covet}
wah 4
19) shes
8 akven, BRS
P= @stra “yo EC oCOsy nd) J
ese, w= eASHHY~Y ye EROSY HHL
Se aresyt, ays dreosy |
fnee, Be = we
$0 ze 2 consexvos*ve:-
To Fd he ceaflorr - polenllfo2 ran fon we
hove. ¥
el = VE
7 (sma tlereay-aayh= Katy dh
compoxiny. Ghe -boIh seles we hove,
Rca esting “di, fy a eheasy- ea,
q
) ae = cos {—-n- 2,
e|
2
addloso9?ng- on bodh Red tee Ge Sx) PrreFomeey
i = sing er ow APR
Q
ae We’
a FF Sages —In+ Ca)
Aepogn draxe tore. APeREXCA GDR —boBh
2 = cosy % +¢4 CY)
P Mheasy-m-A= coset dew)
gi ced) ee
Apna epfeowos.ny on beh ole wrroehy? pos tio |
fees) rq = fy 5 Gea) = TALE
pad ORs vole fn a9 WU), we hove,
Fa Syd eYnrag tc.
Delesmine nv Sseosoes. pollen Fos
eee yoclow FRetol + fa Ry 80 ae she yoko
od F=< 2099 tayr y YR, Bott t32AD +
conssryolin @ » 9a Ra ord Mad om eons eso
Funckioa fot Fe ‘
neve,
w= ation Fe
jp EMAL pestitseh
Bars wl
al ee, ©
+ pp a BA. Sos
ee , 2
Pond = = 40
WH = B C20Wd4 242) =O 5 Bos aad PtOs Wwe _Shooh,
9 °
& tude 9 ane. ‘edleoros. no2ds whore c% Ihe
heh Re =cosP pyoaky = Sing Fox o<9sTT
2) okt
0.
j F (eA), ¥P)) Shc).
6
v7
2 J cog Sng: 3h) AL
o
nea) = ~ sind
doar
ala” Ceco
where MCe)= plate
= fats =
cosh Stab. Gf Sea JB
= fear astra &
si | arte err
0°
tT
= di codG- sing. dg
el
0 A a mmm
ir
ae 4
5 wf aCdA) sel ee of
ry we p -shO-da=dr
=~ fre - RAK 9 fing Ager
ei | e 5 shen g= ay
5 = Srap- y3) aA =cosg=t
of — > whon Q=
rs, = ECU) = ae, ea | B Evatuole ee Pe Ca)? +OIE)D ~ Re Se one.
ae cove der porcnmelefeorry by o xX ON) ye a, 22g
Foy o<0<\
inal Rven, fe cat
is abe = fe ayty carey’ Anna [[ead toes
22) 8 Bacaaze)d- oR
Gude
SE
= aytS2e432-1
2 + ss op) D+ (x anayd safe
+ aRtrQy de
= [es WIG] [28 ce
z
=| {oe 20) 4 (uP) tC.) of ae
!
J (6+ ea 2) oo = 4 teal) +8 goed) SCE)
4&5
| >t
Jove t8One
30
en pte nog Phe shope of She. ove
1 nafRS02 , I=CoP,, z= cosh For 04G< 1 FF ane
Pre. hos Phe demsi®4 Cemiy)2) ent 2. pb Onc
pnd Cae) -wha® “Ws She mOss%
as sont '
weve GOMES = WB
= sth, {=cosQ, wecost afer este &
sod /
moss(ea'y = f eens) dco) Ae
6
ei mye dc) aU
> Fe
2 } meet. costcosh- 2) Ag
‘ egy reserafel oy ;
wh
whese. st) i
= AaPrQ ay 2H)
= cacoshQ + sPrdXQ + Png © cond f asiord
C008 kore
= Ate
Nod .
‘l Sop -cos PE dt
fon ®J ekng.cord df
> af Sad. ord. de Sn ae
pad Coo = AL
a ae vi
ce > sfod dg = do
= aX da he > Sagd@ = - le
( when L=0
\ Ka op
=a [dx when @ = SO TT
: een}
= o2.| ard
eal
= 3(us- cs)
~3(C1-e9)
ne = A.
= a(ith 5 oF Ghe re Indoor ag
YW Dotard?on ond proper?as
‘ ‘i on gho sme0kh “VES tgp Pee
equation mach) pls IE 2h) ) Gher are re tnderred
, ee ater BY conan) ds hs, LEC a as,
oF F Ove C
* coostord eulo- ( wid - {FAS
Sue culos ([6Aa) dS = [Aids t (AS »
{lates = [RS t (ee
©
we) DEWRon of woRe. 9s a Fine
West 70
9,
Qwovetey on pcurve
“the. wos done on a posdfele
ce fnstde ga pone Frac rerresenfed asx voclor FPotoh
F % dhe ufhe indeavol of F onc.
(8) Fundamonfok escoms of are Paseasok Colerr
sek ‘c' ben floce we gmmnGh cusve — porxsomeleraac
| ty phe. veckow -Faneffon RCD), as9Kb ©
vecgor Freta \whfch fs conQPnuows on'e!
F bem
Ae ecg seotor posenfos puncte saudi hod
we =F 9her
J a dR = FCS)- FCP)
where. p onol- ove Qhe eral pon of are curved’
(8) deF0 oF canceswove yeckor FPatoh. x
A vedo Pod Femyyz) = conser + NC 2) 9 EPCHA A
fs concesvoe We PF
am,
pat mee oak aw =
(18) andependenf: of pogh . .
the ne Taflearod (F2-dR ts Spdepeaden® of padh. tr ow
9 Con OTE For ‘pny duo forms poad@ tno ghe skne
Fafeoros nfong ; ovary . proceukse smooth’. curve. fn’ From
P90 hos Ghe some value ond fs derfned by.
[Pak Fle)~ Fa)
(W) geeeng Bheovems deffn?2tbn :
scons gnentom sGoles grog She afne. “Snearot enuos fo
dhe double. Hieoros oF ahs pandas overs he encloseal_
: septon. + i :
ad 2 greens ghowwems' % Qruc For She. sfne
zi Fleeo$ | Cdn at) whexe 0% Dhe chosoa ae
| oat Gho® Bhe’ auhpse. . hing BPE, we eOS
COX nob . x
sof i
ecomeleee dhe euspse. by m= ncoshy. 4 =b8t09, osdey
anon *dQr {dor '
= peosQc beostda)— bstae C-astn@d 2) = ab Cc0s2-+srAdug.
aba&
ea Cra ~ yd)
aA
bop
ait Someie t
+f phaten Labi ae sfob[e yt
6 6 :
= -LobCan-o) = Tab .
Inhooreoh ,
selenene” fleceutse. gmooh curve gho® fe paameb Pao
sek yoo ore punedfor RCD) » ase xh and per Foe wm -
‘auoes onc x
by. ghe- . 2
Catol , whteh fs. condi t Q
fancion Sach oho. F= Vf, 2hen
ee em K Seo
F-dR= §CO)- FCP) ey
woke GEL) onl P= RON), ave and PALS of <
vi Feme) berm gundlfoa oF Shoe vortinblos , such Ghat
E= vFCH Hz)
suppose. ROE ead HOD 422K ord Lol Kbe the,
compose, punesion’ : Woe
Ca) = FLCC), 4c), =H]
then bt chofa whe, AO _ 3F_ a
de ee 4p RE dy OF D2
fences fF ARe veda me BET AT og tee 3a
| lon :
| Yd Qoh.2 ond prove pundomenQad gheovems’ of afne, [em x bya BE de
| egaesye
fe
Sy
om ‘
| Pade AE pale
i
b
= | Aiet? ete)
é
<= Gb) ~ aco) 1 by fuadoimerhoL Bhessee of colle bud
= Fach) yeh) , 20d | — P [cenco) yea 200] 1 bef subs elk
sal F Lecb5| - FRCS |
= &® — Fe)
Hence. Proved)
Show PhoG.d —YInrnt{ _
, woth SOT where. .¢ % Qhe:
Precenks.e. send 0h Towdon cuvve enchos?ng - ahe. oxfein co)
Ae wou )= ot
+ aety L
Ney) = ’ @
ott
awe Sema dw es AG)
“SRY cay NS
wel cy be w efacle —cenfbroal “09 phe. oxfeen
wh dA % go smodA. GhOR Bho eALixe eas,
% corflefneal ne onck sol Ribe she wogton been
he cuwve © omck dhe chwle C, AS showa SF Rawre ,
we «now Gho& BY - dy “hvouah: .
on” SY sey RN
CFrce KR de M09 condo n@ he oy%”,
we oieOY daodaad i) Sek rents 4 x
feet AES IE),
Gh ok 4 ay aS) eeu
fa ott oe
fumes} Eage Le
dee
: counflas Socnws® fnsfel
sroveuredl gh e. veste oF ‘he,
Cc by _ ending. abe skh e
whore —cy %5 chal Sele C 2
OR choateise + %s ovesussds, we con FO
atven j8ne Ingegeos oboud dhe exsve
% he
te ee fomnathe -b4
Pe EME NAG» FOS OL OAT
ond Fond oho : ah 4g
mudetndd 7 esp. Ceestng do) + rensec scasods)
4 Ta WACostO ae
‘jj eee de =f do
cs oysne}
rei" = Can-o) = amt
I
| ches aydoeody of nadetndy me vl
| (fae aoe ty EE oe )
Vy evotuohe ghe skne — enlonros.-
oF dhe sfne segment ¢,
Ids whore, Gcontsg-
by She ppxdPon
t Fron
3:3) 9000/0) Fo uowedk
of curve a 16} =
seat atl betACoso)ondeasy)
| ee ar . ogee
| atoll e453 33)
| MRO on dy EO
| the powromelisfe egy org
| EN teny
wey Ye =a 2.C304 )
9 oaSeS = ad
y-3
mats ao
> Ke £
BARRE EE oo EF
mpage et Ge seg fp nF
aomerk 3 (= St Fr, lt
ax Aalgy= 1, gleay=|
ds = @feherays [tT = Fae
when n=-3 , Q=0
when n= Y) $a-3 ,
hence, pata SagenoR oF FOuY)= mt
ie ds = [ee 9 (342) rae
i)
overs a, Oy
a q-3G¢--39- eirae
=
= , Care 8) J dt
<3
3 & e| (a- da = ay 98 de
2? dH. gdb
ae
5 Fi when C229
2% b . Be = =
| syle veng «he =|
: ek PSS EUiee ys
= Ma “gn. dae
at 3 \
ge. 2
ye)
We)
thys ghe sine Mrdeavat ovesé! 5 efvon bY guy
J vads rss \ ny ds
ce ¥
"
= -AVRt ECS)
2, or on consosva ive. 0
Pheswers fg gore Foe ghe sine &
(we) jour Ghod Che. O8eens
nd 0.85 dhe choseaol padh .
|
ndenros.. (Adee nd) whose :
argh evofuole She fne *afenros :
hxoOI . the, extve @ consksP of she ae fin
fr ONE Cy paghC From Cry) 200110), 2 |
me
i
'
|
fouswed be sombrero Co From
Cly0) bow doco), Sa Say mo
we poromesfze each of ghese
Cys eG YER Ath @Ky
dna d@ dy =o :
he HE OSH (esinu os
ecu) = ~adtnd
now we apply ee
{ead {feo ROOM
ox \§ ad
= ay of sont cFrole)
e anceT oy)
ee TT i
8
oe choseck pale An 'Ghe. phone, Gerd Bre worn done
by oo opseck: tov 080% = C. 8p Be Forca. Fx
oe Foe (red + 2crdy ~ sPaa) F
aay work done. Ws gren by Qhelor)
meee fnhessoh gf F:dR Mho® F 2s
con binnons EFeconioble on Lhe
sogton D erclascal by ‘c’ ond sfnc@ coed
v mpd; Poh
os simp puke WOM OW” poafialy. <= CueCuRT
“tented houndore: Cromety Cc) th ¢
dhooxem 0%. sated The hafomed’s of greens
we. pack — ghoG.
“ a i J FB Canty wat sina) ~ 2 coat
Sowa: say) dA = al] ny dy claw
Oe
4 pot ol :
: {ene . ens
\
A Sas do 3
af: tad- ns! =
conQinnons SY AtProren kage
ong g-hoasem
ey VEL aw);
pene
we we oreers Gh” fo ovoluae rR ee
vot Tye gho — dhe boundary ce yordan AVE ooh |
a (Bd EvooG® Bho sunfoCe “MPEDWL(fyds — () nd EPA ADSS. BFW ownage
whoSe OOM) 2= A220 IN op ts dor gcmay2) = 2 % Bre. shore.
Sts grod pardon’ of she plone aaestheve. 2 =Codenby2ilia,
BH-BUt 256 DhoO sas’ ver he uch
swore R. ASH £3, ASI<3. ae
oe dene
FQ nche Oho Dheea” of she Phone
con be widen og 2 =FCout) where,
Fond) = 6-ant3ayd oe,
E,(nt) = “a. Sefeee. | OVEN
FyOray'= 3 so hod
as [See aA Ne
= Jeptoxrtl aA
af if 3ds= f [foe aa2-3ny) Jere
(The rel
[ame ok 2 hes
={s EXC caine tn a sf aoe Beda pater
dow aa
og ffemsidor « : ef peas |/ a
tester dete = oe
= Esme ffndd Liteon PE
ay} dy ds i a Erk =A
= bf an Rr 2 Ww
2 map he “I oe Tea
= Oy I ' c
a a did}
= 6] 9-2) dow “He . ‘
a
4 cane] REET . Is i
2K C-2) "eb 1 eearaa a ator
7 ee “eePrYesenh gho.nren
ae Ca) = TT + OF 0 checle oF
Suorpop? WC
sont, orth Re I ;
te cong touors vero frald ieee
fF Eo pSmenbs have. conDinuoes Wey
rege dgrtiaewes | Th me oF P
ol ca 0 D wher
fprnns =e
3
5 & 648 oderaord,
i % ghe,
wh ec Doe * pfovol For ohe
suxfole 5,
aire neh — teh S$ be ow gochos( os "] Cyostioge.
She.
Suxfocd dottnedt pvomeltcou]
YE Rew) = Qudwy® tCv-au) 3 4LUtIK
FoY oxadl, o [ Fema) F008) [Ke ten
wean,
Fos) = FCed)
(ard) cid) ) ‘)
con 4005
tema F Ps conffnuors of1Co,0) in es :?F
resuobe {Flas 4 dy where a5 ate, YW asd!
GES i ; et Ue are Cee)
ipo ~ coger i * ae
i gay age Oe) se oleae Bee 2.
pare to la eter
“fer Senda |g Ee Ju
2) gon da a . ° ‘
se ajine ape RAYCOM AS
= ~ON=6, | 9 ¢
ace cam tae
x ;
* forwas dn Cs nae :
i) We
fo)
= Popeye Saja
Y = \- (costh- ces ‘ :
+ mC 6-0) dm cy Coo o- i )
» Ef oben wa"
‘
et pepe [3-8 fopag
G bey (8 J Wad
Arti. 2 tia
(by nis fofarreasion sh .
: If why d din bY
oy
\
- YR cay Xu Ry) ay
ahs “A BAY Sey ot
{| op Cuy Dmaysdmal. aya Bh pe
C “Seg —0 J ie eae
| voume, oF Debra.
chodvon TC founded by She
phone
neat +3276 and ahe
-Bt4 + BI na co-ecd inode ptoned
, neo, 70 ender oT «
4453 ¢ cosh
{ =o
i
et 1
oven ont 3256
od ,
y» B2F 6 eH IM
zak (od)
ee Zao” '
amr =
Pp YEeRD a
pug 40) 270 ; 7
QREG
nod smi9S 05e_
one 3)
6S 4 S6-OK
oft (Gna:
ve “Mffay hae y
Grae)
+ “ISS “ets,
oO
GH kes
“Ft =| Pe a
6 >
62% |
. |
2K
UE saan
3 / J CG-am-a . Uy fe BURA 1M rant) pie, PIM ARS
= ffencee) -eo sn
: 2
UAT ir = TEI NH FUN DE
gfe ae
°
. | fie - mottos | da
ig
N
ide
a
ie
Av
\'
!
oe
op
26
&
Ne Fae Teer dow
o
= 5 (remy) es
(3- agen
~ 3 wy
= [% pak 4e8 “2
®
=e Q-attat
nee. Ore vduwe of ddlawhodran 85 6 cuble unSQ i» ;
(os8) eos Sam so9tco Stee), 9 © ¥e one yeotins 9
| evaduog e, 4 { ee ig nod onghe 9 bol? py ')
ty oye voxPas “Fromm 1+ Casg
} : ecoiase Bo polar * re coesPaSA) oe stoso (greedy
©) fgcoxdlnodo Ste ares oof 2
a fh ghe. om FOr
Se. wepfor of tndeorofor 9 $5 SR Ra lt ones
Ore sok of oud (oihascnrt) hs
59> for coch potngs % tn he ~ 5
fndesnot pe aj varies From eset foe
M5090 Y= fiat nee Cmte}
gy eueha, sO)! ifs de,= Jem scdvdo
2 abe ant e oO) .
weteyne= \ P arose
ants fe dha ean of ov eee oF . 19
xodies a congeed 09 Ch), es ay
F¥a, Degree Ie on hoc
Ay ate pt tnd 3050 do
ihe cos”
| eds Seam sheers 4e0%8
es
whe coe
3 C= 28
TER posox = Oe se ®
weaton fn wihtch ae s
erom oGe AMSO + oses WTR = a (_seos0 {1 1¢056) flo
J Pye dydnw
fs she
=f JERR AA “fe ae
x 30D
“J i (esiro) “Csdrd)
° ns ve (a seco) dé
Fy sind A
6 ci” : §
LJ 16 eos! Nee, e = - in cocoa
4 het] ay a Ue - nigerian
es :
Se. : (
; * : - asoC art) —
i Rion puestTeg,
Ywomsode | {f22I3e™ dv.
1
Fycawae ASE
om "
= at de ds ’ 7
eee Jpg tee
5
the ewan’ Ts Oven by Aha Hese O wites f ‘ =
eo IO O
| Ox \
oy e090) de °
alt $22) é ak 7 fe ar odyye. coo |do
en fo ~ S038] 4 ‘ ° S
ax} ~ Eppa
fS-28)-Co BY - aT -
= [G-a) -Ol- ~ 8° 08 do.
wey Mau - ( . 5 on
(es) Repion—R-—on-crxeQba—bet O=ee0
evosunte (fA da hese. oS he
sexfon Tahog sey Srstde she
ele = 36000 onc cus Pde
uae cordtoP w= (tease
ANS
Ya Bose, THI tCOsd
p acoso = 1tcosd
2 n0SO = * (eacasion 5") ts
. Le 11) detec
die
* —
6
Hsien
= jet) ard
e| ds= 61817 3.
= OC amr) = 1a AT oa
A Gae— to) dy
o
= [ures
seb PER
neato
iF - fesnwe—= [re
. : - fe=5- ,
BoE OM EA, GE et
FH 00. Cay, oy ARB EG
FiJeacguy” E®
" = AAR =T1LO +
Fe ogcayindy = 7
Now ep gansen® plone fs
(2-8 Sem-3)-$8C4= 4)
> GCr-3) +8) - res) |
iQ 2
ORad 6 obsolle enPromn ef che,
Parador . Font) = ed over She
ase amt 2S 1
Bien Fady=
arg 2
Rood) = e 12% = rae
Dn 2
Fycmay= aks el = rae ey
aye
ok a8
qhe iafeos. potag faside She
Dist:
Jokes enamfhe Phe. vole of
Foon she boundord cunve
ndaytet > ye bem
pugatng | gris vole. on afvar
Funegioa' .
; pea) = ee
omtcttntan)
pede treet
> e
ee for 14x41 gre. poiags on Ire phere
fy
| by ALE & Us rhe eg dhe % . clotack’ 2.0 the
| SSnead ge find Ihe sorgagd end Tot) ¢ Cod"),
ti meHasd’ Yalue of Fenyro™ | \ ae OCaryz) FS % FOP oF Oh
Saco As unert Por-tS*Sl gone may tz=S Shon 2= Sm-ay
ia ~ i ord > thon DfeDone@ FO PIDG
fl tyro pate fs
| gfioce amit Pe ofwous avewohe de |e © PA Caza,
Amro pp ystory yee l 2 porte: 2. ome
| Th oho aa oozes. otras I Gard Ewa “sit
ore sashend of pofef2ing oF we
» Corl) ond Coy"\) | nintetze, 7
ctocrtng gne RS FE 1 Femayed2 = orcas Clmaays
Feronig) = @SPr Fld) = dm ad jn-ay)
(qu) F000) = 2= | = umta{-2=9 tH)
leu) Geert) = teemPanain) — Eycaaay = acaraye “AC A)
ory Featyeele MN) | 2 umpleydo=0 -Q)
(9) £ C10) =@ Croximum), aad) =
Cue) fewrec 1) FnlSV= A
— Wes . ° Fy = 10
Loptoce eYlo ~ Rye
Tek FCM) define. & Fueeion. — seyvSng, aaptsy ond ogf(2) we hove.
ckah conGemeus 189 ancl onc. ee ean
poxd fos. doseve9tves ghen. dhe.
| enplocton of F PS
| gap = 9 IF
= SE y De 4 AE
Sr Morte.
= fant Fay the, ,
| THE OP PE HH 24 bende ,
|) Lopdoce’s oat ,
FE Fema) 5 con@ineers over”
pecDorgulor’ pedion re 1
Te where ocmsh ondCSy coh
Shon
[fresarder= PP rena) anal
, ke wh
a [eee '
Matieg-lOE
ay ey
-6y1B=0
a ey e8 ye Bek
peer eae
on mee
peld
e
u99%a dese. vosKe Co eVPA) we
hove.
Pe Ob Ste hay
= (Bs Get Cea
~ [eye Cony t CBS
. ast sanss =i ge
a
ee Bod one. * oxen oF ane nepPon ,
phart YE Coen ard 4° ston
q 4 Hagan) ~Ca.orace)] Danae HnSoOrOk ams If
i drole. tndoarod,”
6
- boy ufird ©
Fey see re “toons. =
= % Seahe. “ferres—
8° i ~Roray don
OY a tedeoned. 9 ) er We
oY b peat) n
ic) anol } = Jp! [esha Som ens {
o 8 \ (Cane Oh J - Ginores) |
2 a = al 2 { (
Tee eg (ES
Senin Cabal Oe
5. bpd QI |
~ fer) Gr rs) 1 ; ea
<1) = £6) = 1
2 :
(eer Cx
eet.
= as hoe * tee.
- °. Lanta
t
2023
- kt BONS. rh) ee enlorxod
ae
~ tbat] [beds
< I+ abs O. sin,
| -l- a cas
. wre a8
| MM 3 = Ey oe
HB San
Qa
|. i {
ore io “J (.casm Bern din
x
7 chim cos] i
°
SASS) SCs
=Cetbay= 58 eet
2
rhe. acobfon °, *
perl) 2, Con) Hem)
aw) (
®
tw) 3 cbi)
=[oF| deb.
becouse. eb>g we hove
ond per oF & 85 diven
Jp aiden =f abdudv
( a “ay dudy
soba
= obf noe]
mast 67s 1c Prealor oF podius4,
[ob| ab
4 g5 COPA B- ers rer al
at dydn where
2 %s ohne P
on
Sa Sne. my
en,
AR, OUhA
TF 9d subsotouge,
= Lonel cooTd nage
ARE ETL compule din
Da Vs mode. the
MEM 06 dhe MWe dro sunBesD
fe Ghe cubsohIuVion ,
a a
j - wondy Je. obtain
| m= Aeuavy beds cuen’
ond. Qhe NPAC)
\Tocobfor PF,
‘ cs ada
} Bee =| So) Baty
Races) Bes)
pti a .
aires \- Jes
NOW erofuole dhe, Sn eqsog
J (ERS aad,
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