8
1/15/2015 Hiểu về khái niệm 'giới hạn' trong toán học (kỳ 2) | Math2IT http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 1/8 Math2IT Dinh Anh Thi | 12.9.14 | Hiu toán hc | Toán sơ cp | 3 Like Hiu vkhái nim 'gii hn' trong toán hc (k2) Bài viết tiếp tc vi 2 nghch lý thú vtrong đi sng là nghch lý đưng tròn và nghch lý Nghch lý đưng tròn Xét mt đưng tròn và mt đa giác đu ni tiếp đưng tròn y (Hình bên dưi). Scnh đa giác tăng t

Hiểu về khái niệm 'giới hạn' trong toán học (kỳ 2) _ Math2IT.pdf

Embed Size (px)

Citation preview

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 1/8

    Math2ITDinh Anh Thi | 12.9.14 | Hiu ton hc | Ton s cp | 3Like

    Hiu v khi nim 'gii hn' trong ton hc (k 2)

    Bi vit tip tc vi 2 nghch l th v trong i sng l nghch l ng trn v nghch l

    Nghch l ng trnXt mt ng trn v mt a gic u ni tip ng trn y (Hnh bn di). S cnh a gictng t

    *

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 2/8

    R rng, khi khng ngng tng ln th a gic s cng ngy cng tr thnh hnh trn m n nitip. iu ny cng khng qu kh tng tng. Khi y ta ni gii hn ca a gic khi tinti v tn s l ng trn.

    Tht ra thc t ta vn rt kh chp nhn rng "lm sao m mt a gic gc cnh th kia li c thtrn mt nh ng trn c?" Nhng khi nhn li, bn cng khng th no tng tngc l i n v tn ngha l n i n u? N s mi ln ln, khng c mt s no ln ni rng s ti s . Nu bn chn th s li c ln hn. Chnh v takhng th tng tng c l i n v cng n nh th no nn chc chn ta cng khng thno tng tng c a gic gc cnh li mt m thnh ng trn n ra sao.

    Tuy nhin, ging nh v d v mi tn bay mi, y s cnh s ln mi. Ta s xt mt thc t.Thc t mi tn trng ch, cn y thc t a gic s tr thnh hnh trn. Nu xt mt cchtng quan, mt thng s cho bn kt qu y khi gc cnh ca a gic vt qua gii hnphn bit ca mt v ta s thy l mt ng trn ch khng phi l mt a gic na.

    T ci nhn trn, cc nh ton hc ny sinh ra tng tnh chu vi hnh trn, in hnh lArchimedes (287-212, TCN). R rng khi ta ch cn o di cc cnh ca a gic v cng li thn cng chnh l chu vi ng trn nu s cnh tng ln rt ln. Archimedes lm ng nhvy, ng th vi mt a gic s cnh ln v o xem chu vi a gic y l bao nhiu t suy rachu vi ca ng trn. Cn ch rng, thi ca ng hon ton cha bit ti s hay nhngha gii hn.

    Bn cng c hc rng chu vi ng trn chnh l

    T cng thc ny bn c th s bit c gi tr ca s nu bit chu vi ng trn v bn knhca n. y cng l cch cc nh ton hc i tm gi tr ca s bng cch th vi s cnh agic rt ln. Chng ta s tm hiu k hn cc nh khoa hc t xa n nay lm nhng cchg tm c cng nhiu s ch s thp phn chnh xc sau du phy ca s , cng nh bitc con s quyn lc ny l g lot bi khc ca Hiu ton hc.

    V d v mt s ch s chnh xc pha sau du phy ca s . Ch rng cho n nay s lngch s pha sau c tm thy bng nhiu phng php ln ti mt con s v cng ln vkhng c du hiu chng li.

    Bn c nhn xt g v a gic cnh y nu nh s cnh c khng ngng tngln, tng mi mi n v tn?* *

    *

    *

    BHJD `OHUSOMJN*

    *

    * * UU * UU

    *

    R

    DIVWJOHUSO` Rg `COLOIOHUSO

    R

    R

    *

    R

    R

    R

    TRANG CH LATEX TON LINUX OS X CNTT TRI THC

    KHC MATH2IT

    tm

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 3/8

    Nghch l Chng ta cng xt thm mt v d n gin nhng "y tranh ci" khc. Khi ly chia cho , bns thu c mt s thp phn v hn tun hon dng sau

    T ta suy ra

    hay

    Lm sao m li c th bng c? Tht kh hnh dung iu ny. Tuy nhin,chnh v y l s thp phn v hn (tun hon) nn theo tng v gii hn, iu y hon tonc th chp nhn c. S con s phn thp phn l v hn, bn khng th hnh dung n lnn c no, ch bit rng, nu s con s y t n ngng "v hn" th gi tr ca s l . Hay k hiu li

    Khi y, ci THC T y l gii hn tn ti, tc ca chng ta bng .

    3peoplelikethis.Like

    Dinh Anh Thi : Tc gi blog, xut thn l sinh vin s phm ton, hin ang l nghincu sinh v Ton ng dng ti Php. Chnh v nim am m Ton hc, tin hc ng dng

    g g

    MJN

    *

    . /-,000 000

    *`DIT

    tng hnh thnh v gii hn nh cp trn c lin h nh th no vi nh nghaton hc chnh xc ca n? Mi bn theo di k tip theo.

    12.9.14 , Hiu ton hc Ton s cp

    Vit bi cng blog bng cch lin h [email protected].

    Ln u trang

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 4/8

    Bi ng C hn

    Hinthtntcgingyngnhnbnditiubivittrongblogger2comments5monthsago

    inhAnhThiHix,bnnichungchungquthnhramnhcngkhngbitgiplgipsaona.Bn"lm"llmnhthnori?

    Ngilngngoitnh?3comments6monthsago

    inhAnhThimnhmicpnhtpnbn:)

    Ngnkhngchocopytextbivittrongblogger5comments6monthsago

    holalatigeranhichoemhicinotevngvngtrongbivitmnhdngwidgetghayththutglmcvyanh,em

    HngdncitLaTeX4comments5monthsago

    AnTranThychoemhilemthybindchtextcmyciTeXnicCenter,...emthyndunglngnhhnTeXlivert

    ALSOONMATH2IT

    2Comments Math2IT Login

    SortbyBest Share

    Jointhediscussion

    Reply

    HienPham 4monthsagoAnhchoehiathngccctinvtonhctrangnoth?Bivitcaahaytht!

    2

    Reply

    inhAnhThi 4monthsagoMod >HienPhamCmnbn,ylnhngtrangmnhhayxem http://math2it.blogspot.fr/201...

    1

    WHAT'STHIS?

    Subscribe AddDisqustoyoursited Privacy

    Favorite

    Share

    Share

    Bi ng Mi hn

    v qua trng lp s phm nn Thi rt quan tm n vic ng dng Ton hc, Tin hcvo trong cuc sng thc t cng nh vic truyn t kin thc Ton cho hc sinh theomt phung php hin i v tch cc nht, gy hng th v hiu su cho ngi hc,ngi c ni chung. Mi chi tit xin lin h [email protected]. Blog c nhnAnh Thi blog.

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 5/8

    Tuyn tp cc eBooks hiu thmv th gii ton hc k th (cp

    nht ngy 10/12/2014)

    Hi p Ton (my tnh cm tay) -k 1 : tm hai s nguyn dng

    tho iu kin

    Gii ton theo tng bc vitrang web CyMath.Com v

    Symbolab.Com

    Tuyn tp thi v p n ihc mn Ton Khi A t 2002

    n 2014

    Tuyn tp thi i hc mnTon t 2002 n 2012 theo ch

    Bi lin quan

    Gii thiu

    Math2IT l chuyn trang v Ton hc+ Gio dc v Cng ngh. Mongmun chia s tri thc v kht khao imi nn gio dc nc nh. cthm.

    Theo di chng ti

    +38 xut url ny trn Google

    Nhiu nht 7 ngy qua

    Math2ITTon&Tin1,461Like

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 6/8

    Nhng cch v hnh chnh xcbng thc k v compa

    Nhng vic cn lm sau khi ciUbuntu 14.04 v mt s phin

    bn khc

    Nhng phn mm nn ci choUbuntu, Elementary OS, Linux

    Son tho ton hc trong LaTeX(k 1)

    WolframAlpha : gii ton theotng bc

    Tng hp nhng vic cn lmsau khi ci Windows c mt

    chic my tnh y mnh m

    Ti liu tham kho dnh cho itng t hc LaTeX (cp nht

    ngy 6/11/14)

    Bi ngu nhin

    Tng hp v tuyn chn nhngphn mm nn ci cho Mac OS X(k 2)

    Tuyn tp cc trang web chuynv gio dc m bn nn bit (cpnht ngy 19/12/2014)

    Tng hp v tuyn chn nhngphn mm nn ci cho Mac OS X(k 1)

    Nhng iu m cc h thnggio dc tt nht th gii anglm (K 2 - Cuba)

    Tch hp Compile FreeFem++ viSublime Text

    Nhiu nht 30 ngy qua

    Nhng cch v hnh chnh xc bng

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 7/8

    thc k v compa

    Nhng vic cn lm sau khi ciUbuntu 14.04 v mt s phin

    bn khc

    Nhng phn mm nn ci choUbuntu, Elementary OS, Linux

    Ti liu tham kho dnh cho itng t hc LaTeX (cp nht

    ngy 6/11/14)

    Son tho ton hc trong LaTeX(k 1)

    WolframAlpha : gii ton theotng bc

    Google+

    Math2IT

    + 38

    Theo di

    Lt xem

    111189

    Nhn xt mi

    Ti liu min ph

    bn c th cho mnh xin link face cabn.. mnh c th trao i trc tip vibn.. bn gip...

    To phn trang c nh s cho blogger 2 hours ago

    inh Anh Thi

    a, mnh thy n khi n lch th mi pm bn, khi y th cc bi n "kht" lic vi nhau...

  • 1/15/2015 Hiuvkhinim'giihn'trongtonhc(k2)|Math2IT

    http://math2it.blogspot.fr/2014/09/hieuvekhainiemgioihantrongtoan_12.html 8/8

    ANDROID BLOGGER-BLOGSPOT CHUYN TON HC

    EBOOK GAME GIO DC HIU TON HC

    HI P HI P LATEX HI P TIN

    HI P TON KHC KHM PH

    KIN THC CNG NGH KIN THC THPT LATEX

    LINKS LINUX LI LATEX MATH2IT OSX

    PHN MM TEX CHUYN NGNH TEXTIPS

    TH THUT IT TON TON CAO CP TON S CP

    TI SAO T HC LATEX THI VUI

    To phn trang c nh s cho blogger 3 hours ago

    Ti liu min ph

    Bn inh Anh Thi cho mnh hi thm ciny na nh !! hjhj trn trang ch blogbi ng n c b...

    To phn trang c nh s cho blogger 12 hours

    ago

    inh Anh Thi

    Hix, mnh cng nh mua n bn, mnhkhng r bn i, thng th bn nn hicng ty bn tn min...

    To phn trang c nh s cho blogger 1 day ago

    Theo di qua email

    Emailcabn... SUBMIT

    Chuyn mc

    2012 Math2IT | Thit k bi Template Trackers | Chnh sa bi inh Anh Thi