THI TOÁN L4-2011( ĐDT HN)

-fRU'oNG rr-rpr EAo ouv rrj un Tnr rgtl D4.I HQC LAN lv (2710212011) mON roAr'{ Hqc xHOr a Tttdi gian lam biti lB{) phitt; khong k€ thdi gian phdt di PHAN cHUNG cHo rAr ca cAc rni SmH Ciu I: Cho hirm'6 Y: mx-4m-r3 x-m 1) Lrhao s5t vir vE d0 thi hdm s0 khi m= 2' 2),chf11;;; ;il;;; ili; ;1 "-ao t i .h'r.'? 1u6n di q"i lT di6m c0 dinh A va B. Tri hai di6m A vi B hdy lap phucmg fiinh cua hai duong thangc6 hQ s6 g6c bang 1,5' Tinir diQn tich hinh thang gi6i han bdi AB, hai dumrg thdng niry vd trlic Ox' CAu il; i; GiAi b6t phuong trinh: 2a{4*1ra <L x 2) Giai phucrng trinh: sinox+cosox i ^ 1 5 sin 2x 2 Ssin 2x Ciu III: Tinh tich phAn: ft ? ,. ' rl+cosr l= lln(l+srnx) &. 'l 1 + cosx '0 CAU IV: Cho hinh chop S.ABCD, co da,v ABCD lA hinh vu6ng, dulng cao SA' Gqi M lir trung rli6m SC; N, P lan luqt nam tr€n SB va SD sao cho * = + = 1 ta, phang GvO-lP) chia hinh -'^" sB sD 3 chop thdnh hai ph6n. Tinh ti sO AC tich cuahal pUan dO' Cfiu V: Chimg t6 rang vsi mqi 916 ui cua tham s0 m, hQ phuong trinh sau lufin co nghiQm: l*+*Y+Y=2m+1 i 1xY(x+ !)=m2 +m' X6c dinh m ae ne cO ngtriem duY nhdt. pHAN mtNC ( rgi SINH CHi LAIVI MQT TRONG HAI PHAN A HOAC B ) A. Theo chuong trinh chuAn: CAuVIa: _ j ' l) Tinh diQn tich tanr gi6c dAu nQi tii5p elip (E), ;+'r- = i. nhan dii5m A (u;2) la dinh i,ir trpc turig lirm truc ddi xirng. . ?)Trong kh6ng gian voi h0 uuc tga dQ oxyz, tim ba di6m M, N, P lan lugt thu0c c6c rJucrng thing: (d,) + ='=' =+, (dr) + =*=+t tor) i =+=+ sao cho M' 1 2 -)' \"j/ 2 7 -1' 2 1 i N. P thang hAng, dOng thoi N lir trung di6m ciia doan flrang MP' Ciu VII a: .lnx1 Cho x > 0, x *1. Chimg minh rang: ,_l.G' B" Theo chucrng trinh ning cao Ciu VI b: 1) Tinh di€n rich tam gi6c dAu nQi ti0p paraboi (P): 1p :2x, nhan dinh ctra parabol ldm mQt dinh vir tryc hoanh Ox ldm trgc ddi ximg.' 2) Trong khOng gian voi h0 truc tga dQOxyz: a) Tinh khoang crlch gita hai duong thdng: I x =2-I (o,l? =+:-i,^ o', 1r-::t*, l.! - r b) Tinh goc gitadudrng therrg (dr) + =+=+ voi m{tphang (a):x+y-z+Z:0' \r' 4 | -2 Cfru VII b: Gi6su u1v. Chrmgminhring:u'-3u < v3-3v+4' Gi6m thi coi thi khdng gi6i thich gi th6m-: . -2 Cfru VII b: Gi6su u1v. Chrmgminhring:u'-3u < v3-3v+4' Gi6m thi coi thi khdng gi6i thich gi th6m-: . kh6ng gian voi h0 uuc tga dQ oxyz, tim ba di6m M, N, P lan lugt thu0c c6c rJucrng thing: (d,) + ='=' =+, (dr) + =*=+t tor) i =+=+ sao cho M' 1 2 -)'. rAr ca cAc rni SmH Ciu I: Cho hirm'6 Y: mx-4m-r3 x-m 1) Lrhao s5t vir vE d0 thi hdm s0 khi m= 2' 2),chf11;;; ;il;;; ili; ;1 "-ao t i .h'r.'?