rot-.. - · j~ j == j:to . clea-~) ja-.• ~f. uwrte .. in ?"-o./, fkre . t1-re ~f~ tuoj.#tf...
TRANSCRIPT
@ le+ 0- heMe r~a/ dud ra~ wiM W?~ed -/7> J. Then __
.~: 11 ~~}-> It p-I(H)
. . We.. ca->. ~ +!ta.f b /$ also tl J,'~'Jf..q..1 c;oe~~t frrf~. The La.r(a.a.. 'f~Q.~ ccv..be clef~
A-:dtfo4 In fcw1-icJfJN', art f£'€ tftJ-CtL i rftAs, 01" () -lm>1~
4 = I'd
We ftave +he fo/k.,,~
Theorem CWe-ifzeMbi'c1 r~) FlY> rot-.. f, flJelare .
/J. f = hi; -== - 2J f1e·rJ;·f
)n ~e-ra.I, we ~ f£~ r flcwins . . A-=-- ~ v,: Vi -t QtWVQ.iure .-ftwm s
u;/uch. is o.lso cal/-e.e! W~ize~.,;ck r/7llt(q ,
· 7k.s We- can /PI7. o~ -Me ~dt' it'+o ct
d9hSeJy rJ.-ef'lIeJ j) gelf -aefm+ ~~,
ReoJl -Hza.f ~ ~8'Nlfn. LI ,'s self-afd ,1'/Ymn (<1) = ~ (LJii)
ant{ <LJf, ~> -=-(f~6J/
F~ f, g E ik..(A).
/n ~dihz~/ tltnJys/s, 4e hAA? fie;:fh,.o(f ~
, "--./
[;'udt ~ ~rr A- ,'S illj'acfwld ·!-fieJ)MJ.ld L?/aciOln ~+ry-. . .
As a", e:erci'ses, .1Ve t~ -f/.~-f tYn~ any . 'fI1PKItf 10/, L Ii flh'fMhf C r c-l-t07l ~-I ~e cdts fa.-d:
TA~: Lef /9 ~e.. de 'J),rlc~ief e~I'~if 7/.e Lty>ta.eJo.-ra 4. A !/lIndu..,., f,' s ('al/~ A ~ hO/r~c ~ /fffH~lA) ~ Af==o. /f f E L? (H) +hen f t's a C6J1S~+·I
prGof f· The ky f~+ is -fho.-f Q( f~f, f) = ~cr~ a{ >=0
Tlw.s us;~ -Me Same- ?nei-k/ a" tr ,f '1.is C(Jn~~f·
fMion S«.ch tk-l-J Cf eO
.Th8tl hf -I/,e Jt?f:-h~o f AI ,M hQrlL ... rll1(fH 'f) I~ .- ~ A, ..J(f-rey;f .
HnAfe;~, If (,.Ie fcJe 4e f'rd- ~eky -frn.~ - /Ne rJd
!,:;S Cf+~J~f fA,-£) ~co No-le +h.q,+ :.r .
J0f+J,v =0
@]J. - _. -
as ~II.
L(~r J!lf t:.. eLl) . f;t J~
By (4), we ~s+ have . --f
. ftklJVrls' = d~=(r [vi 1
T~
J~ J == j:to clea- ~) Ja-
.• ~f UWrte .. in ?"-o./, fkre ~f~ tuoJ.#tf 11-/t1-re
- o. 8uf by tl .. .;-h~ i Sew/.. fie Se+
{gfr~/ fJ-J{d)~oJ
1$ o-f -Z.e-rfJ ?nea.Sure. Us;,'!.? ~ ~rw! Ct1Yer-;'1feeLJre, /AI'e. cam fr~ file .ram e 'l'eSIA-!+.
As a.n. Off"caf,'(/1l. l' the Ilbt!le Co -Otreo. !U>-1f/.U'/a..) (Ale rve 1I.e {o/ko i' reS~ (pI sekiu ill~udi-r'
S./,o/er ih(!.-r-a.kf;' Lei H be (L Culnffid 1JI.am'f/1 W1'f/,. boun/()./V'1' Th~ there is a. CDn~~f C >0 Slie~ ~
:£1
C ~ tfJ-li) 11 ~ f,. (qll
frrr ~ sm.~fJ. -fUPlC~ f/~~ "" 0 (J) - CfilC!i!';'" ) Q'Y' Tf ~6 rJ;V~ C6lIddlDJ-t).
ISo~r",e.-b-ic iheJu.a!ry Lei Jl be. a k~ ,;,. t1 , JL cc H . 7A:.,. ~ is 4 0d1t..~+ iltrJreJe...-f fo n f u..c~ flw.+
~ C J;o/{JL) n ~ II~ (dIG)
@ . Ai- 1M ~e - Side- 1 iJe i;ylica-tlo...was ekew-; a.SSlt;IIti'J
,-------,,' -the Sobo/e,v- iheju.aJy , tf ~ le-!
J I Ir -€oil ~ dcx, (}JL) . ~ £. if (x)::= fi.;).A,) Xf.U, dtXJ d{l)~ E
. 0 ~1't/r wise. TLm USi'!j tie So/,o l-w 1I1ejuq)/y, #.e- ,'Sot er }1lefri c.
ilteJU-aJr-y f f~ ~ £1 INhj ~ 7 o· ..
In. O't'dfl'r. to r-ove-lkf fhe IS0l*"mefn'c ihe!~~?;, iWl-f lies +he ~ 'kfer rKeiullFl-ly, /)Ie. use- fhe CP -~'fr.llfl(,.; We a.SS~'f fha.f f ~t5, 7km, ...
~ Ivf/ = 1 ,4-r.e" (f~ (]-) Jrr()O
We. a,ls t> ha.ve. J~ IfrR = foo v./( f~>).) vA
:=: ?/'YI-/ j ()O /Iof (1)0-) (J'-f!rcia
. Ub'I/rj tf,e isorrme -h-I L l),ey i<Ql7 ' we AtWe. ... . .ltv!/ =-100
Area. Cf=o-) ./(J'-~ ctlJortf{f>a-j~..
r4s III ""J"t- .f-o r o ~ -Me fo/'41e.- iher4.''i;Y' ~ r. ned. 1b f'fdlle flllff ..
1000 v~(f >q-) J!i! da--- >..- C rr. 00v~ CI>o-) 6"" Jktlu-) "-;.'
w~ fe-f
Theorem ccy Fv; V;rlcAle-f cmzrJjf.6n / we Aa.E.. ), ~ ~ hV
Frrr ;V~ t!bndL'-Il~
FilloJ!r I .t,w- frM- a reslJ,,-/+ wA.:cIt ir tuel/ ~l>4't<)h t,.lCa-n If reo.di't be. ro/ ih Ihe !i~. ..
Th~ Lef H i.e tl. CD7nftUf ~fl/ tu-e'h{ ~ Srntn#' ~jtN1-r- Le+ <
fit == in f- WI }1=0 f£'
