BO GIAO DAI VA DAO TAO HUE Ho vd, ten thi sinh: 56 b6o danh: DVC HQC KV Sv THI TUYEN SrNH SAU DAr HOC NAM 2AO7 M6n thi: Giai tich (dd,nh cho Cao hpr) Thdi gi,an ld,m bd,i,; 180 phirt CAu I. 1. Cho hdm hai bi6n f (r,a) KliAo s6t tinh liOn tuc cria hilm / 1x ', A2f lr6n hsp d;N(O,0) khong tbn n6u (*,y) + (0,0), n6u (*,a) - (0,0). Chirng minh rHng dao hA"m riOng cia R. hoi tu vb 0 -I -I 2ra ,2 + a'' 0, tai didm (0,0) tai (huu hat) 2 F_{i 1I I P' ^ tz'J')4)s)" Cdu III. Kj' liiOu X : co z. KhAo s6,t su hoi tu dbu cria chu6i hd,m f ," .i" ,,fu tr6n c6,c tAp sau: fl':L ,) A: lp,+-), p ) 0i ii) B - (0, +oo). Cdu II. Trong khong gian metric IR. v6i khoAng c6ch thong thulng, chitng minh rXng, 1. E - {t,2, 1, 1, 1, . !.u-L^'-,2,3)4) 1n' ).*^^^Y""7 . , 1, . . . . ) U.Ong phai th, mot t6,p con compact ) th, khong gian dinh chudn gbm c6c day s6 thuc llrll - sup lrnl,, Yr - (r.)n e co chudn Euclide rL llsll - WiZ, va - (ar,. . .,un) eY. V6i m6i s6 tu nhien k ta x6t 5nh x? An : X * Y x6"c dinh bdi Anr - ("n+r, fr1xa2t'' ) rk+n), Yr : (rt)zeN € X. 1. Chirng minh Ap lit" c6,c 6nh xa tuy6n tinh lien tuc tri X vh,o Y. 2. Chirng td rXng J* Ann - 0 € R.' v6i moi z e X. CAu IV. Tren khong gian Hilbert phitc 12 vsi tich vo hu6ng / \ S @,il :2*^y,, *ong d6 ,: (r,-)n e {2, U : (Un)- e 12. '"_ : Cho o - (a), ie mQt duy c5,c s6 phric bi ch5,n vA, ,4. : 12 - t2 Ib" mot to5,n trl ducvc x6c dinh bdi Ar - (onrn)n, Yr e !2. 1. Chirng minh rXng ,4 th mQt to6n trl tuy6n tinh lien tuc vd, tinh chudn c:d:a A. 2. Tim to6n trl liOn hiep A* cia A. Khi nb,o thi A ld mQt to6n tr] tu lien hiep? v6i chudn vb,Y-lR'v6i Ghi chri z Cd,n bo coi, thi, khong gi,d,i, thi,ch gi, th€m VIETMATHS.NET . 12 vsi tich vo hu6ng / S @,il :2* ^y,, *ong d6 ,: (r ,-) n e {2, U : (Un )- e 12. '"_ : Cho o - (a), ie mQt duy c5,c s6 phric bi ch5,n vA, ,4. : 12 - t2 Ib". A: lp, +-) , p ) 0i ii) B - (0, +oo). Cdu II. Trong khong gian metric IR. v6i khoAng c6ch thong thulng, chitng minh rXng, 1. E - {t ,2, 1, 1, 1, . !.u-L^&apos ;-, 2, 3)4) 1n'. BO GIAO DAI VA DAO TAO HUE Ho vd, ten thi sinh: 56 b6o danh: DVC HQC KV Sv THI TUYEN SrNH SAU DAr HOC NAM 2AO7 M6n thi: Giai tich (dd,nh cho Cao hpr) Thdi gi,an ld,m