qxxx8!^&3&" ?2(3*/456))5(5/'*43)4 !"#$%&'()*++, /+0.#$1./!2 "345$67886 9:":*;<=& >>>:?*;?;&@>>>A*B?;&@>>>A*B . !3"5HE **+D+-J**+D+- L **+D+ - ) dOddOdRONOM R MNONOM dOdMN ==⇔= +,* *) *+) + ) - )) - ) ++++= xxxxONOM [2 -J)-L,D, - - - -) - ) ++=⇒−=−= mmONOMmxxmxx - - - ) **+D+ ==dOd 4.! &+,*!3:p −= = ⇔==++ , C J - - -J-J)-L - m m mm !R3TS. , −= m 78'*! ⇔ xxxxxx