ung dung dao ham tinh don dieu.pdf

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BigingI.5ngdngcaohmTHHONGNGC SUNDAY,SEPTEMBER30,2012

BigingnythucKhanthiH2013.TholunvtcuhitiyXembigingI.1I.2I.3I.4

ThngbovlchhcngklmGingvinngklmhcvin

Vicgiivbinlunphngtrnh,btphngtrnh,hphngtrnh,hbtphngtrnh,...bng ccphng phpnh:Bini tng ng,t nph, lnggic ha,hnhhc,...khquenthuciviccbnchunbthivoihc.Tuynhinimtvimtbitondngnyccbntnhiucnlngtng,chatmcligiihocxcnhcnglinhnglikhngaracktqucuicng!

Trongphmvibigingnytimunbn vmtphngphpgiiquytccbitonvphngtrnh,btphngtrnh,hphngtrnhvhbtphngtrnh,...khimccphngphpnutrngpkhkhnhocbtc!l"ngdngtnhniucahms".

Tnh cht 1:Gi s hm s lin tc v n iu trn tp th phng trnhcnhiunhtmtnghimthuc .

Tnhcht2:Nuphngtrnh cmtnghimtrntp thphngtrnhcnhiunhthainghimtrn .

Tnhcht3:Nu lintc,ngbintrn v lintc,nghchbin(hochmhng)trn thphngtrnh cnhiunhtmtnghimtrn .

Tnh cht 4:Nu hm s lin tc v n iu trn th vi ta c:.

Tnhcht5:Nu niutrn th lnghimcahphng

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ReadMore

Vn1.ngdngtnhniucahmsgiiphngtrnhVd1.1.Giiccphngtrnhsau:

a)b)Nhnnh:ivicu1,cthbnnghnvicbinitngnghocsbnh

phng,tuynhinbnsgpkhtrongbini.Cu2,ccphngphp"truynthng"khngkhthi.

Nubnchukhquanstvchuynvnginthvtriulnhnghmsngbin(trnmttpno).Lcny,sdngtnhniugiiquytbitonnyratrongubn.Vncnlilonnghim!Cngvicnykhngkh,nhngnubncthtngsthsmtthigian.Hyutinnhnggitrca saochoccbiuthcdiducnnhngitrlschnhphng!Ligii.a)iukin:PhngtrnhchoXthms trn .Tathyrng:+Hms lintctrn+Cohm vi .

Dohm ngbintrn .+Ktlun: lnghimduynhtcaphngtrnhcho.(Xemtnhcht1!)b)iukin:PhngtrnhchoXthms trn .Tathyrng:+Hms lintctrn+Cohm vi .

Dohm ngbintrn .+Ktlun: lnghimduynhtcaphngtrnhcho.

Vd1.2.Giiphngtrnh:Nhnnh:CngvitduynhtrongVd1.1nhngskhkhngnhchmslin tc, niu trnTX ca n.Tuynhin, quan st k th thycc biu thc

diducn2vcchungmtmilinh:

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PLUS.MATHS.ORG

Mathsinaminute:Modulararithmetic

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Do$$f(u)=f(v)&\Leftrightarrowu=v$$

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Vn2.ngdngtnhniucahmsgiibtphngtrnh,hphngtrnhVd2.1.Giiccbtphngtrnhsau:

a)b)

c)Nhnnh:Cu1,bnhontoncthsdngphngphpbnhphnghocbin

itngnggii.Tuynhin,timunhngbnnvicsdngtnhniucahmsgiiquyt,tuynhinoncmtnghimcaphngtrnhnymtkhnhiu thi gian(bn ch chnnhng s sao cho biuthc di du cnl s chnhphng).Cu2,cthtnph,nhngbinikhri.Bitonnginnusdngtnhniucahms.Cu3,khphctpvcngcthtnph.SongnuquanstkththycmiquanhtngtnhVd1.2.Ligii.a)iukin:BtphngtrnhchotngngviXthms trn .Ta c hm s l hm s lin tc v c o hm

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Khi lin tc trn v c o hmnnnnghchbintrn .

Hnna .

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Ktlun:Tpnghimcabtphngtrnhl:c)iukin:Btphngtrnhchotngng:

t v th(1)thnh hay.

Xthms trn .Khi lhmlin tctrn v co hm trn

nnhm ngbintrn .Vtnhngbinnnt suyra hay .Kthpviiukintac:Ktlun:Tphpnghimcabtphngtrnhl: .

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trn .Lpbngbinthincahm trn nhsau:

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Vd3.6.Chngminhrngvimisthc ,tauc:

Ligii.Vi ,btngthc(1)tngngvi:

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Vy:

Vd3.7.Chngminhrngvimi ,tauc:

Ligii.Xthms trnkhongTac vimi

Dohms ngbintrnkhongTsuyra vimi

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Bitp3.2.Chngminh:

Bitp3.3.Chngminh:

Bitp3.4.Chngminh:

Bitp3.5.(D2007).Chngminh:

Vn4.ngdngtnhniubinlunphngtrnhvbtphngtrnhBitonvbinlunsnghim,cnghimtrnmttphpchotrclbitonm

hunh trongthi nmnocng c.Ngoivic yucuhc sinhnmvng cckinthccs,bitoncnihictduy,sngto.ividngtonnycngcnhiuphngngiiquyt,trongphngnsdngtnhniucahmsschotaligiingngn,covcnhgirtcao!

Vd4.1.Chohmsa)Tm phngtrnh: cnghimb)Tm btphngtrnh: nghimngc)Tm btphngtrnh: cnghimNhnnh:Mtcchrttnhin,khibinlunphngtrnhhocbtphngtrnhc

chathamsthvicutincnlmlcgngathamsvmtvclp.Sausdngcctnhchtniucahmsmbnbit.tinisnh,tixinnhclimts"hngngthc"sau:

a)Nghimca phngtrnh lhonh giaoimcath hmsvith

b)Nghimcabtphngtrnh lphnhonh tngngviphnth nmphatrnsoviphnth

c)Nghimcabt phngtrnh lphnhonh tngngviphnth nmphadisoviphnth

d) Nghim ca phng trnh l honh giao im ca ng thngvith

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h)Btphngtrnh cnghim

Ligii.a)Biniphngtrnh saochothams nmvmtvclp:

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cnghim th philnhnhocbngGTNNvnhhnhocbngGTLNcahm trnon (Xem"hngngthc"(d)vhnh1),tcl:

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nn lhmnghchbintrn .

Do,$$\mathop{min}\limits_{x\in[12]}g(x)=g(2)=\frac{3}{8}\\\mathop{Max}\limits_{x\in[12]}g(x)=g(1)=1$$Ktlun:Gitr thamnbitonl:b)Vi ,tac:$$f(x)\leqslant0\Leftrightarrowm{x^2}+2mx3\leqslant0\\\Leftrightarrowm(x^2+2x)\leqslant3\\\Leftrightarrowg(x):=\frac{3}{x^2+2x}\geqslantm,\forallx\in[14]$$ nghimngvimi th ,iunycckhi

(xem(e)vhnh1)

Vhm lintcvcohm trnon[14]nn l

hmnghchbintrn .Do

Ktlun:Gitr thamnbitonl:b)Vi ,tac:$$f(x)\geqslant0\Leftrightarrowm({x^2+2x})\geqslant3\Leftrightarrowm\geqslant\frac{3}{x^2+2x}\\(1)$$tvxthms (2)ytagpchtrcrilon chaim"cbit"mlmcho khngxcnhlim .Kthutltastchralmhaionvixtringim .Cth:Xtcckhnngsau:Nu ,thaytrctipvo(1),btphngtrnhtrthnh .Vnghim!Nu th

$$\text{btphngtrnhcho}\Leftrightarrowg(x)\leqslantm\text{cnghim}x\in(03]\Leftrightarrow\mathop{min}\limits_{x\in(03]}g(x)\leqslantm$$Do nghchbintrn nn

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Vd4.2.Tm pt: cnghim.

Ligii.iukin:Biniphngtrnhchovthm nhsau:

Vic tnho hm lkh phctp, tuynhinta dsuy ra v lhmtngtrnTX,cn vlhmgim(tcl vlhmtng)trnTX.

Suyra lmthmstngtrnon .Nhvy:

cnghim

Ktlun:

V d 4.3. Tm phng trnh cnghimthc.Ligii.iukin:Biniphngtrnh(1)vxthm nhsau:

Cthtnph th ,vi .

Khi(2)trthnh: .lmthmsbchai,vickhostkhngcgkhkhn!\parTac .Lpbngbinthinchohm nhsau:

Nhnvobngbinthinddngsuyragitrca cntml: .Ghich:

a)ivi nph trn, ccbn bucphitmmingi trcan, chc stbcny.

b)BitonnythikhiA2007vcnmtscchgiikhc,ccbnttmhiuthm!

Vd4.4.Tm btphngtrnh:

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Ligii.t th(1)trthnh:$$mt^2+4(m1)t+m1>0\Leftrightarrowm(t^2+4t+1)>4t+1\\\Leftrightarrow\frac{4t+1}{t^2+4t+1}



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nghim.

Bi tp 4.3. Tm bt phng trnh: nghimng

Bi tp 4.4. Tm bt phng trnh:ng .

Bi tp4.5. Tm phng trnh: cnghim.

Bi tp 4.6.Chng minh rng: Vi mi phng trnhluncnghainghimphnbit.

Bi tp 4.7. Tm phng trnh: cnghainghimthcphnbit.

Bi tp 4.8. Tm bt phng trnh: ng vi

Bi tp 4.9.(A2002).Tm phng trnh:

ctnhtmtnghimthucon

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