7/30/2019 Olympic Ton Sinh Vin 2010
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K THI OLYMPIC TON SINH VIN 2010(HU, 07-12/4/2010)
THI MN I S
Cu 1:Cho l cc ma trn vung cp vi h s thc sao
cho
a/ Chng minh vi mib/ Tm v d chng t kt lun trn khng cn ng nu ch
c
Cu 2.
Cho l cc dy sc xc nh bi:v , ,
Chng minh chia ht cho .
Cu 3.a/ Chng minh ng vi mi snguyn dng , biu thc c th biu din
c
di dng bc khng qu ca cc bin
b/ Hy tm tng h s ca
Cu 4.
Xc nh a thc thc tha mn
Cu 5. T chn:5a/ Cho l ma trn thc vung cp , c tng cc phn ttrn ng
cho bngv . Tm a thc c trng v a thc ti tiu ca .
5b/ Cho l cc ma trn thc, vung cp , trong kh nghch v ng thi
giao
hon vi . Gi s . Chng minh v giao hon vi nhau.
7/30/2019 Olympic Ton Sinh Vin 2010
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2
K THI OLYMPIC TON SINH VIN 2010(HU, 07-12/4/2010)
THI MN GII TCH
Cu 1.Cho
a/ Chng minh vi mi . tn ti duy nht s thc tha mn iu kin m
ta k hiu .
b/ Tm
Cu 2.
Cho dy c xc nh bi , , .
Tm
Cu 3.
Cho v hm s kh vi trn tha mn , , vi
mi . Chng minh vi mi .
Cu 4.
Cho hm kh vi lin tc trn . Gi s . Chng minh
tn ti sao cho .
Cu 5.
Cho a thc bc vi h s thc sao cho v . Chng
minh c t nht mt nghim vi
Cu 6. T chn:
6a. Tm tt chm dng kh vi lin tc trn tha mn
v
6b. Tm tt c hm lin tc trn tha mn
v vi mi
