Bộ đề thi tự luận toán học nguyễn văn nho

510.76 B450D JYEN VAN NHO - LE BAY - NGUYEN VAN THO MOIi BO DE THI ^Tii LUAN TOAN HOC Danh cho thi sinh Icfp 12 on tap va thi Dai hoc, Cao dang Bien soan theo ngi dung va cau true de thi cua Bg Glao due - Dao tao Ha N O I DVL.009154 NHA XUAT BAN DAI HQC QUOC GIA HA NOI N G U Y E N V A N N H O - LE B A Y - N G U Y I N V A N T H O BO Df THI T U LUA TO^n HOC ^ Danh c h o thi sinh I6p 12 on tgp v a thi Dqi h o c - C a o d a n g ^ Bien soqn theo noi dung v a c d u true d4 thi c u a Bp GD&DT NHA XUAT BAN DAI HOC QUOC GIA HA NOI Jltue lue Lifinoiddii ^ PHAN 1: T H I T U Y E N SINH D ^ I HQC - C A O DANG C De thi minh hoa B Mot so dieu can luTu y A Cau true de thi de thi tuyen sinh Dai hoc, Cao dang 2009 r Dap an - thang diem De thi tuyen sinh Dai hoc, Cao ding, khoi A 15 Dap an - thang diem 14 De thi tuyen sinh Dai hoc, Cao d^ng, khoi B, D 273 E Mirdi de thi i\i luyen tap 21 D Ba mi/di de thi CO IcJi giai : PHAN 2: T H I T O T N G H I E P T R U N G H Q C PHO THONG 289 291 B De thi minh hoa 289 A Cau true de thi Tot nghiep THPT 2009 314 D De thi tham khao 297 C De thi mau TNTHPT 292 Dap an - thang diem 318 De thi tot nghiep THPT phan ban 2008, Ian 316 De thi tot nghiep THPT phan ban 2008, Ian 315 De thi tot nghiep THPT phan ban 2007 314 De thi tot nghiep THPT phan ban 2006 Pfi^nl: THI TUY^py SINH a/^l HQQ, SAG BANG K CMi TRUC DE THI TUYEN SINH DAI HOC, CAO DANG NAM 0 I PHAN CHUNG CHO TAT CA THf SINH (7,0 di^m) Cdu I A^^i dung kien thvlc Diem — Khdo sat, ve thi ciia ham so — Cdc bdi loan lien quart den tint; dun^ ciia dao ham va thi ciia ham so: Chieu bie'n thien cua ham so Cifc tri Gia tri Idn nha't va nho nhat cua ham so' Tie'p tuyen, tiem can 2,0 (d\Jng va ngang) cua thi ham so' Tim tren thi nhi^ng diem CO tinh chat cho trtfdc; ti/dng giao giCfa hai thi (mot hai thi la du"5ng thing); III II IV V PhU(fn^ trinh, bat phu < : = > - < A < ( ) D o do: + H a m so nghjch bien tren m o i khoang ^-co; -2) va ((); +cc) + H a m so dong bien tren khoang ( - ; ( ) ) CiTc t r i : H a m so dat ciTc tieu tai v = va ycT = >'(~2) = ; dat cifc dai tai A" = va J C D = y(^0 = ^ • Gic'Jihan: iim y = +co ; 0,25 lim y =- o o B a n g bien thien: y' -2 X y + 00 + 0,25 \ Xo " X- CO Dolhi: + D o thi c^t true tung tai d i e m /\{0 ; ) , citt true hoiinh tai diem 0,25 ; ()) va tiep xuc v d i true hoanh tai C ( - ; ) (0,75diem) Ham so da cho nghich bien tren khoang (0 ; +oo) o v' = -?>x^ « 3A-^ - 6A: + m < , VJC> +6x>m , VJC>0 (*) 0,25 Ta CO bang bien thien cua ham so v = 3.v"+6.r tren (0;+a)): s I Tir do, ta di/ffc: (*) o w < II {2,0 diem) 1.(1,0 diem) Phi/rtng trinh da cho tifcfng difdng vdi phi/dng trinh: (2 sin jr - \/3) (V3 sin A-+ cos A-j = sm X = \/3 sin jr + cos A: = x-[-\Y^ + n7t, « e Z A- = - — + ^;r ,k&'L (1,0 diem) Dieu kien: x > - A-^5 0,50 0,50 (i V(3i dieu kien do, ta c6: Phifcfng trinh da cho tUdng dUtrng vcti phu'cJng trinh: log2[(A- + ) | A - | ] - l o g C>(A- f 2)|.v-5|-8 ' A - - A - - ) ( r - v - ) = () 0,50 v' = f - =>>'' = c ^ r - = < » r = - € { - l ; 1) M a y ( - l ) = 169 ;>'(!) = 49 Suyra: max >' = ' ( - l ) = 169 ; -1;1 j = v ( l ) = 49 -I A Vay : m a x y = 169 k h i x = -— + k2n ; m i n y = 49 k h i = —+ C§u I I I Goi 5.4 {ABCD) M a t khac : ^ SA L AC ^ SAC = 90' ABLBCci {ABCD) SBC = " ^BC1SB=> TiTcfng tiT, ta cung c6 : CDISD^ SDC = 90'' TiJc la A, B, D ciing nhin doan SC diTdi mot goc vuong nen chung nam tren mat can di/dng kinh SC * Vay mat cau ngoai tiep hinh chop S.ABCD C O t a m la K trung d i e m Ban kinh R^-SC SC, = yJSA'^ + AC^ = - ^ ^ ^ + a ^ = 2 * The tich k h o i chop S.ABCD V^^S^,icn-SA^^.a\2a= 2a ^ (dvtt) Cfiu rv.a Trong khong gian v d i he tpa Oxyz, cho diTdng t h i n g (A):^^ = ^ = ^ v a m a t p h i n g {P): x + y-z +5 = Tim tpa dp giao d i e m cua diTdng t h i n g ( A ) va mat p h i n g (P) Tpa dp giao d i e m M = ( A ) n ( / ' ) la nghiem ciia he : kin x-1 A- + V y^-\ + -2 •2x + j - = J C - Z - = O - z+ 5= X = >• = - ? •'=^M(5;-7;3) z= V i e t phiTdng tfmh hinh chieu vuong goc cua du'dng thang ( A ) tren mp(P) De thay yv(2 ; - ; - ) G ( A ) , g o i N'= hch^^^N ^ N'= {d)n{P), (d) la du'dng thang di qua A' va vuong goc v d i (P), nen phtfdng trinh cua 'x = + t y = -l + t T o a giao d i e m A^'= ( < i ) n ( P ) la nghiem cua he : z = -3 + t z = -12 x+y-z+5-0 >' = - z = -3 + t x = -l y = -l + t t = -9 x^2 +t •yV'(-7;-10;-12) H i n h chieu vuong goc cua diTdng thang ( A ) tren mp(P) la diTdng thSng • -12 - - 5 • Cau V.a Ta CO : z= N e n z la so thiTc 2/ Cau IV.b T r o n g khong gian v d i he tpa Oxyz cho d i e m M ( ; ; ) , mat p h i n g {P):x va mat cau + y + 2z + l = (S): x^ + y^ + z^ -2x+ 4y-6z +8 =0 T i m d i e m A^ la hinh chieu cua d i e m M len mat ph^ng N hch^^fj^M => N ={d)n[P), (P) (d) la diTcfng thang d i qua M va x-2 vuong goc v d i (P) , n c n phifdng trinh ciia +t (d): y = + / Tpa giao diem z = 2t N =[d)n{P) la n g h i e m c u a h e : 306 x =2+t t = -l y =3+t x =l •N{\;2:-2) y=2 jc + v + 2z + = z = -2 Viet phiTcfng trinh mat phang (Q) song song v d i (P) va ticp xijc v d i mat cau (S) Ta C O {S):x^ + ^{x-lf+{y + :^ - A : + V - - + = + 2f+{z-3f=6 Do mat cau C5j C O tam / ( l ; - ; ) , b a n k i n h R = y[6 M a t phang (Q) song song v d i (P) =^{Q): x + y+ 2z +D = 1-2 (Q) tiep xuc v d i mat cau (S) =>(/(/,((5)) = R + 2.3 +D I'+2' D + = D = l D =- l l Vay C O hai mat phang thoa y e u cau : (0 ) : jc + >' + 2z + = , (02): A + V + - - 11 = Cfiu V b X - mx +1 T i m m de thi ham so y >= _ Ta , CO V = x'^ -mx + l x-\ = jc + , 1- Y-1 /77 m-2 X'\ C O c\ic t r i thoa => V = 1+ m-2 {x-xy Do thi cua ham so' cd hai cifc trj o , ^ = 2.V, Vxe 2) C5u III (1,0 diem) Cho tu" dien SABC c6 ba canh SA SB ,SC vuong goc vdi tufng doi mot vdi SA - Jem, SB = SC = 2cm Xac djnh tam va tinh ban kinh cua mat cau ngoai tie'p tiir dien, tinh dien tich cua mat cau va the tich cua kho'i cau II PHAN RIENG (3,0 diSm) Thisinh chi ditdc Idm mgt haiphdn {phdn I hodc phdn 2) Theo chU(fng trinh Chudn: C&ul\.a (2,0 diem) Trong khong gian vdi he toa Oxyz, cho diem / ( - ; l ; - l ) , B ( ; ; - l ) , C(0 ; ; O), D(l ; ; 1) Viet phi/dng trinh diTdng thing BC Chtfng minh rSng diem A.B.C.D khong dong phang Tinh the tich ti? dien ABCD CSu V.a (J, diem ) Giai phifdng trinh z'^ + = tren tap hdp so phtfc 308 Theo chiMig trinh ndng cao: CSu I V b ( 2,0 diem) Trong khong gian v d i he toa Oxyz cho mat p h a n g ( Q : ) c6 phiTdng t n n h ( Q ) : 2JC + 3}; + 6z - = Mat p h i n g ( a ) c^t Ox, Oy, Oz Ian liTdt tai A B, C V i e t phifdng trinh mat cau (5) ngoai tiep tuT d i e n OABC Tmh toa tam cija mat cau Tinh khoang each tit M{x;y;z)den mat p h i n g ( a ) Suy toa d i e m M each deu mat cua ttf d i e n OABC vilng x>0,y>0, C§iu\.h (1,0 z>0 diem) T i m can bac cua so phufc ? = - ! - Cfiul Khao sat siT b i e n thien va ve thi • Tapxacdinh: • D = R\{l} Sir bien thien : o Chieu b i e n thien : v ' = ^ < , Vx e D Suy , h a m so nghich b i e n tren m o i khoang (-co; l ) va ( l ; + < » ) o Cifc t r i : H a m so" khong cp cifc t r i • Gidihan: l i m y= lim y = l ; l i m y^+oo va l i m > ' = -co Suy thi h a m so c6 mot t i e m can duTng la dtfcfng thang x = 1, va mot t i e m can ngang la diTcJng th^ng y = • Bang bien thien : X y' -co + 00 - I-OO y -00 309 Do thi : Do thj c^t true tung tai /4(0 ; - ) , ca't true hoanh tai B Do thi nhan giao diem eua diTdng tiem can / ( l ; 2) lam tam doi xtfng Dirdng thiing {d):y = -x + m cat (C) tai hai diem phan biet 2x +1 = -x + m CO nghiem phan biet jc-1 x^-(W-2)A- + W + = CO nghiem phan biet khac , ' A1 =- (( mm 22 )f.-l 4+( mm ++1^0 l)>0 [mW >0 CSu I I Giai bat phiTdng trinh : 3^-5 3A:-5 V X>5 x + l > 3o (l)o 3JC-5 x+l X-l - ^ j\jl-x^dx Dat = sin/, jc => / = ; x = l ^ t ^ n 2 • / = |Vl-sin^/.cosr.rfr= Jcos^/.rff 0 1 t + — sm2/ 2 J ~2 u J |(l + eos2/).c// (, 310 Xet ham so : / (.v) = sin v + tan v - 2.v, A e V 2y -2 cosx + cos X Ta CO : < jc < — => < cos x < : o cos x > cos^ x D o d o : f'{x)>cos^x • f{x) +— ^ - > - cos^ X la h a m so dong bien V.v i V Vay: sin.r + tan.r >2.v, V.ve V = 2, /(.v)>/(0) = 2y C§u I I I Goi M la irung d i e m cua BC, siiy M la tam dirClng tron ngoai tie'p ASBC Mx//SA^Mx nen Mx la triic 1{SBC), di/dng iron ngoai tiep Difng ASBC Goi K la trung d i e m cua SA, ke Ky//SM, suy Ky 5/\ nMx =J S ^JA=JS Va y e Mx ^ J S ^ J B = JC' Vay y c h i n h la tam cua mat cau ngoai tiep tuTdicn SABC * Ban kinh cua mat cau :-* 2J = - (cm) D i e n tich mat cau : 5,,,^ = ^nR~ = ; r - - 9n {^cm'^ * The tich k h o i cau : V,.,, =-7r.R^ ' ^ - / T — ^-TT (cnr) ^ Cau l V a x =0 Viet phifdng trinh diTdng thang BC: BC = ( ; ; l ) => B C : y = + t z = -l + t 311 Chtfng minh A4=(2;l;0) fiD = ( l ; - ; ) BA,BD = ( ; - ; - ) BA,BD fiC-0.2 + l.(-4)-^l.(-5) = - ^ Nen diem A,B,C,D khong dong phang BA,BD BC J-.-9 * The tichtu-dien/\5CD; VAliCD L C&u V.a Giai phiTcJng trinh + = tren tap hap so phufc z = -2 Z^-2z + = 0{*) V4 Mat cau (5) c6 tarn / ' PhiTdng trinh (*) c6 A' = - = -3 = (S.if Suyra phifdng trinh (*) c6 hai nghiem z, = - / ; z = l + V3/ Vay phuTdng trinh da cho c6 nghiem: z, = - V3 / ; Z2 = + \/3 /; Zj = CSu IV.b Viet phifdng trinh mat cau /V=(a)nOA:=>/l(9;0;0), fi = ( a ) n O j = > f i ( ; ; ) C = (a)nOz=>C(0;0;3) Mat cau {S):x^^T! 2ax-2hy-2cz + d = Q) di qua diem O, /\ fi, C Nen ta c6 he sau : rf = a =— 9^-18a +rf= ^=3 6^-12ft + d = 3^-6c + J = d =20 Vay phiTdng trinh (5): + + z^ - 9;c - 6v - 3z = 3^ , ban kinh R = 81 „ N/T26 312 Tinh khoang each tit M{x ; y ; z) den mat p hl ng(a) Suy toa diem M each deu mat cua tuTdien OABC vung jc> 0, >> > 0, z > 2JC + 3>' + Z - 2JC + 3>' + Z - = d{M,{ABC)) d{M,{OAB)) = \z\;d{M,{OBC))^\x\;d{M,{OCA)) = \y M each deu mSt cua ti? dien OABC 2A:+ 3^ + 62-18 jc = y = z = l '9 9 ^ Vay CO diem M thoa yeu cau bai toan : A/, U'2'2 , M2(l;l;l) x>Q\y>0\z>Q Cfiu V.b T a c o : z = -\-'2Si = 2-^-2^^i^[j2-Si) So phiJc w la can bac hai cua z = - - 2>/6 / va chi =-l-2V6/W^-(V2-V3/) =0 w - (V2 - V3/)irw - (72 - >/3/) = Vay = - - 2N/6 / c6 hai can bac la : w = N/2 - 73 / hay w = 72 - 73 / 313 D DE THI THAM KHAO THI T6T NGHI^P TRUNG HQC PH6 THCNG PHAN BRN NfiM 2006 I P H A N CHUNG CHO THf SINH CA B A N (8,0 di^m) Can 1: {4,0 diem) Khao sat va ve thi {C) cua ham so y = -x^ + 3.r^ DiTa vao thj fC), bien luan theo m so'nghiem cua phiTdng trinh - r ^ ' + S x ^ - / ? = Tinh dien tich hinh phang gidi han bcli thj (C) va true hoanh Cfiu 2: (7 diem) Giai phiTdng tnnh ^ - ' + = CSu 3: (I diem) Giai phifdng trinh 2JC^ - 5.r + = tren tap so phiJc Cfiu 4: (2 diem) Cho hinh chop S.AflCD c6 day'AfiCD la hinh vuong canh a, canh ben vuong goc vdi ddy, canh ben SB bSng a>/3 Tinh the tich cua khoi chop S.ABCD ChuTng minh trung diem cua canh SC la tam mat cau ngoai tiep hinh chop S.ABCD I I PHAN D A N H CHO THf SINH T l / N G B A N (2,0 diem) A Thi sink Ban KHTN chgn cau 5a hogc cau 5b Cfiu 5a (2,0 diem) Tinh tich phan - '"\e'' +\)e^dx In 2 Vie't phu'dng trinh cac tiep tuye'n cua thi ham so" y = - ^^^^ big't x-2 tie'p tuyen song song vdi di/cJng thing _y = 3A- + 2006 Cfiu 5b (2,0 diem) Trong khong gian tpa Oxyz cho ba diem y4(2 ; ; 0), 5(0; 3;0),C(0;0;6) Vie't phiTdng trinh mat phing di qua ba diem A, B, C Tinh dien tich tam gidc ABC Goi G la trpng tam tam giac ABC Viet phiTdng tnnh mat cau diTcJng kinh OG 314 B Thisinh Ban KHXH&NV chQn cdu 6a hodc cdu 6b CSu 6a (2,0 diem) I Tinh tich phan K = j(2x + l)e'dx Viet phi^dng trinh tiep tuyen cua thi ham so' y 2x + tai diem thuoc JC + thj CO hoanh jc,, = - Cfiu 6b (2,0 diem) Trong khong gian toa Oxyz cho ba diem A ( - i ; ; 2) B(0;l;l),C(l;0;4) thamphang so cua diTdngM 2.1 ChuTng Gpi M laminh diemtam saogiac cho ABC MB =vuong -2MC Vie't Vie'tphi/dng phiTdng trinh tfinh mat di qua thing Afi goc vdi difcJng thing BC va vuong Di THI T6T NGHI^P TRUNG HQC PH6 TH6NG PHANBRN NAM 2007 I PHAN CHUNG CHO THf SINH CA BAN (8,0 diem) CSu (3,5diem) Cho liam soy = x'^ -2x^ + 1, goi thi cua ham so la (C) Khao sat siT bien thien va ve thi cua ham so Viet phiTdng trinh tiep tuyen ciia thj (C) tai diem ciTc dai cua (C) Cau (1,5 diem) Giai phUcfng trinh log4 x + iog2(4jr) = CSu (1,5 diem) Giai phiTdng trinh jc^ - 4ji- + = tren tap so phiJc CSu (7,5 diem) Cho hinh chop tam giac S.ABC c6 day ABC la tam giac vuong tai dinh B, canh ben SA vuong goc vdi day Biet SA = AB = BC = a Tinh the tich cua kho'i chop S.ABC n PHAN DANH CHO THf SINH Tl/NG BAN (2,0 diem) L Thisinh Ban KHTNch{tn cdu 5a Itoac cdu 5b Cau 5a (2,0 diem) Tinh tich phan = ^ ^^'^'^ 315 Tim gia trj Idn nhaft gia tri nho nha't cua ham so y = x^ - Sx^ + 16JC-9 tren doan [1; 3] * C&uSh (2,0 diem) Trong khong gian vdi he toa Oxyz, cho diem M (-1; -]; 0) v^ mat phang (P):x + y-2z-4 = Vie't phtfdng trinh mat phing (Q) di qua diem M va song song vdi mat phangCP) Viet phtfdng trinh tham so cua dufdng thang (d) di qua diem M va vuong g6c vdi mat phang (P) Tim toa dp giao diem H cua diTcJng thing (d) vdi mat phing (P) B Thi sink Ban KHXH&NV chftn cdu 6a hoqc cdu 6b C&u 6a (2,0 diem) ^ ! Tinh tich phan K = hxlnxdx Tim gia tri Idn nha't va gia tri nho nha't cua ham so f(x)-x^ - ^ + tren doan [0 ; 2] C§u 6b (2,0 diem) Trong khong gian vdi he toa Oxyz, cho diem E (1; 2; 3) va mat phang (a): x + 2y-2z + = Viet phu'dng trinh mat cau (S) c6 tam la goc toa dp O va tiep xiic vdi mat phang ( a ) Viet phu'dng trinh tham so cua difdng thing (D)di qua diem E va vuong g6c vdi mat phing (or) THI T6T NGHI^P TRUNG HQC PH6 TH6NG PHAN BBN NfiM 0 U^N I P H A N C H U N G C H O T H I S I N H CA B A N ( , di^m) Cfiu (3,5diem) Cho ham so3; = 2x^ +3x^-1, gpi thi cua ham so la (C) Khao sat sir bien thien ve thj cua ham so Bi0n luan theo m so' nghipm thiTc cua phiTdng trinh 2x^ + 3x^ -1 = m Cfiu (1,5 diem) Giai phu'dng trinh 32x+\ - ^ ^ + - 316 CSu (/ diem) Tinh gia tri cua bieu thufc P = (1 + 4lif + (1 - Si? CSu (2 diem) Cho hmh chop tam giac deu S.ABC c6 canh day bkng a, canh ben b^ng 2a Gpi / la trung diem cua canh BC ChiJng minh SA vuong goc vdi BC Tinh the tich khoi chop S.ABl theo a II PHAN DANH CHO THf SINH TLfNG BAN r^, ^ diim) A Thisinh Ban KHTN chgn cdu 5a ho^c cdu 5b C&u 5a (2,0 diem) 1 Tinh tich phan / = jx^il - x^fdx -1 Tim gia tri Idn nhat va gia tri nho nhat cua ham so y = x}-yl2cosx tren doan [ ; - ] Cfiu 5h (2,0 diem) Trong khong gian vdi hd toa dp Oxyz, cho diem A(3; -2; -2) va mat ph^ng (P): 2x -2y + z-1 = Viet phiTdng trinh cua dtfdng thing di qua diem A va vuong goc vdi mat phing (P) Tinh khoang each tijf diem A den mat phing (P) Vie't phiTdng trinh cua mat phing (Q) cho (Q) song song vdi (P) \h khoang each giffa (P) va (Q) bh\g khoang cdch tir diem A den (P) B Thisinh Ban KHXH&NVchgn cdu 6a ho^c cdu 6b Cfiu 6a (2,0 diem) £ Tinh tich phan K= ji2x-l)cosxdx Tim gid tri Idn nhCt v^ gid tri nho nhat ciia ham so f(x) =^x^ -2x^ + \n doan [0; 2] Cflu 6b (2,0 diem) Trong khong gian vdi h? toa dp Oxyz, cho tam gidc ABC vdi A(l; 4; -1) B(2; 4; 3) va C(2; 2; -1) Viet phiTdng trinh mat phing di qua A va vu6ng goc vdi diTdng thing BC Tim toa dp diera*D cho tur gidc ABCD la hinh blnh hanh 317 THI T6T NGHI^P TRUNG HQC PH6 TH6NG PHRN BAN NAM 2008 L^N I P H A N C H U N G C H O T H I S I N H C A B A N (8,0 d i e m ) ^ 3x-2 Cfiu (3,5 diem) Cho h a m so v = ^ , goi thi cua ham so la (C) X +1 Khao sat sir bie'n thien va ve thi ciia ham so' V i e t phiTdng trinh tiep tuyen cua thi (C) tai d i e m c6 tung dp bang - C a u (1,5 diem) G i a i phu-png trinh \og^{x + 2) + \og^{x - ) = l o g , CSu 3(1 diem) G i a i phu"Png trinh x^ - 2x + = tren tap so phtfc C S u (2 diem) Cho hinh chop S.ABC t o day la tam giac ABC vuong t a i B, dirdng th^ng SA vuong goc vc'Ji mat phang ABC Biet AB = a, BC = a S va SA = 3a T i n h the tich k h o i chop S.ABC theo a G p i / !a trung d i e m cua canh SC, tinh dp dai doan thang BI theo a II P H A N D A N H CHO THf SINH T L T N G B A N A Thi sink Ban KHTN C^uSa (2,0diem) chgn can 5a hoac cdu 5b ' (2,0 diem) I T i n h tich p h a n / = (Ax + \)e''dx , T i m gia t r i Idn nha't va gia t r j nho nha't cua h a m so / ( v ) = - ? ' * + r ^ + tren doan [ ; ] C S u 5b (2,0 diem) T r o n g khong gian v d i he tpa dp Oxyz, cho c^c diem M(I;-2; 0), N(3; 4; 2) va mat phang (P) :2x+2y + z-7 = V i e t phiTdng trinh dU"ttng thang MN T i n h khoang each tiT trung d i e m ciia doan th^ng MN den mat phc4ng (P) B Thi sink Ban KHXH&NV chgn cdu 6a hoac cdu 6b Cfiu 6a (2,0 diem) T i n h tich phan /i: = J(6x^ -2x + \)dx I T i m gia t r i Idn nha't va gia trj nho nha'l ciaa ham so' f{x) = 2x^ - 6.v^ + tren ; a n [ - l ; 1] C S u 6b {2,0 diem) T r o n g khong gian v d i he tpa dp Oxyz, cho d i e m A{2;-l; 3) va mat phang (P): x -2y -2z -10 = T i n h khoang each tiT d i e m A den mat phdng (P) Viet phiTPng trinh diTcing thang di qua diem A va vuong goc vdi mat phang (P) 318 MQI CHI TIETXIN LI^N H$ QUAO|ACHi: C-ong }y \HWW mot vien dich vu van hda KHANG VIET 2bijAflinhlien Hoang, P.Da kao, Q.l, TP.HCM AT: 08.39111564-39102915 - fax: 08.39110880 Email: binhthanhba)kitore@yaha).com Email: khangvietbookstoreQyahoD.com.vn Website: www.ntiasachktiangviet.vn BO DE THI TLif L U A N TOAN HOC I BO DE THI BO DE THI TBAC IMCHieiVI KHACH QUAN VflT LV, F BQ D E j n i BO DE THI TTWC NGHEM KHACH QUAN Phot.hdnh tai: -Nha s a c DE THI TU LUAN TO ^" 2bisA E>n DT: 08.391 Email: b i r • 101100957 s Email: kh( Website: 5C,000,I/C bitha.b -Nha s a d 36 N g u y S h T m i v m n Rnai, U I, IH.HDW DT: 08.38227346 -Nha s a c h MINN TRI 559 Di§n Bien Phu TP D d N d n g DT: 0511.3723868 giiiiii -Nha s a c h 51 Dinh Tien Hoang COa h a n g 32, G i a N g j , H o d n K l e m , Ha NQI DT: 04.38246605-39260477- Fax: 04.39365215 Email: n h a s a c h D T H @ y a h o o c o m -Nhd s d c h MINH TRi ; 103 Ly Thai To, Da N d n g ? 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