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IIIBESBE19 PHAT TRIEN KHA NANG SUY LUAN CHO SINH VIEN TRONG DAY HOC TOAN CAO CAP ThS Nguyfin Thl Dunn, ThS Di Phi Nga Hpc vi^n Cdng ngh$ Buu chinh Viin thdng SUMMARY The paper presents the types of re[.]
IIIBESBE19 PHAT TRIEN KHA NANG SUY LUAN CHO SINH VIEN TRONG DAY HOC TOAN CAO CAP ThS Nguyfin Thl Dunn, ThS Di Phi Nga Hpc vi^n Cdng ngh$ Buu chinh - Viin thdng SUMMARY The paper presents the types of reasoning (deductive and inductive) and the issues that students need to consider when deducting For example: Understanding the rules of logic, combining both types ofdeductive, using diatoms, Identifying common mistakes while reasoning The above strategies will help students have good deduction and limit the mistakes as a result, students 'deductive skills can be Improved Keywords: Reasoning, deductive Inductive, advanced mathematics Ngdy nfifin bdi: 15/9/2015; Ngdy duyft bdi: 16/9/2015 L Md diu: Suy lugn la thdnh phan quan trgng suy nghT cfla mSi ngucri Qud Uinh suy lufn s6 tgo thdng tin mdi tfl nhQng dilu dd biet, nd giflp Ich cho vifc gidi qi^lt cdc bdi todn, cdc van dk cufc sing Vifc rSn luyfn khd ndng suy lufn la mpt nhfhig bifn phdp dl cd thl phdt uiln tu phdn tfch, tu d\xy hf thing, tu sdng tgo, Bdi vilt nhim giflp sinh viSn hilu rd hem ve cdc dgng suy lufn, cdc kieu suy lufn sai lim thudng gfp cfla hg gidi bdi tfp Todn cao cip Tfl do, smh viSn cd thl bilt lya chgn vd vfn dyng suy lufn tit hem n Khdi nifm vd cdc dgng suy lugn 2.1 Khdi ni^m suy lupn: Suy lufn Id hinh thflc cfla tu duy, dk rflt mft phdn dodn mdi tfl mgt hay nhilu phdn dodn dd cd Cdc phdn dodn dd cd gpi Id tiln de Phdn dodn mdi dugc rflt gpi la ket lugn cua siQ* lufn Cdch thflc rflt kit lugn tfl tiln dl gpi la lgp lufn MSI suy lufn dupc bieu dien duin dgng mpt mfnh dk kdo theo md tiSn dl Id rapt mfnh dl ho$c "Suy lufn dien djch Id suy lufn vdi each % lufn di tfl tien de phdn dnh hieu biet chung din kit ludn phdn dnh hilu biltriSng"([ ], tr 39) Vi d\i.: Con ngudi khdng thl sing dugc den 200 tuoi Ong Hodng Id ngudi, vfy dng iy khdng the sdng dugc den 200 tuoi 2.2.2 Mgt so vdn de cdn chu y SIQ> lugn diin djch Dilu kifn cin vd dfl de suy lufn dat tdi kit lufn dflng id phdi xuit phdt tfl nhQng tien de ehan thyc vd qud Uinh lfp lufn phdi dflng ddn, nghTa Id tuan theo cdc quy tdc Idgic (cdc phdp lien kit Idgic mfnh dl, phdp phfl djnh jugng tfl, lugt d^ng nhit' ) NhQng vin dl ndy sinh vien cin tham khdo Uong cac t^ lifu vl Idgic todn Chdng hgn, xdt raft vdi quy tdc sau: 1) Mfnh dl p ^ chi sai p dflng, q sai 2) Mft cdng thflc rafnh dl dupc gpi la hdi^ dflng nlu nd ludn nhfn gia Uj vdi mpi thl hifn ciia cdc bien mfnh de cd cdng thurc Nlusuylufn Pi,p2,—P„=>q IdmfnhdShdng (cdc p^ Id dflng thl ta ndi suy lugn hgp Idgic Ngupc 1^, nSu cdc tiln dl, q Idkltlufn, / = 1,2 n ) P\>p2>—Pn =^ khdng phdi Id mfnh dl hdng dflng Cd hai dgng suy lufn co bdn: Suy lufn dien djch thi suy lufn dd khdng hgp Idgic vd sity lufn quy ngp 3) Vxe D,S(,x) •» (axe A^OO) 2.2 Suy lupn diin dich 2.2.1 Khdl nlim: Mpt sl tdi lifu dd dua khdl 3x e D,S(x) o (Vx e A5(x)) nifm vl suy lufn diln djch nhu sau: "Suy lufn dien djch (cdn gpi Id suy dien) Id suy 4) Luft ding nhit lufn theo mft qi^ tde thda mdn dilu kifn: Nlu tiln (Trong qud Uinh suy lufn, mgi tu tudng diu phdi ddng nhit vdi chinh nd, nlu khdng tuan thfl qiiy luft dl A dflng thi kit lugn B dflng Ki hifu: — " ([5], U ding nhit thl sS din din lgp lufn Iflng cflng, sai lira 13) ^ suy nghi) hfi cfla nhieu mfnh de: Pi,P2f;p„=^q 12 • TAP CHf THI^BIGlAO DMC-sti 2 - / NGHIEN CUu & UNG DUNG LiSn hf Uong hgc tip todn cao cip, ta thdy: Games va mpt tan t ^ Sin^wre"; 1) Mfnh dl "NIU chudi sd ^ u „ hfi ty thi "Tgp X = (0,2] cd vd sd phan tfl ^ A' khdng bj chfn" Nhgn xet: Ngodi viic dp dgng cdc quy tdc Idgic, ngudl ta cdn ket hgp dp d\tng cdc dgng sa de qud trinh suy lugn duac rd rdng mgch lgc han Chdng hgn, xet vi dg sau Vi dy: Tfl cdc tiln de: "Tit cd nh&ng ngudi nudi ong Id nhd hda hgc", "Cd vdl nhd hda hpc Id nhgc sT', suy "vdi ngudi nudi ong la nhgc sT" Suy lufn ndy cd dflng khdng? Gldl: Dung so dd, ta thay cd thl xdy trudng hgp sau: B=l lim u^ = " chi sai tdn tgi mgt chuoi so J^ " ndo dd hfi ty nhung lim u„ ^ 2) Suy lugn ((^ =>9)^p)^q la hgp Idgic Th|t v|y xet bang gia tri cllSn li, ta cd: p Q p=>? 1 0 1 1 (P=>?)AP 0 ((p=>g)Ap)=>5 1 1 Tu ket lugn ndy, ta thdy neu m^nh de p^g dflng vd mfnh de p dflng thi suy q dflng (Dilu niy thudng dupc dp dyng mgt cdch hlln nhien cdc suy lufn md khdng cin kilm tra lgi bdng gid trj chdn If) (o: ngudi nudi ong; h: nhd hda hgc; n: nhgc SI) Vfy suy lufn USn khdng dflng 2.3 Suy lupn guy ngp Ching hgn: Ta biet ring "Neu hdm so /(x) lien Suy lugn qi^ ngp Id suy lufn khdng dya theo tyc USn [o,b] thi / ( x ) khd tich trSn [a,6]", vd mpt quy tdc ndo, kit lufn thudng dugc rflt trSn co sd xem xet nhflng tmdng hgp rieng "hdm so /(x) = xlnx liSn tyc tren [l,e]"- Vgy suy 2.3.1 Suy lugn quy ngp hodn todn Suy lugn quy ngp hodn toan Id phdp suy lufn rahamso /(x) = xlnx khd tfch tren [\,e] nhim rflt kSt lugn chung ve tat cd cdc tm&ng hgp 3) Tfl djnh nghla: "Hdm sd /(x) dgt cyc dgi tgi cy the dd dupc xet dSn XQ nlu tin tgi mpt lan cdn C^(X(,) ndo dd cfla XQ Chdng hgn, phucmg phap quy ngp todn hgc Id mft dgng suy lufn qi^ ngp hodn todn saocho Vxef^(xo),/(x)a + tuoi^ fi~af+fif khix->Xfj, ty Id +NIU mien V cd ttah doi xflng mft phdng r = va bilu thflc cua f(x,y,z) le ddi vdi z tiii lllfix,y,z)dxdydz = khlx-^XQ Nhan xdt: "Moi quan hf gifla quy ngp vd dien P~P, khix^XQ dich Id moi quan hf kl thfla, tgo tien de, bo sung Kit lufn ndy khdng dung mpi va ho trg cho qud trinh nhfn thflc" ([1], tmdng hgp (Chdng hgn, no khdng dflng U.47) Quy ngp cung cip phdn dodn, ldm co sd cho a = x-x^; a,=x + x^; fi=fit=-x'> Xo=0).Tuy dien dich Dien djch giflp kilm tra tfnh dflng din cfla suy lugn quy n ^ , dilu cd thl dua din kit lufn nhiSn, ta thiy nd dflng nhieu trudng hgp khac, phdn dodn la dflng, ho$c nlu bdc bd thl sS d^traphdn vfy cd thl iQri dyng dilu nify de dua gid thiflt vd dodn quy ngp mdi, giflp quy ngp sau din gin vdi ban tfl dd ed cdch gidi l>di todrt chit hifn tupng hem Vf dy: Xdt sy hfi ty cfla tich phan suy rpng Bk phdt Uiln khd ndng suy lufn, sinh vifn nen thudng xuyfn kit hp^ sfl dyng cd hai dgng suy lufn USn, ddng thdi phdi chfl f dk khdng mdc phdi nhQng Se -e sai lim Uong suy lufn Mft s6 vi dy vl suy lufn Phdn tich: khdng dflng cfla sinh vien hpc tfp Todn cao cip Trong gidi bdi tfp todn cao cip, mft sl sinh e ' - l ~ x khlx-*0* vd e " ' - l - - x JtWx-^0* viSn cdn cd nhflng sai lim suy lufn Chdng hgn: Nhu vfy, ta dodn ring cd thl + Tfl mfnh dl dflng p^q, c6 q dflng, si^ Ue' -1) - (e"' -1)] ~ 2x x^O* hay p dung + Sai vilt phfl djnh cfla mft mfnh dl, sai ( e ' - e " ' ) ~ x khix-*0\ j ^ ^6^ each gidl bdi suy lufn vdi mfnh dl cd lugng tfl phi biln, lupng tfl tin tgi todn Id nhu sau: + Sai vfn dyng suy lufn quy ngp khdng hodn Gldl: Cgc diem: x = Dl thiy — Id hdm so duoi^ USn (0,1], e'-e ' khd tich tren mpi dogn [a, 1] vdi a > lim '•^ye'-e~' : — = lim — = lim ::- = 2x) i-to'e'-e x->^e +e + Sai khdng chfl ^ din luft ding nhit Sau day Id mft vdl vf dy vl cdc sai lim nfu Uen T«j ^L ui i J-, ^ x*sin— Idil x^O Vi dy: Cho hdm so / ( x ) = x A khix = TimAdl / ( x ) khd vi tgi jc = md J— phdn kl nSn tich phan dd cho phan ki ^2x Vf dy: Khi hpc d phan tich phan tm Idp, sinh vifn d3 bilt ring: + jjdxdy = S (S Id dif n tich miln D) D Gidi: Dl / ( x ) dilu kifn fix) khd vi tgi x = * ! cin lien tyc tgi x = 0, nghTa Id lim/(x) = /(x„) = ^ Tacd lim/(x)=limx^sin-=D +NIU miln D cd tinh dli xflng qua tryc Ox vd bilu tiiflc cfla fix,y) IS doi vdi y tiii JlfU,y)q, cd q dimg, suy p dflng NGHIEN CUU & UNG DUNG Vf dy: Xet sy hgi ty cfla chuoi sd y\— ^ ^^[2 +n Gidi;Tacd lim =lim— = = * ^ hfity • Sai lim tuong ty d vi dy tren, sinh vien cho rdng lim u„ = => ^ u„ hfi ty Vfdu: Tim gidi hgn: vi = lim cot*x—;- ^) '^\ Gidl: , , fcos^x I^ , f'cos'x 1 , -sin^x , -4=lim—1 r plim—j r- =lim—j—=-l'-^^sinx r J '-^\_sinx sinxj '-« smx * Ldi gidi sai vilt , fcos^x ^ , f cos^x I I ^ , hm —5 r =lim -7-; r-;- tuc la suy '-* XQ ( bii aky dip 6n diing Ik A = 2, ~) Vfdv: Tim cvc trj ciia iiams6 f^x,y) = x* +/ Glai: C / ; = 4x'; / ; = / cre(a,A)saocho —-T- r T = -77T'- Gidi: Do / lien tyc tren [a, b]; vi tren (a, b) nen theo dinh li Lagrange, t6n t^i c G (a,b) cho nb)-na) = /XcXb-a) Tucmg ty, gib)-gia) tdn tgi ce{a,b) cho = gXcXb-a) fib)-fia) fjc) Vilyi g{b)-g(a) g'(c) * Sai lira chflng minh d ddy Id dd khdng chfl ^ din lugt ding nhit Sl c bilu thflc f{b)-f{a) = fXcXb~a) vd sl c bilu tiiflc gib) - gia) = gX^Xb - a) Id khdc K £ T LUAN Vifc hieu rd vl cdc dgng si^ lufn sS giflp mSi ngudi bilt vgn dyng SIQ* lufn tit hon Be cd nhflng suy lugn dflng vd nhanh, ngu&i hpc cin nim vttng cdc quy tie Idgic, hilu cdc djnh nghTa, djnh li mft cdch chlnh xac, chu ^ dieu kifn cln vd dfl mSi djnh If, liSn hf gifla cdc cdng thflc Idgic vdi cdch suy nghT dl hilu hon Hai dgng suy lufn dien djch vd qi^ ngp cd mdi quan hf vdi vd deu quan trpng sy sdng tgo "Suy lufn quy ngp khdng hoan todn" mang lgi hifu qud cao qud trinh ^di quylt vin dl, Tuy vdy, chi nen dp dyng suy lufn ndy dudi dgng gid thifet, cin kilm tra lgi sy chfnh xdc cfla kit lufn tflng tmdng hpp cy thl H t a s6 c6 m?t dilm t4i lljn 14 M, (0,0) Tdi lifu tham khdo T^M,(0,0) c6s'-rl=0 Phan Dung (2012) Tu Idgich biin chung Trong mpi ISn c§n ciia Mo(0,0), x^t cfic diem vd hi thing, NXB Dgi hgc Quic gia TP HCM Dy dn Vift- Bl, Bf Gido dye vd Ddo tgo mx,0) Tac6 / ( M ) - / ( W „ ) > V^ylltasddSt (2000) Dgy cdc kS ndng tu duy, Hk^^u LS Bd Long, Gido trinh Dgi sd, NXBTTVTT, cilctieut?iM,(0,0) v i / ( M , ) = • Sai ^ c6 till vl chua iiiiu rd dinti ngliTa cvtc 2010 tri, cijua llilu r5 ve cSc liriTng tii "t^n t^i", "mpi", Chu cim Tho (2015) Phdt triin tu thdng iip$c da dflng suy l u ^ quy n^p ]di6ng liofin toan qua dgy hgc mon todn a trudng phd thdng, NXB Dgi Vf dv: HSy ciiijmg minli dinh li Cauchy hgc su phgm, Hd Nfi (Cho f, giAckc him s6 iien tyc trSn [a, b]; Nguyin Anh Tuin (2012) Gido trinh Logic kh4viti«n(a,i); todn vd lich sir todn hgc, NXB Dgi hgc Su phgm, g'(:t)*0 v6i VATS (a,*).Khi d6, t6n t?i HdNfi TAP Off THifrBIGlAO DMC-sti 122-10/2015 • IS ... vl suy lufn Phdn tich: khdng dflng cfla sinh vien hpc tfp Todn cao cip Trong gidi bdi tfp todn cao cip, mft sl sinh e '' - l ~ x khlx-*0* vd e " '' - l - - x JtWx-^0* viSn cdn cd nhflng sai lim suy. .. tich phan suy rpng Bk phdt Uiln khd ndng suy lufn, sinh vifn nen thudng xuyfn kit hp^ sfl dyng cd hai dgng suy lufn USn, ddng thdi phdi chfl f dk khdng mdc phdi nhQng Se -e sai lim Uong suy lufn... tmdng hgp rieng "hdm so /(x) = xlnx liSn tyc tren [l,e]"- Vgy suy 2.3.1 Suy lugn quy ngp hodn todn Suy lugn quy ngp hodn toan Id phdp suy lufn rahamso /(x) = xlnx khd tfch tren [\,e] nhim rflt kSt