Problem Sheets and Demo Lectures

No.: . Date: 1-2 / ,-o / 14

€{nN?aoL Mian*ptnr,vafcs , ?rob!-on k* L


t a) Audoul:fvw n4ldfiu ?n ?gtbt .row ls,, Ub,uvt6

tLPM?
u (s, Z ) ( o, o) (r.z,r) ( o, o)
O (o, o) (z,Z) (o, o) (r.+. r'e;
? (r, tjl) (o,o) (o,o) (r:,o)
)np (o,o) (t,g,t-hy (o,o) (r,o)

@ ,Jo dt,vbwL br- ywvwb<n ?n e4d/1 col,w,rt+ h- VDw



L fZ P lrlP
1.2
1.1 u (i, Z) [o,o) (r T) tCI, o)
aL
L- P D o) Q,?)
(0, (o,o) l-+ r.E)
o p {r,g\ (o,o) {0, (0, o)
O T\,tP {0, o) {,r-6 ,+
) {o,o) (0, o)


Pure lva/h r,ti,,libn-a aYe (u, t)^ a.^tt ( o,

L) qya I^^k uafuuvil *il,0, clwoCc rfrtntt U sY- b
,ow
wLw w!.unvl el,wOW L E I a,,wl MP P e^ol MP Ar<.
L d.w" h- /o\N t.
WatA ra.tto,aal c,ohsmn ,^rill- elpot &l,r+ L * e
wl^bA' vow el^.angLg ut r D P Ar^rl JVtP P 44^ MA <)Ye.
^li
IfYl d,ou*, t'D- 7elPna

c) Gp"v"rt- +lAhF ru^^-art^g :


[ -!'
L IZ

^. {t (Z,z\ {0, o) .r o{t- )
t-1 D (u,u\ {-z,E) ., "?{f - f.}


O hsgu,rrv C-Olyvnu, t^a4 v'fu$l ( L_ ) t"- (L, L)

--'"' ti '-'1;

,No. Date:




,S




U:3 + OIL-
): () r 2(l- )


g,rth ll^0+ '(v LM!.

2(t- )


5 =)



hggtww row fi^Tetd. I s ( 1,- ) h- ( u,o)

0ch,r^n1 k r ,14<


L I o(l-
fL o + 3( r- )


@ e ueh ,hd re uel
3
D -_3
(_

2 3/g
= a l,rr6*ed ).larln aiJb;vp




lry#..:Eg+

, Date:




) (^) A hy,'s u qrp eo lo, t ,2 ,3, 4
g D It 5 o-S at e g () L,2 3 4\


(Ul Guu, lt^a,*
ilo= L- U wWrt W = )mn'e a/f "u{ [v,L vru
lrtg = J- b' Ue = Eob'5 %{Www
L' = l-o Ua''z(




s c '8o,^ ( b^ It Ann,s bia A be Ts Bob's bnrl)

O 1 4
--\ o { ) (o,a) Co,g) {c,.s) fo,a)
I (2,0) { I - (o,z) 1or}) t*,2\
t I (2,0) {t,o) ( ) fsrr} {orr)
3 (:, tl) I
,0) f,r:,0) f ) {u,*1
4 ( r';
) { o) f,o,o) {-t,o) {1 )


Cowtitlsr a tle }n iLx whtw b^ = be = Q

b' -- o
Ua = 2-O -2
[1g 3 3- o
L bV+ {rrr(s WVtwV g c\-dobA {/fm a, cot',l iosg , Un -- 2 0n
tNLl{ ,l .W -#,,,L Ann awl eirn ftn ZoL
Ad'rl (a: 2xO.5 = L
Ao+lAl Uq = 3,r 0-5 = 7-5
Tlltr. ga:ww tt, k oJl" hQt) la^'As &n
Ln
A 2 +
o t-g) {or?\
( t, (d,3} f flrtsi {*,Bi
(z,a) {Dst,) f CI,t} t*r\} {*,t\
t {2, a} ( r , o} fo, e.g) { s, r} {.0, r}
(2,u dr ri ) {o,o} {-o.s,o} f0,o}
4 /-
\t- o) { o) * fCI r:) (*t,a) (*1,-o's)

.^-*s i";

, No Date

aLl 4w Lr^S

(r) For Ann , bA = 2 woaLl- c{,oyrnMal.< bo =3 o\vl o\ bo \4
awl ltntw aly !4o 6d^n' dwnhakcl Lcanu+e,
at w;*d & L 2 or O ovd L or 1 a,^d 2
aa'^d
dpeg ,@+ o\ l,,ov oW htran 3 ov 4
a"(( alW- 5;,L4

6r Bob, bg= 3 ol'wnd+c ba + awt *lNr4
l^O dg,^r\fo^{i4d @ &on +1,* elyYtL re;..tstg, ag

A^t''' tdc lh&l d" \^o+ a ht. )w" 4



3 C,i, e, *t"a+


Hnoba
"{ l=!, T{ (a,<) ov- s tr)
h* k/+, (




uA A'g ^

q E S Q^



6v (e , a) tt
6r (e E) Utr
!- (t- c1
L u i_ (r- o = 0.q ^w\
\A-cL vc4^ lor ( S, e--)




?ov ( 9, S) &ta = O (t- o 0
ttg = o (1- o) = o



[rt s c Fbrm


B -C
L
l- -:!.


€ ( L-c,r -c) ( (t-c ) ,0.5)
S (r.g (t -c)) ( o 0\



#Er-{