Chap-05-solutions-ex-5-1-method.pdf

1

>1.

.

D Q3._.i)‘»..W"r\.l_\/‘\’\Q~/~v~j\V~’,)

CW

%

M

/\

<

N [)

am:

=

0

~-~-——-

=

0

~._.________@

M

~

\*

LL);

X

n\4am_9J>@i;2L9 “\/\€\'\"|Q<\

_,m;W..J.h»~..~J~

°~-1 + ‘PL

‘J

T,

(

Q)

TLUU

Qqg-“A

'

I

‘g A

1

I

1: -3.

FAn~q®

Q:

w:'»»® Q;K-

I

“TM;

0

-0L\¢,\ -\-0\\\ru=

can

°~\

\

»

1):

*~

0.

C5 21;}-.


4‘

5

W1»

Juod-J»

1».

.;

= Q

‘AI;

ck-.iu~“;w\...,i

mu»

‘W

W»

Bu

(KL

'>-Q-.,;g\\o@m<»~1\>\

1»!§k-

wmrw '

)5»

m

W

L.x‘»\1AJ‘-L»

»»,.“\»0s1-Mm,

Pvh

:0

(X\\3,__-(1L\p|

a-\-

0

)~<MJ>

Tb»

~\

d\Ju\Mv;MMk

s%§*'?'1

C“""(J"‘*"/‘--\J‘~-\»-_l!-F,

--1‘

<+/\~<*’%v~\

1-

¢\3»;M ,

m

c..»"<»b,.

W»

-1\#~+ \>\ o\‘w\

01* \_._t

U0)

d.»@

@»~@~@ 1

1

hIC_5__\M)C_L

=

-i 1

4‘

0

»-W-~~»——~-@

'°.

--~———~"‘®

\9

.\3'\lv\/\

-"

3

O.;C3..C1.1,(.;__

Qgb} -¢\;\;\_

4

(Q ‘

.

'#C_"$

—

»-----~~-

£9

r

+~

‘u\C}..\1}'(.\_ V

_¢\ ‘

bl‘)

...i;1

_____________,____________

+

3

+ B1‘) ‘F

.

5

‘<\-vw¢

\\~v=1

@\r.~

\

<----—--———--'*"""‘“"'“‘

0'~\.\)'§--‘-\"5,\'h..

.1

0~|.C1,u;-wiltc-x___‘

°\;_‘n;

-

(7‘~1\>L

1

\-

Anioi

"

LA

\:¢J.,...»,

_._.m__..,..._ Qya,‘b 1—

(\ 1 ‘g;

(9 0qC;_.0\ Q (.. _.__.____1_1_)

;\-\

\>":a_§-1,..\s>'y,C\_

,

L\17_

‘

\, § +

‘

'_

+ C‘

Q1-\>1-°\3\ox

*

0

_

M».

‘-5'\\k\>1_C.;..\>"5(1_)__\:|(Q1Q'; .._¢\3v(1‘) 4.

\_

M,

;._;¢

'v> J>wL¢\

lkk

-

K0.1\;;Q.o,;\)1\

o

TS‘-

4

CM»,;J,)c»,

C_\

J\M4,m..u.

mp.

C.L~....w5,_J..,.

__

*1

Q-1

ox"

AMAB.

-.‘_

V

+4 M~v~+>%;»~~1~= Fn33'*\#-A-;-~j

:1) UM

Awu.

0U\JL \J¢1Ul».~.IL

-{

\’l'1.!-|u\.l»-

MQ.

id.»

l~q,.~x....)<

4;

dwiv-v~1-.,..,<)<

<5».

T*-~..»,‘>.4v.

in

d¢12»'m;w..._x.,

,3

Tb.

‘

. A

‘

L

;‘§!\) ‘Nu. WA

\»\\>M'§

€F»~>-\»¢‘\.~..\

~,;>Q

9%

Hm-3

M QJ) .,%

“kw-.\

-a

9%

J~..w>

-»

<=~

-A.

--

—

C.9,....,_~,.:>

M

in \:<>.L.1

‘Jr

A

‘

--Q.

'\~< Em»

K»

o~ 11»-M

3%»

J1-Mu

~‘~

\1o.Q4.1 '

/'>‘¢-°-A

°>

.

.

.

Mm.

31*»

C09-'-ks-v\\-J)

o~_d1-iu/-~AM.....a‘<

QJWMM

Odd,

1»

4

(__‘;w\.

rm

m

,

<1-kw.“

W1

M;

1'3-4

-}L'qLu)»

#4.”;-Ma

uxbw;-MM: k\1:‘>

vi.

Q\:~u/vw \,j

\..~»mA

A

J\~\.w\.

JxJZ.|jv\

wl

U")

‘Q,

‘

31*»-

Q-QMM“ *“~I~

<

’

"W

"‘~

I

1

5l

L

(v .1.)

‘I

~11-;_

cl,»

‘FLU-..~.1,._i;

d\Li?LI\,4,“_§_~._4-,__Ak

bu :lJLL

on

C\

;

£15-t-§L.

CL.

<\1

h*/‘i=1;

C1

COlS1'\A/v\/\'Y\

’

»\

*5;

A

Q94: .,‘_,\_g' x K1);

“*1

'\ ‘ml

/‘hi-'”~\

\

_<

“K

IO“

bx

C\

Q\

i\

C-

QL

Bk

Cl

an.

{,1

C}

,

bx

C,‘

41}

-{M3

Q]

2.:

n.

J> c0.1.a)\.

C,‘/\‘\/*3

-‘C9

t

Q.-9,-\

u UJF

)2 ow-. 1'.

~{_

'\‘\ wk

4%

“Q1-JL

b\*\-\'-\

R

O\.

_/$J~.b-~\

“

A

A. Lg

0.

,

O

“£1/\.

)\-0 DJ

V (1-QAAJL

Hun.

/\

\-v\..~.U1$‘,1.L

“Q

il)\-

-

°‘ Q

c-_

JR.

V‘

M

»._1

iitlv--{,/X3

(11

.

.---i.._____.._..-—---____ ~

'.’_\_é-_>_+§1:.-_-

\-it

:1--.

¢-1(-1&1.-§*.>"~.

Q1_\

a"l.I"-

be.

0.

2

**“\n

v\_

L\

O\.~\

\

Ba

QfQ,,W

,)\,lu_

A

,_£

,9.-.0,

m

,

’- 2.94.-JJL~j

1*-‘((5

J\[email protected]~,

-

(A

‘L5

,

u

4

QILWMW,

On.

.

-(“ax

OK

:

(\‘)

eQ(~v_Ll)

Jx

<1“

uh;

.4

A

0».

.P\().

‘

7'

Qi\AL\

1.

0.45 ALL;

‘\' ‘I-Kl P‘i.1. “P ’\'

“L5

—

-

~

~

-_—.-\~ °‘~L1\P\i_"n

*4

Qwx

*’J\¢-.»\.A-5

L

{{4;\.O\MAi M5,

,“_

Th

Q

Q

<=\=1¢-4»;

‘.\\('-far-’\

£‘i£‘.&.

U“

0%

(RU

C~

13"

.4‘

-L,‘&t¢*:v\t¢&

RU)

L“

CLy\\\

'

vkrlm

r)\\J\

~'-.-.

*

.-u!

La-9.~i.C)‘~

-

"

3L»..g~\ "Y\-\‘~z\0~"\

-

—-.(1.L,n

-

dm .

*--(QL|“

Qdl

\

A

“

L-K.“

0

R L3

\‘~1»"-

CU)

u¢~d;)>

\\l'\'\'\.)

“J_

Di/7.

Cl..l‘\}_'.L\‘|‘v\-1;/v\4:>..../\.-1%

L;-H

7)

La

M

\§»'»'\{,)‘“?>¢‘f

Q1"~V~.Al)

km

, I

wlull

o--J><,>-0»

'P\o\j-$..,i:

.')>ftn.AA.L

Voxi

M,

L1

W».

,

um

QQ

5\

.50

0\>1'o\.'.,._|_1

ova.

<~>\¢LuL

31*»

V

w\¢CLAx$_-_

'

\\~.\\1A

omm

'

\..

‘

--~I..w\ @

Y\\Y&

\>».M;A:,¢§

w-.,.lI}¢\-!.»;;l__\°‘)

cum

'


l¢.m.

;.

<\\ 53»'~.».1

-Q

A,

\>.m,¢JJ..\i

LL,

R15

B3

<1.-\z¢.¢_iM

0%,

<§1JQ¢...o.

Wm

CH5.

|

’t. --._..___._.--._._..-_

“>--w~1?>a My

,¢uw\.v- "f\.

,

J'>'u+*’~' _- “'“'*1~F'*'-

'4:

La

-r\¢~»~_

KM

)>¢vJu\M.

vwu.1I_ln$_

Us

Q

i¢-1¢u>4_

1'

’

-

Q

AAQM

I >

’

1

‘

\v~\

vs

v

1

-

.------»-1—-—n

¥

gig

erg

A

B

a,

a2».a--)>-v.u-*J-

~r~d2$.u_Js

~{_ _~'\:lr.AY\

r

W

L

7

(\\

mun»

=

<M<(m-¢hM$>

M

4,,;
1

<mam»4.¢u\\

\x\\;‘ Wm

,3



k
(,w<\w~>,. (3Lli(p\“‘)

wq

<&.a
c

= =

.

Anxun

.

V

-\

1

ws

.7

P L

'

"

7

» 1

ml» we?‘

(<1-*
3

\Z‘.<>wum

sq

"

1

U

Available at www.mathcity.org |=

»

\ %

ML

‘L

u\,

s c.1:

'

W

°*’

L“

.

~-

B3

““‘-

'1

‘F"l1&

C

'm’)\.

C.~..;\J.u\

wm“,

-Yxno.

k")

~41

N mm)

mm £5

?

M1.

\‘u._

‘\£-1'

\\A2'\'\nQ1!/‘I8 M

Q,.u}\~

<»-ii‘

Q

L,‘

W1

QHJK

/1-uu___Q_

é)-Q

KM

ggx’

{L

.,

Wk

6:“;

n

_

q“ Q

OJ}

/3>\'\ra=‘\.u

:1 ,

’

<5~A-\'\P\\

=\‘:

(ink

\J=~4-wcn‘

M

':'\

U“

\--A. ‘F

E)

\>j

'\>-7\»v~k¢L

=9 d.u.9‘_.

%_,;L

1

8‘

wum

‘*

\\<|~_u._

M1‘

e.v_¢<~.~?,Q_4I_

M

P\

G.

(M dd»

U,

“~—'~

(

6

;~_.

A1-Wu‘:

0»

S:

H

PM

hm“

-J1,

J}

all

WM

33>

‘A-5A/\"(

J

H

&O
Mm

>

RAK

,

m

J-1§

"Wrv\,~4j1¢\)\C.-*,.

-\,q,‘,¢_~.$

M

-

H»

7-XL

V

§\K\ $“'“"\"M

mu

W»,

M-

=

F\ __~_,,

Mt

Y‘-P*——>>A~k\m~

‘at.

4

.. w)w\M.\€.1vw\=d,_~\

M

-\,,

M’

M

1~= W4.

V-

wxwx

'

MW

>11

8%

Q-—€)

=

m

<,

*\~\W&

V

~:\-m>U_f\) 3

Q

,3

iv;

=.

(hi W3

(

3X

UML; M

4

‘

Available at www.mathcity.org ’

'

.'

*s~'+>»-..~»..»-¢~r.\-.-,_~....¢=..~_\‘ ,

-.~

.,

mg x

1,

I‘ *

1 L

FQFL

74,,

B‘

aw

’

am;

‘~’-"LLux1I&....._L.

U

'id‘3U\+!;\

5

M

4

en

~

.

\

J4.*(h\+;h§;§§)

=

3:31-

"LR

“kw-\~.

11

~

=;::1~[z

11

:1

>

PM,

|

5

FQ#

“*5

a

$

I

\_¢~h

iakl

Ma)

*3

'\

<1-+v~

"“

~

_

‘m+§

5,3

C+\\

Claw»

_

2

: C\c\-\-d.¥..|,§d_*$l‘_y___$c:_\k_3c_5k N ‘(VJ

dw%
=

&

<1d\~\)C+-$-\(__j\.\

-3

’§-»~®»x@ <,~4»\(A+M

‘““

°\~*<'\-~% rel="nofollow">1

M. L

1;

<14,\A _,|_d‘k‘_

YMm+m]L

=

%

t

!

A

K.

I

1&6

|

§

E 4*.

YEW.

.

{"2 :1 m. 6“,

5

¥;=[k K]

A

_~_

_:

“'~'

S

M

‘\' 1

:1

.

I

I

‘fl

|

-‘r M

i

6‘ 44I 1

4

%

5

W

.

3'

Q

£P\-~

M

*

our

4111

.¥~-\-‘5

<1+§~

ch-\,;

Q-M»,

_\»-H5 .

C».-h

-


'

L

A (AA 9»;

(Q*§>U° *5) “

(a*€\ -(\'v”kc*\‘\

':.

(c+\~\(=1~»',\~(A+\¢)(¢+\\)

(C-'b\\)\‘n'\"))

'\’§§\,d*rVJ

~\<

(<1-;\L)L

s. _l.“~§§+\\>+1)(¢~M

£<»~-~';)&~.+~;\ A-k\¢,-\-'j)kr‘.‘r\‘—§\

L

|

\C+\\‘)(_c\~q,§§+(<1\-\\\(€+\\\

'Hn\»J

M

X <§\+Y~

A

on-Q

-

<1aMf\

=

~) 15

4.

1

.'\'l‘;\.a.\~u\4,.$\-K

.~\¢h.\(rm»\]

¥»,--5

C+\\

(’\+Y~

‘*""§

5*‘)

: \c*k

i‘

\ u

&)t¥nc~\\

-»~...._..*__@

(C4-\»\\¢\~§\+\&~\L\(c~\\)

du(:\+M -[d¢A(¢\~n] d~4J\((\fB\1

.3

I

U

A.v;

Q

.1"

9"“! M \.

1

'§.g

1’,

=

'\ \> ,-\

L

1

V

:~;=..

.:."|!'

1,

,=

1-=

. . -

..

*-1'

iv.-‘Y:

..=

".~

\\ ‘

1.3‘-I-'

-15.‘. U "UL ‘J1 -».*. ~.-,1.

'

>

,

:9“

5 l

“*6

Q.

V

dl_*U,\1_R_%1.§

\‘\~A..».

'

(c~\~1(\n'$)-\-(¢i+\<3

L

1

Lu;

'

K“-~§\\&+~,\~u.v;)ga\+\<)

-

€-»@~\®

S__J_5.

’

\~'§

as-§

= '

.

1

I

~\

\<**‘i>L-U=+"nkc+m

L

\'\'\-\)

.

\>'\-"3

:L

¢*v\r\

-

(H ‘L-XL

_

‘Q1-8'

P\%~$-

.

(cv\.,)U,+” A‘ (d

‘

OQQ

\7+§

c+k

¢+Y~3

.

»

"

'

H 1. % ‘vb

Maw’

5

I

‘"'cvv§

ya“ .\.

‘HQ

b~')

¢

»@

$4-3

J.“

V

Mm

“mm

-um

\<»».;)u.~-n~4\~»,;La+\q

\~M§>L+k\»~m<~»~\

>_

U\*~%‘>)

'

:;_

é;

§.@_J,\,)U»r;n_,\4*»¢\(¢.,\,.\

(c+\O(\»\-5\ + (<>\+v~)‘

9,» 'L

‘

<=>~~%>

'AaikLP\+rb§'

=

Lc~\~>\¢~r,)».\~\~n\<~\_q H

»

<-=»m\=m +u.~m-Mn

» <\-+s>u~\~\

(¢+\~\\\.+;\

* \<>\ +\#)L

1;

-4—-

i

(D

i

1

i

,,~._;

cx

.

1..

I

P‘

Kc.

M

°~

<§~}£<.

03"-+\oC.

ACTCAI

\’

'

<1]

(

0\\ §-MA BC

4-A" 1

wm

1*kkhk

W

'$fM+'3\¢\

mg», am.

' i‘

1§1+5'\'~ 1

é

‘1\~+ K‘

ii»

L

1

@3+\o¢

APE

§-5+-;v~

1-‘

_\_

7.

K

r

»

a\r.+<;¢k

\¢c+-<1‘

‘$\"\*\* J

1\v\§+Y~\\

1

A

Y0}"l"1_'\’

P\q_J‘€;~

"

‘

2

Lc\c+c@l +\\§~v-M

AAA

Vt»;-;»\

<>\\.+\<,.1

‘~

‘")

Uura

&‘-wt +\>c

*

'5\\

<>:'&¢-\-\>'1'*S\\.

<>~¥\\»c\‘»\-[ij .\.§\L

(Ac-»C
¢-\"J\'\

1

‘

1;.

t

%\, '

‘Q

Q

I

Y

Ml’) <1.m\+m‘ 4

‘

"

‘»

wu\‘~».e‘>

--

+51)

3~4)£\P\1+l.P\$

=

d4_k\P\-vQ>§

(\~0\

‘\

-[: ~21

50%-

:1

\’L~.... -

:

P\*t§ N no

‘

Q K

*

:

5

C.-\\

‘kl BE‘)
\_c-».k

>

'

-

\'+)

'\\¢\-§ J,

1

1

Aw.

Lc+k

"\--ss‘+u.+-m¢+\A\

‘L

U\-1:5)

\+§

‘<\~§

1

I

Q-Q‘

‘

(¢~~§>U»~1\+k\@+s\k<M\¢) 1 ‘

<¢+\.»\Q~sm»\m\¢~\\\

<@~\~W-~-ax + k<1~\<>‘

a_

5°

‘

A.liU\+§\

<¢~§m.--,\

(-~s\‘~k\»+->\
:

‘

P‘

:

1

B

_

4

L

‘

‘(c-\,k\(o\+§~)+ \d+v.\\c+\\\ Haw

m, +))(z‘+V~ Y”

‘:1.

5]

Q

3

¢

‘*3 1

“

¥

w

1

s

X“ \'~“

~\-5)

+

(cX+\¢‘)1

(

"H

o§+\a'L

o.\¢+\=>8~

o\¢A+c_l

\>c+A‘

"';‘+:\~

%'>+a~<

1L\\§+\<\\

5\\+v.‘

=

*3

(¢*&\\Un

-

¢

1% ‘

\:x\Yr»\ aux o~§+\,\~_

1:

-L&<1\+c1\\

onga-\|V~

1C.+
K3.-*§.,1.‘\\/~.

1c§~n.M\.

‘

1¢5{4.¥K‘§ 13¢-\--1A\
23"

H30

r

‘In:

v

--

’

\

-

|<,

p

1

§§)Y1f\%*%;_ :1a§+‘»c.

0&4-¥)\3

{1v~§+1bh.

10.3-+lkv.‘$

5+-31]

[§‘~5\~

“N-

:*°~+<4 F‘

A

‘_°‘i*1*‘~

‘L

1-

m

1

“H4

->\~-Hf

A\»+\»¢l+1¢\']+1\a\L§§§¢,3\L

,o\C»~LA+1c§*rL
\

+ \\§».\u~.

.

Mr. +~»~§+1.\§-\+§+3\'_\-

@~

1'><+1~h=

‘

\nc-rd +1161 +L¢l¥.+')\\+\(

L

L. -».

‘Yam

M W‘~1v~r>~§\

°,:*“'*M§ J'U°"‘*§'l*§\“ K

°*""\"\"'1°\"'1+7_\»¥ +§§+5Y~ =

¢

o.c+cA-&1r.1;»,1¢l\\+\~Ii~\L\\

Y

,

\>¢+<£"+1-3c *1-:\\¢~g\~~v.l

_

*6)

%~A<3

ch-*(P~‘+1f\B +2.‘)

<‘*i\*+@>k ¢

\l QM

‘M

F“1~~4~

qM,b)

',

M

.2

"Q

I

Hm

V

-

I

U

L.;,
=~\2 '-‘-

A

%~

i\-“Y1

\(7-'3-Zn)

-

0

=

~L +1&~4

R

-L~w

2.

i\+1\i1\ A-1.L\‘\-~10) %

l!..--Q

AvaiIab!e at A

www.mathcity.org 5

L~\?>\

‘I. -\ M‘ 3 1%

(‘.0 4|

3

0

-—\

C

-\~\

2.

‘>39-1'

4>=\3

Lu;

xx

ax

1_

-\

0

'5

ii; 1

_2_

\

‘

H

o

-\0 -\'5 \‘“ \"\ A-\

+(‘\ -\-H) +(0 +1..)

2_(L_o)

2-U-)-+\'5+1

1;

1

\l

1

11

A

-\-\

\

3

(

+\§

-._...-%_._._.__~..._.._ _.

u\\) ~

-L

( 1.

1'

ii»

_ L

:

A

L

1

S’

‘ N

\$

\

-‘L

H

\€

Lgk

V

-S

(

-

Merging C

S’

(‘*\"“§°\*‘§’ \\~

=

6

+¢

\1

S

\S

-L\ -+1.

Y, IS

S

*1

-S

\

1

((10-'$o_\ -\-LK\s+_‘\»\-\-((_\°__(hb)

=

.‘(-\~\

=-

A

-§

-(.\

?~\

=

4.¢(\-1.)

+ ¢(\=m)

__(>o+Lu'o -£410

-60-+\‘8o

=

\2.o .

'1

:\/33,1:

and maths

W. i v

£355

iv

+>\1~+n»x»~

L

'5

'1

H

U‘)

\

1.

*1

3-\'

‘)1-3%

"‘

-L

5

0

‘*\

‘Q31. ‘- L

4

L_6..t

1.

3

[§>.n1

M

\

r

3

~LH

o

1

1

3

1

L,

\ an

‘

1

:

\o

1

'}»1_

-:.

I

_

‘1

H

S'\ ‘L__H‘ '}

\¢o

R1-R

llibsi 5

x

Q

Q

S

\1

o

u

~1\

\-

\

.. \

Y

0

M»

g

H

'

R"‘7*"'5

l

i

I

u

1.

iv-_\>,,~_,_,;_;,,_Q

S 1.

1».

O-Q *

-as

i1,

\\

\‘L

\\

" 3'!

\\

2.

\u

S

ix‘?

5}‘ \~

a\‘*2‘ is

wc» -—\1.H‘

\\\

$

9~V1-111,

-o

\» g

'1

"“’"*"Y‘?~'~“~

.

\0

\\

\v

s

z.

9

$51 -~\1».»\¢'\\~*r\1\S'S'-Z-»)

\\

'1‘ \“

1-\-‘A

\ \\o

4:-

1L)

H35

-

=

5(--1%-\ ’+n.\'s§) +vH\\1iL)

=

-—\‘\S'o~\-K7-0

'7\\L\

—\

-\*\$o+\\‘-H

2

A

I

:

_1QL —----i.__--i-»--_-

>

K“)

3

1

\L f

._-L’

O

\

\

V

$3.»

L

"\

5

1

\

\

u

0

3

_

\

H

31$?-

uiaz‘-“\\ -100” \

'\

3

\

Z

i

K

1S

-;-1_(_\

\

\*

.»

‘5

>

1"

*

\

‘*

M

K‘ ‘

=-

.-

Ha-1,) —$(\L~\)'+ 1{\1~\) us -sus»-~1&~~\\{

‘E

‘E

= ‘II

‘Z-

_1_K'1--'l§ J,-LL)

-1. °\ 1.

K-MU

‘

'

.

»-—--——--_.-.-.--.---—-——---

Available at www.mathcity.org

1

Ligl;

\-A's—‘1 (\‘\'\)

\\

_

D

\

\

3

0

~1

3

~.c»

\\

...}h \

5&2“

‘\ L423;

A

=

-

-1

M1

3-

0

\

»\

\

\

3

0

-3

;@

-1

3

\

!\

-1

3

0

‘

-\

\

0

€

-3-

\

o

'-'1

k

-‘1

\|‘

'5

R3‘-Q‘

=--.\

=s-x\ -"I .-

\

3

\

\

\

'4

‘

2.

O

—‘\

-u

w

2 1.5-

-:~

R1-§l\

-J1

0

‘\2_

‘

R}*-'R\

?>\

J‘ a

\(,_\L 0 -__-¢_._._...¢_-—i--_-

(N) *

5.2%:

q

‘H

\1

-L

\

*’u

N

...(

1

\\\$

\d'\

-\l

L‘

3.10

\\‘

-1'4

-

Hi-§

'\“3\1.-(.

‘

La 1:>=\ u

~

A

~4-

\Ҥ

\q-¢

_\;_'

7-Jo

ma

~u,

*-4J\.~.l,.j

i_‘

A

__(

n_

\

qr.

IH4

1'

‘L

mi

\
L

N

11¢

mg

1,

'

n.

\

—\

-3

11

0

R141‘

--\L

"\

1‘

O

9\3__"LQ\

H1‘;

o

‘~11 -'..1 i

-Q

‘-\

11

-\

1L

-L -H.

4%,”

-\-1 an

~11

W.‘

\

‘Q

.

¥\‘\1-

=

\

\

L

\

M

A

I» K

""\'\l lo

‘C\,‘c1‘_)Q»1

\

\‘¢v

,

H

\'='L

37

’

W

\~\

\.1

31

-\ _\

-n» P\]..'LQ.\

__\-I

-as

Ra-HR\

<J\\e

~\

t

—\“n.

we

»

W

wa

Q

Q“

;

-~%)--\)"\

(_|.)(-\\'>k¢nu)\1_

=

9._\‘~\R,

.

4-x\r».,._(L_;,i

=

CA1

<11»

,1

E

,\,W__

~\

I

,

-—$

as

\

-\1 -11

'2’ W

YR

‘\1-

1.

\

'Q_\

'

~

~

>

L4?>(>

43

MU)

_v»n_(\'!-9+

,.;

“ -\*=n~\\1»\) in

-3"L.QS“\'L

1».

‘___,__._____.._---—--——

1

1

lw)

\

\

\

..<

\

\

,-\

~\

-\

\

__

\

-\

\

-\

~\

—\

... \

\

.-

\

-\ \

\

\

1

3151

Ln. Y.

A

2.

\

\

\

-\

-\

"\

o

0

-1.

\

.

I

"\

—‘-

\

\

l

L

1>v¢

1

C1-J“

°

Q

_L

U

\

-1

0

u

..,\

0

-'1.

0

__-1

¢-

A

\AJ'.»d<\~MJ:

<*_>L\€¢.~_¢\;_7

\@

C.

,

¢_

_)>\\¢\»

\

K

A\¢.§’~J~°‘-‘J K

R

K

+-C.

I

CI4-C,

U

0

-_-_-__

I

C'1+¢-\

1

(“:C|.,:())

Q

fx

1

\

-\

CA.

.\\")

'"

~\

-_-

‘

'-\

\

aw.

(M

\

"\

\

A

_

\

‘g

J4!

“\

...\

s"\

1‘

'~\

s:_C.K

H-<»d\

H357

¢

.-

Vi

9412:-

"0.

\»

1

A

e

E

3

k

v~

d\

e.

Q

C-A4-'J.u~. ,

AMC

an,

\~\v~‘

*5

.\‘a

Sn

Cu.

.

'1:

M

M

A

o\

‘3

|§

C

B;

’

\1

T)w».J>\>.,Av.

I

0c\><-

¢\,kl

s*~\*

@~\ t..____...__...--._..__.

\o

W)

B‘

on

-0-\>

O

C

-c

O

;

O 4

SQ»

LQA

,_, /'

o@\> ';-OOC. -\»-co -Q

0 -:

<1

b

0 l

-—'\>

Y

-C ‘

C

Q

\-\.A A+b>

:

-A

=0

¥

ck

C.

f)\,|;&A,_)1\i,,);Q

'

:(_\;\“° c\ 0

B3

0

.'

B

(

~,wH _

\c.W

') \{_ \W .

l

€.\v!‘>L _

>%\,1

-.

(45% <

‘E

§_,(I:\ 2

1

:1

O

'=-

O

1 1

A.

J ‘1

\ A

n

D

-AA.

0%

5|

0

5-

-\,_

Q

W“)

2

_

O

0

m

\»

c.

\

£4-Q.

(1

\

C4-a.

\>

\

*1"

\

1

i

:.

D ~

2&2-~ I

Mk

Q

x

¢\»»\-_

C

\

$+(

m

\

$

\

C-um

onkw.

c

\

‘m-'rC-H).

Ox

\

LC+m+\

$

\

‘A~\,+(.

’c

Qka

3

1m+k+¢

C‘-\-C.;_

I

Q

V

*

I

I

1‘.

b

\

c

@(¢a-r\»-\-¢.§\

G.

\

\

k

1

\1

Y

Q‘

2:

C ’

: h1#\+L)(0) A

“4_\°+c_

.

3

C‘:

Q3

\

-

Q

AM»

Q,

\

kw-(L

~

\

<1-vmbx

__-1

Q V

--—_-_i._,----.--i.

Avaiiable at wwwmathcitv-0Y9 .

X-.

L1

‘

Q3

?'

Jwvx

“"3

“'\U\k Cm

m\n

‘nr

‘E

‘pl.

0;

i

5

°

=

C-L

511*: -

A

Led.

=

\»c

CL¢nC1~.\>

_._

.L.

»

1-

<-_

:

j‘ ._ ..

i

\ -(11-Z

be bc of

A

C41

ELM

¢?

.

I '

5°

P\1_

.

_".‘

9~\_:Q~7..

0

mm»

Sc.

.L.

:;'O

-\——~L-’ b Q

cx

.

J

0}

Q“)

”

0\\g>CK

Q‘-

\>

'-'---\—-k°> 06¢ Z11-:'.

-

0L\o

Q"

$1‘

O-Mp

\_(_

(_q~

L- C

C-1».

0.-\>

(I-0.

<-\-

-=

_. 0

\'-1

\»

(

Sm

-

.

L"k'§’:

Q

- ‘D

\,_¢

lC-0;

‘~.-

L

c_¢ (K-Jo

¢- ¢

,

Avaable at

ww'\'rv.n1_athcit),'.org

-1-M

\-L’ Q-

‘»\L\D ,i

':

‘

\-(..+€-¢\~a\-\

‘

JQJ0

C--‘~'3~

o\+m-\+\,-;

C

c'°“

*~¢

'n#b~b-<~c-m

C.\ -\-KC\_+-‘C 13

A

‘ll-¢

<1--5

-

I

La

1

Q

‘

C-(L

‘ .

C-on

-<1-\v

on-M

5-Q

1

I

Q

\

\

_

'

4

s

[;\:'.0

I 3 1

Q-\,

.

5.

v_\C.\':-Q

\>-J.

C-11-

4

\-=.

¢—v~

<*—\°

C-m

0\—\n

\‘-~£

0

=

+—*_____

X

U313

A

Q}

Q/‘L

u.

Q

Hm

‘

O .

‘3Ic.\\,

C

C

.

$4,. ..--

A :

LI.*

0.

0:.

“AL

5

kl

3/ CD-

C

(LL

c/a‘:

0.0-"°}

=\

0. k C

A I

A

I

y

ii"

kg;

ct .

"

-M\..\7-§1»yl(Q3’°"1°“"'-.

E»

cg

.

9)

-

o~\»<_(

\e°" 1';

Q

aw

~»\“““'

043 .

H H

.5.

‘i

0*/kc.

\»

L,‘

\»/C

c_

Q‘

C/(M,

\

,

,.»1‘/5‘

K

:0

0.

_._-__..~._._________

)

QV

It

R“!

\

a

C»,

=6

‘ii~:<%>\Q§-y 9:‘ “V

‘L

C»?

\

<81» _._-.

Ltt

‘$30

\

-G0

QM»

\

<24»

U5-;:."l’

‘

A-':.

ii;-01:

\"I‘»§6

$+}.~\»-\~G:~\»

1

A

‘

\

\

Clo

\

\

G-5*

‘

I

(HEY

‘L

6

5-5&0

\

C: 6

<»i

\

<1;

\

Qqk

\

G:

R\+R.;

w

1

;

‘l’

C:-\

mill

on

<1»

+

=

O

‘MatmIily.0rg|

‘

Merging Man and maths

_

‘J 3

1

3*“-I

0.1.1

1 6.11.14

:

Q1‘? 9:3‘. Y

SJ}. -.-_

Qw

CJY

'0 i

’-ML A

LU.

am M?

=

Gmuk

c.-1

c;,=.?

ab}:-j

Cn1.Y

C-.Y

.

1.

R.

€>;_.Y

Y

C..>.a\

014-$¢.§&

C=.1.\l

Q=>tY-"9'*‘:‘Q

%£:.a

1:

igglw

C-n.Y

‘$314

0.1.;


*1»

Q1‘,

(;.1\>

Q

1:

~

-

*1

QLY

"

CALW

=

Cry-»$;:~6 A

cl 2C3

"3

s.

c\"C\

0:1-S.-iv

-

GM-Y

.‘¥‘~l*

A

Z1.

1

L

C-JA

$;.':.\

C»-wk .

wx my

'1-1~\\

“Y

‘%

clv

cm

~@---i-__-----—-——-

km

\C.:>.1

5-"ML

%»(»\+83

¢.,,\\

~'».\§

2-~\\»+s>

\(,_\,(

‘I:-';-‘(

q>'-““"%3

= 0 ‘

‘%£~&.-

\_a’1:

A

C»;

€»~_.a

O~\¢.

‘S-~:-..\>

i;-AM-S3

-.:

\

QM

I‘

‘kmv

~

.3-'~I~\"'$\

.°~¢-~\""5)

I

MHZ»

F

0'»

)

~*

\

Q»-1

$."...1

$.,;~\(,,$ *¢,Jg;__$

<*-x»

$4»

Mus

0”

5*“

$*~»Y¢-'>8+C.»>\1‘i§;.g

C-u

RML

I

A

A

r. ,.r

+ G.}$;S

i.;..¢c.-,3

C.>,.1

2-Q4

Qdug

Cw

ivy

c,,\,\,<,;\;A3

-Q

1

‘{-

3

1

CW

T-;.YC,5g

‘5-.;.Y

I

Q-bl

$,;,,¢

$V=I\J\

" C-‘ml

f

%°’\‘

W

¢.-Y

9;»:

‘*3’ cu

“"3

"*

Q;._,,,{

<1»?

we

Q?‘

¢>Y

sw

¢,Y\

V

.

Q_;,J_

I

=

C-53(0)

A

j

-.

Q»:

’

two

CJ.~...,_fh 0)»? ._‘_C1;_'j1

O+()

1 4

+%,.\ (o\

0

-.

S.

1

6.}

sq.

s<..(\,,-g)‘

G"

'9*-Y

%;.\v+u

i \J '\'\)

_:_,O

-@

'1

‘QM

J

1

Gm

_

‘~=P

T‘

M-\->

"

1 A

iii

P4

..-Q

O

__

E

%

\ -

'

I

Q_.(d*\))

\ 7

$

my

H

rg

‘~

%

‘T

maths

/

..

Q 0

\c;.~,§§

(§;,¢¢.‘,_ g__“‘$;*?

\

Cub-l

12

’—‘~

my».

95¢

\

Wm

\

¢~..\c.\\-s»..¢s;.§

Q,___\(‘,;,4>C\

vv

c”"'l

—$.'.~.1$,,;,_'§;

\—¢>§.L

<11

fa)‘;

\_c_,}}b

—§.;...L<;;_,_\;

- $;..L{,;._‘Y,

6->1

‘Q.-.344

CM?

- 3,-\.1g,,‘

~kc.».\.;¢\

,

I

I

.

\

0

Q

A

**\'\'-41

I

\$~*--\)k~~v»¢§\

C»).

§;~'~J\

C~\*

—$;..\\

‘Riv.-l

(‘,__

%:v..\_

Cx

7.

'

_;g;__

Q1

--$;»-QL%:v-#\$kCl3

Q3

42z=o ‘D

\

C-ml iC"*\!»

(‘.5

C4»b¢L

’\

C,.>>(,L*\P)

C*.~U.-\,-Q)

:

O

\

i._..,,_.,______._____

Ava£!ab\e at

www.mathcity.org t

‘

f

t

\|\

HHS 1.

‘

gin,‘

(¢\+\»)

;,

(Vm)

as

1

>

1

F"

C4

C_1*_A~L

(cu!)

'2

'L')+\\)L

.

O

:1;

Maaaaaworg

3\'\_,

Merging Man

S-. .11 i

\-¢-’cb.-'

(Q +5);

uf + Q

¢\\;

(Q-H13‘

c.'“-H1‘

cA

§‘3+\\§L

1‘+\r:'

jk

I

I

0~.+\o

i

.,

‘Q1

Cl-\-AL-

Lk

5

5

+u>.\,,

c‘+¢\"-\-2.cJ.

=_

an mat

§L+\:

')\'\.

E

1

, .

*1“

A:

'

:

I

9“

S.

I-<‘-A

C!'+d

1

CA

15k

a‘+\~‘

sh

M»

oC‘+\>"

C\~C1

adv"

¢.¢

c.‘+&"

c4.

5k

5‘ +\'~:'

‘jk.

.1C'MmMV€“Wp:‘ ~

‘

1(0)

1

A

Q5"

<£~+\,‘

-.2

K‘?

Q.‘

Q3)

O

MQ-\-\>)l L¢—\~6~31

\(1~\~x"

0k‘+\>1

CI-\-J}

o\\>

£5

'

4

;

:__

O

1k .-___.-_-—~.--_..._.._._-__.___

Available at www.mathcity.org

l

t

I L.

1*

Hqg u1"~&>i“>‘

<.;r~e1“>‘

4\*“+\3“>1

(\.“_\:“) 1 (J- 5')

an an

\x 3

5'9

(c.'+

W

Y

1(-

=

Q

.,\\,<_

%£: l>L
L

A

QWJC

‘Z

IL

\\>+\>)

<1.

(chi? >1

(ail? )1

¢\>c

@.+w@ 1 \)\'\JT

-\v\

19

-19

\C‘*C— 'L-\

- aka N

£>

1 _.i a\“+cxM_l

\

-19

1?

CL

-1 -

‘_-1&4

+

.

\

\

o~

-

C.|...?_C1v

t

‘L\-\ ..xv\ B_~¥

k1“ ~b~-In

1}

_x$ C + Q

If

_1Q

Q + C

"3

\

C_+c_ ‘Hm

_~u-1.»\

-L

cl + 0.

+1

0. *-0.

-"\-~\

‘-‘~\

+~l

\

.

(M-\>)

\x-~ -1“ .... 050C.

GLBC‘

1

_.“ Z

‘A

‘

A(cl\~;l.“)L‘

kc'“\°L)k°)

1

\

>

‘?

\

‘

C-\ -:

CL

:0. -—--—§———--—--—i_._.____

(*)

\-

J»~ ]_\ ML.

1\

1;

_‘-\ 1‘.

~;_

1‘

H‘

:

\

1[

Am %.»&

0

\

.

L@<-A.-_~,,‘:_"5_‘ ~

ELF

3*.

»_\_ 1‘.

-

O

A

\ R \

R

ow

W

gm‘

,9 %

\ 7 ih~_____ lb I

CL

Warm ‘

_

|\|\||||||‘|l|\

\|\! Q_ °\L0 ‘‘L _ L\

‘\\| ___

'1" °,__\

__“_

v>

301|

7_ L‘C‘0 1 L ‘D _

H

\o_~Uh ‘LIL/u O\L

1‘ HO

\‘|_

L

MW m% MW‘ ‘\\‘lQ _

L__‘_‘\___ L

\ib‘ M _W~ ‘T L‘ 1 L

O ||\ Q ‘K \,0.$ _

_

__ %__ \_o____

AAU _*_Q

_W \__ \_U 1__

v W

____

M

I

RE ‘ ’

LME '1-B

\§J...L..Ci.'..LC.¢L

\>$;..\-c$:..4c,4

7-

0

9~\-C-"~¢--I

0

\»~’C-.'“-L

'

Cam

C‘$;.-Wk

Ry

‘K1... '

‘

Q1.

J5-¢?s=<E.1

$;..n(\>_cc.»-\\

-»

&&¢

<;.~...,\(\.-<".,n’

L

<2,-§i¢\{¢3_cI"
=

\

¢{$;.,';.,\

_¢‘d.\

..\,,‘<;,Q*a -c.‘<;.¢~.10}.x +>_\D¢$.&A_<->»~‘-_

._d<;Q‘..1

_\}$;l.,\ _c5$.-&.\\\-$.-.}a.\

;_Q1/£-~'H.l

._\<,1$~'~1'¢L

*

=

=

{.,z..y*-¢.‘/ +»4‘»;¢7-

i

¢»1‘\&-iok

unwox

‘

C)

\>'~ \'\)

<1.

E»

C.

A

\

bx‘ da
\,

¢

C.

d~

A

ca.

\

on

\>u\_d.C.\

+w.\>c£-E»\.G..\

+c.L¢:.:.L -\-i\>_¢?>;§=L
"L L L $5101 X¢3.'_\>"_c_“+L\>c(k’-'5-c1~'—°-*-A 18 c -

=

[L

._c1‘$:.":~l

1 1_ _*¢_L +=_\,¢c.5.1]s£:¢ [O~.--B

.,,_

'-

g;}“,[(\,'“+<;‘d.L'._ 1\>¢;CJ>.L)-

I. ¢<,;;_:__L

w Q

_<,;.E.L\\>_cC.Ȣ\

*

o

M

V

HHQ ’

'o.\>Ld_\

SA‘

1%

Ld(b_\><-5~o.\

L3~m\>\ J~m\o¢\

‘Bo-d\c\ *+\+C~c1

I =

I

-

.¢

L

¢__d.

’\n+c.+cL\-0.

ck

\

'cx'-

\ \

\

°‘*(°L+‘~s+<>~

¢+¢».M\.

¢\

.1



%$11+-o. +¥-\-¢-

Q.

b

r.

,\+a+J+C

ILL

d~

C

o\+\»~c+A

\>

Q

o\+\=-wu-A

‘lé

d~

0!

\

a-H»-\-c~A

A

ca

\>

\

a+\>+c+A

0k

vb

L

l

|°\+\>+L-\-A

Q

mi

c

\

=(O\-\3'o+C+¢)_\

I

\:

\

i

a@\

\

B

Q

A

\

Q

6.

Q

\

|

A

o.

B

\

\

on

‘v

¢

|

\

o\

A

c_

|

‘\

\

‘

.

I

(cu-\o+C-\—cULo§

__4

Q

CS

O

A: _i__.._%._____

iQl

Available at ~ wwwmathcityfbrg =..

.1

A

‘~§.n._~-,'=_._

'

‘.1

4

‘-(SO 1

_..

\7‘~\\\)

~,

\"~

+\)l

(~v\+ Ur‘

('§))‘

‘:11

Uwq‘

(B-H)‘

U-n)!“

cf‘,

(emf

(¢~'~)'*

(c+x)"

(;A+\)"

(¢1.»;‘

(0

um‘

gig.»

\

%

‘of bur

)

03

A

(u+\f

(a+l)l-

Km-st)‘

\,“

um‘

um)‘

cf

(MN

UH»?

(C+s)L

,0

gdm

Hm‘

c<m>‘i

=

(\»+_%)‘

I

<.»‘n~,\

of+\\u+h~

W:

\:‘+1\,+\

\>‘+\~\-H4

C!‘-Q-ICQ-\

C.

x. (‘_

&+(\u+'\ \»‘+l‘v+‘\

\ -\-‘V1-\-‘Q

‘ c*('c'~‘

a‘».\.A+u

=*‘*'~“*‘*.

Ht

a‘+1=1+\

7i

lA+\

~@+»_

;4+\

L\>~\

us W

LL + H

<5"

1c_+\

ur.+‘1

Lc+°\

J}

13¢-\

\\J.\-R

Lia-"‘\

41

"Lu-+\

L

Q

1_\,+\

‘L

c.‘

1c+\

1.

\,‘~

\

-

\.

‘_ \

.<1‘v1.\-.\

'

‘Q

1¢\+\

=39-1\.~\ c." ‘|

:. 0

1c~\

'c'

c3_c‘ C? ¢~._C,

C3":-C1.

6

c""3c*-

4 \

1

1.

1-1-_ 1-

1-

L -_~

-

C

1.’

141-q-\

'

‘

.

A

“

<1;-_\_;Q\.

'\4.h..;.."5(',.~.~.~Q,w.c_H

Q

‘»|5\

<. .

Q1

¢.‘t~.vc(.~,.LJ.'av\

W4:

3

>\

PM):

4

x

i

L

kc

o.

cu‘

¢¢

\.

5‘

0.K

c

C."

-

\ ‘

‘A

= t

,,\_‘

4

\

s‘

\~‘

\

C}

C}

-r@_~2»

|i'

“oC-ml)-1'

A1

1

Ll-k

C“

,

k

bl.

C'-

,a\\- c

‘

o.\. .

A=__\__ d\\L “Me

'

of‘

3 (A.

M ~.1x~.p..,,.-.‘

vs‘

V

h” Ci

o\\;c

I

V

oi?

c\§\~’

\

M‘

9

\

C.

C.

\

<15

an‘

\

\»‘

5'

|\

\.

C.-

\\ oak “ML

,

A“-.—.

R\,R;,g,\,3 “JUL

\

-

-

<1, ~wv~’4-/~

~.'-¥\l>(-

%\»»\

>

‘

Q

\

i

\

J

C.

S»

_

\"'

°“

°~x-

¢-»

\.

xi‘

i**\\

L

‘\

of

\

Q

\

C-‘L

=

c‘

c.

¢§‘

if

3.

C’ *-——-@_.__-....__..-----—

Q...

‘~\

"\ \\

~*

3 Y

W

‘

~.',\

"*?\

Matn€,2%y@0rg

~L

\

=

Merging Man and maths

v‘

\_

[\,

Y1

.Y

.

=

$5»,

‘\.m§~¢‘ \-¢i¢~"~ \\v~:.m‘ \\

Y

“W1

‘ A

‘

._:,‘4\

‘if’ .

‘v

LISL» Qgi

my‘

Wwm ck

\>

L

d~

_\>

ox

~11

C

»~c.

A

ck

-M

ndk

_r_

B

cm

5,2»

3'1’

'

\°_|.+\°w_*L\_+A‘)1_.

z

\»c_‘d\

~

'-“

‘at.

..\, \.\,\'_

A

<1

b...A

0.

B

of‘

b‘

Q‘

A‘

A-“

M»

-ca

Q1

*"\~'1'+'»>»>~1

-cw.

ot

\uJ\

-\L

ac

-Ml

kc

0\J-

~\:- 5+ J}

C1

;

¢~1

°‘\"

>

0

BA

0

-\,¢_

CA

an

-kl

\,¢

mi C

0\\v

-c.A

\ 1 1.‘) (o»»\-‘=--\-c‘+A

wk

at

axtd

-51;

C

‘D

Q (0‘S&-\=1*vc_‘+8.")' (1..

1'

I

0;‘ .__c_

--6. Gk

b

-

‘

l

\

ouk

-<1-

-‘

-v-Q3 *1-C-*4)‘

.

__\°-

Q‘;/4'-<3~

V

_»5d_

“A

&

.

C.<1

\oL>

Q

§&*w\n\+QL+¢¥‘)

C\-5-(C1

'_‘c‘L

{.*r~\»-w~:l,l,.,-Y

1

.\>~s _.

CL)’

o~.\»uL

—,;

»'.°-1

°\>¥>>c'->6‘

El

O

--‘-——-—~

:

¢~»¢1

~

\-mi.

1:

__¥

~r_

4:

O‘ L

Q

A

'=

--=--‘C-n

—-J\

C.

__\,_

G.

\

‘

&~\-Q

‘I,

CR‘ c\>c'1>c3

C’.-.»-.~'v..~\

"

.

Q“

w\

I

I

H55

'

w

%

w

‘"~\>-4'-;

1

A

=

an

(03-\-\§+<}+A\\ {‘a(oh_\_‘x§_'Vd(a~A_\.q _\_cQb&_‘_Ou_1;;.‘} an

-

§o»~\-\-¢‘~+<}\\{¢1*a\;~+_dAa._"/éa +\y€‘L_\_dc:.} as

=

A

(Oh-\>‘—~

<-‘+d"§§ 0~‘+'\>‘

-§_¢"+

N)

LL I ‘L°\+\a-’r€..+A) L.

._

-

ii__?_.__,__._.,

Q2

Plwv-n_'\’F~»d
UM» £31’ ;

U3

t

of

OLL

‘gmI

\>

¢‘-L

ck

-

3

.

V

s‘

1<*\~<-k¢+\.+¢)

=

(a~\)L

V

$4.. .

Ltk

cm»1.

‘

A2

.1:

bt

.

LL

8'

‘-1;

U» a-Q1

'

1

1L

0

1

Q

\

-

.-

C‘

‘

(t-H») '

-

‘_..

C‘

CI.-Q}

1.

-\v~+H

‘(\+c+¢)(B+<-Q} |

'

'

|

‘

iii.-:“a~‘;*1vPg>»>; 5» .,

m

‘

l

(“J-\.‘ V

<1-Q-\-\»‘)

>

'7”

,

(¢ W)"

-0}

O 1

'

(LL

-

0.‘

Q

._

3

0 \

i I

.

i § »

(cw -mu: -1 _\.)

(c+.+\-5t<~¢-\.) (=’+>-‘~\.>g¢ _-\_\.)

V

‘

&q+»>‘“

M

-

v

1" HS H

.\

‘

~»i ‘

X

g

‘

\

,

A

54..

‘U>~¢.-0-3

O

O

‘¢f,H,;_\,,

k\<;_q-‘»)

(¢-<1-W

kQ.\»h*..(_>.“

f

¢°~

M;{

\,,‘

3~‘1

gM\.;~¢)' cmM.,.,.

2'3

"

M

(owl-3‘

\

L

A

4

0

CLL

CJAJ-,

$1.

in-\-C-¢~ 1

P;

=

?

'

(a+\n.-r_)

\

__1\D

1.

—

\

IQ

R3-

-

-

Q9.\-\-(KL)

7-1*‘

i

ii ‘=

H

“#153

g

I -—1~(ow‘a+L)

\

=-

1?

v

I4

.

~' .n~

4

11-

0

0.

O

c~“~_\‘

\>

m ‘.1\¢,.,\¢L;,_,‘

|

M‘

.-

\>

<1"

I

\n

-15

l

K‘

%_“~_

.=

n

-1-[a~\-\o+L§fJ

=

—-1-\v\+\=+¢3‘\

(‘*5-°\§iQ °~\>)k_C+¢1-B)-0\\ol}

-u

-\-

ofio -\>(_C-\-G-\c)}§

as

vI\¢ 3,»:

.

,

w, GI‘

1*’

I

,

V; :3

(\+
-o\\c_u§\+;(\‘-/U‘) +

of Q-kc. -»o.\=+\,"'

.. 4

a

»:

_']._'J

' ‘ -1\cx+$+c§<“(._oUo3\\»+c_caq(<1-rd.)

.

+(-¢\.)(4¢.c. +o,\.'fA-ad-)}

.

3‘Y * 1

i

‘ax

f’

\-

~

5 ".1." l' ti? 1'

-1K<\+\.+¢‘;4I-¢\,3iU»+¢_q\kc +o\\ + <1c'+

1

out

- dub

I

.2‘

Q’

'l¢_z

Y; V;

51'

5i

.5.

,

+04

1. 1.»\\>La+\>+.<.§L{ kc +<>\)¢.{+;:.i‘-4-;(c. __¢'y£_./llf" =

1o\\>\o\+\,.\.c.;-(\>c +C."'+gL¢§

‘

‘

-J

1 7..0\\>Lk0~\»\p+(_§t(\;.>,.(_+@§

.5‘!

Qt :-

..

..;

A‘

2AD,c,(c\+l.+c)

1

1:: I2:

J

.

Q

q!.

1

$3:

F211

'~;|

Available at www.mathcity.org

1; '

.

1:

mi

-»..

1

*

-Q-

1.. 7.‘.

¥>

LL52)

'

Ii

51>

\\\)

-

-

»

L

c§‘+‘v

C

C

-

C. £1

‘

1

\h

Cfv}

.

0}-‘Vl

C.

C.

C.

Lgkbz

\L+ (L

O.

¢-

CL

xx!»

.

A__

__.V[,

"

k\,

(LL

‘)1.

1

.

.13‘:

C1.

-€,1§i

9~1,Q~1

B3

.C>c14.,\4

funk“-¢

°~

L

'(‘.—\-0..

‘-

t

k

b

I

0.L+\>L- LL

"_“_ ¢\!(.v

Y

'

O

B‘- c‘._o_1

\§"..¢"..41I

$‘-CL -It

‘

'

C‘

O

\

=

I

Q

\>

1.

o\\\.c

\

cK1.

\. 1. o.+\o

\

t‘

'

O‘

O.

'8

A

-

L10-\pQ_

-

C

‘

$3: _.._ .

ck

a~

B

_

1

‘I.

-_t_"_..

0~.

ll

\

0}-\-\:—C.L

\.

=---—

I

I

o

¢

‘

0-L

-

-C

-

3

C1~C;

I.

C-won‘

(‘_l

Q

I

JG. "dc

B‘

'

R3 _

Qt, AL»

z

0\\>c

-

k_;_,,_‘

- C.1.

.1

= 3

—-k

‘

‘

J‘

1. -

__

’o

L

.

_.2.¢-_

.

O

Q1”

‘at;

°LL

cf

0-

.

-1

g

"C-‘)k°-5-"<-1'»-~ 0

o\\o<.

‘l

L &_-ac. 03¢

\v§-\-\»‘

--Q")

__

KAN 11

C...M.,\,.,\

-\-

c-L§°- ¢*}(\>‘w-'1‘-mK))

1.1. Qb'+C‘._¢_'-)} &¢_

wsé, -=

_..

_3~.__..(-o5c.‘~\{9y+\:-(i

+\:+()/~19}

M

H’

onhc.

we

‘ "T'"\“""‘ A

1!

\

\

L\0\\r;Q

_----?..i.._____

Q“

\'k4J'k

?A.rv~.Il.

it

ax

ox

ck

Q1

&

0~

1

:

CLO‘-'Y~G.

_Ul+'5d-\(‘Ala.)3

;o-enema. ‘K

&

ad

5-

O\

7»

(1

Q

(1

X

“.v\+"5c».

ck

oi

OK

§&~‘!,a.

‘A

cm

ck

V14-K0.

0.

"A.

ck

1\+34n.

ck

$.29

L.m..\;

axaax

bx \

M

C» -1'

1

CL

ck

0..

\

1

<1

ok

\

m

\

0_\

1

-\-C1, a-(Lu

\»\+;¢\C......~..;€.._c’\

<1

X

an

\

.~=

(1-F50)

\

m

0

7\-*1

0

u

ox

ex

°

O

1-an

o

.

0

0

o

)

1

0-

\

=\,M-5“)

(51

"K-m

‘"

'

Ra‘ K‘

13-V“ 9“\‘"9*\

L157 '$‘ I

\

J

A

0

K‘A~>\-3o\§\‘A-m§3

-4

\

0‘ §

I

Q

CA

V

(*-

0

hw‘

o

'\

Q

u

0

-

(X

-

-_

OQ

'

Q»\n-.-~

u \

o

0

c, \ 1

I

U-\+1\~<»>3

3‘

L»

..

'

<=

\

'

<-

u

'

H

\

'5

C»

1

1

Q\1._

=1

K\\+‘$d§(‘1 - ax)

“xskk

Skaw

‘f:

.

A

E

\

\

\ \

}

:1

k°L"_‘Y§\‘Y"‘Y\)&\""“L)

Z IA

1,1

§

a

‘»\\\

Suka-

L@»*£>-=..L\;,Y iv‘;

‘*0

:

01‘-

YJ~

\

c>

.4»:

}_~r

k~¢(1-¢n

M1-‘p -1}

C\—C">

Y

C4... C‘;

‘H

.

§-.:>...»

4,

¢.~1~'\5

.

I

\b"Y

‘p(\r~¢)

I

=

R

(.;1-~r§\\>»Y)

-l(Y—\1\ \

" \‘

~

\4\ "'L

ul~‘(

1

H-o\-\ c\'|C-L ‘Q

‘Q-Y

C;f~-.-~-

L4

S

51; \

‘,5 1

ll

L5--Y§(_‘§3._Y)(-.L+‘})

1

A

U‘-})(‘1u-~r)(_Y-J~ )

=

ClL_\_?‘5\-ww

‘V

N\4JK \

\

\nL ‘L3.

\

\

\\‘

Y

v)

Y1

|

Q?--YXHKYI -l\((~l~\l~3 Q-l¢\\1—\<‘()

::

1

l\

S»‘AL

A

>

=

i K

\

\

J

*3

Y

t"

‘,1

Y3

0

0 v_Y

-'1

S.‘

v\

\

\(

I

C\._.C.'5

C-1.-Cs;

.5

A

Y

-_1

\

O

Q

‘p

(cl-Y)

Y

-1'

\

\

y‘-

5K"-Y)(.[+.n'+1") kv-\>(\>‘».';m1) 0

0 =(-1~_\r§{\>-Y7

\ bdl.-..l.~Q

\

\

1

1.

n.

Y

\

k-1-WW - M .

J-t*)‘(~‘:

>

v

i \

QNW;

‘;

c\.;,c1,

1

,>\Ju,\»1

Y

i*‘9<»..&.'.,Q =

\\\~~<§ Q.k~_W.Mf

V

1

\*+}Yw

*-\--lY-oi

_(-J~--‘l3~,

\"

R\ 1‘

kl-1-‘I .~‘{1

4

2‘

~.

~_-

<

.4-w>(‘pp-\r)§

(¢>l-.Y§(

Q1»

-'1)-&]s‘~A.A1-1-vv-_v -L§

F

Ir

H§o\

u_Y)k\,,Y)i\W--OKY-w-1)

A

A ,

QW

k»\-w>W-YSW--1)\\s+.uY\Lv

=

Q?-v)(Y-.u3(..1-\,\\.1+ \‘> m3

Ma .

_

\

\

Q

\

\\.

’}\

\

,

\

.\

,

Merging

'

<1}\

(a"'33(.@—\\1 -.

Z

'

\

\

\o._\\ \_

\\¢\ \| \0l.

Llkx

A

a-"vi

\»\CL\

0.

v

(

‘

I

‘cu-3

‘

\

‘\

\

ow")

ox

\

\

“+1

\

<1

\

11-F}

“

_:(d*_5)

,\

.

‘*\

\

\

\

Q

\

\

\

\

Cl

\

\.\

*\\\'\ '

Q

0.-\

o

0

11>

o

'

'

C

\*'(¢1+Q1+Qw\

\

\

,\

=(¢\~'5\

0

0

an

-\ 0

C"-.~,,\,~,,‘

~

on

Ra-Rn

'

R3"a' Q_R

a-\

Q

om-3

..

“

'

v

G-\

'=\(1+3§

'

L

H]~;F‘:“%#vsr.]

*1

S181‘

“

“wk

5\'\4vo

_'_

3"i

+Y\\1_-;L)1§

=

%

V

O

°_ q_\

>°

°

0

0

'°"\

.

V

C.‘

guwcl

maths

Mao \

'*

15-

L0~*3)Lc\“\)3)' 0

A

-.

°

O

°\

‘

a"\

'

%"_ p~\zP~12k3

c¢-..~..~¢~

>\

o

H

1

((1%-'5§\:14-\)n$

\‘\' ) \

+

\

‘

¢%__’_@»

i

\

\

\

\+\

\

\

\

\

‘\+d\

\

\ \

\

,=

\~¢\

»,¢.1(1_-_\_ _\_ \+¢~\'b+c.+¢l

_\__

ck

\+J\

\

\

S.-l..

M“

\

b»_d
\

\

\

\+\.\

\

\

\

\

\

\+C

.\_ wk-1 J- \+ L

=

@\\or_¢L

‘°

-L

L

Q

ti

J.“ A

A-_

L. %__|)_

.\._

Ag

L

O~;‘b-,C rel="nofollow">&

'0

B

\

-L»

HA

\

\-#3..

\

\-Lz _\_.

.L

=-

~.»~\.~:.L

F4,‘-

H‘

'

L \+d

'-;Q\

P~1,Q~,, tn,

\+{-..ac~%~i

‘*-‘;+l,-_;+l;~§;

\-si--v-&--c

A

J.. in

.L.

‘

\

\L_ *\»

.\_

.L.

\~._\_

_L. ».

»=.

c

<-

(_

.L

_‘__

-L

ck

ax

a.

\ 4,

R\1 t\§'~1:v“\ ‘UL;»'

‘

1'.

M.L'~~¥.

**%:*k

W

Lo~\>(.J~\(\~'--k-*"'\--

+3€~.\;)

\+.\_

.L ‘/<1

‘/4

C_

L\+-L cl

1 \

\

\

\

“_L

tJ~:.-( \\+~k-+ 3‘-+1‘-_-»,‘J _\__~

Q‘-

\q.- 1..

‘I J.

‘M

_\oc>o ’=o.\>c4(\+i;+l‘-+A-t+l-§\/\_

(“Ca

'

4%@>

\

¢

\/(_

‘\

Q

‘/‘Lo 0

Q»

0

b

\_

Q:

O

Llélm

C1—C|

A

'1~\»c.

O

0

\\_~o \ ==»\.<.\§\+A_;+~>;+-)-5+3-)

»

0

O

’

\

f~»M e,

‘*>\\>-~#»g

\

N‘;

0\\>C.&K\+-5‘-+lb--y-.§€q-<.L_; ..._..--___.__.'____------

\-‘L

\

'

\

|

\

SAL.

‘i

Lzkb

\

\ +‘)_

\

\

\

1

-_

\-‘Q

\

\

\

I-3.

\

\

\

\

H-5

I

\

\

o __mv

\

\

_,_

0

\

\

‘j

‘-

~

_

..

-1.

1 Q

cl-Cg "

‘J

<3

1-» <1 ~..

,

§_M-'.,R,

4.1\,.~__,L¢,$-

-1

1

‘

¢»—(\+x)c_.,

‘Q

;

*1

!

\_5

o

K-'~+~m>)

I

\

o

...~;_

5

'

\

\—\-1

_:

\

‘IT’;

1 1. ‘/M‘)

-::.

.

\

.<‘_Id.\'. ~

\

O

,\ 7

-‘A-P)-'n\‘3

'5

5

SLY

1"-"'05

L-r e.

-‘A

0

0

--wk

O ‘I-..

._w\_

‘Q

‘j

-'7\-N1‘)

:

0

L-

“‘

T"

\)

\

'7'

Q

‘)

wk‘

"31

")

-‘»\MI‘.")

-

VA 1:--1 \~* ~*

R\5V

*

-'1l'r\‘j

=

")

*sԤ

Kf>(‘> *)(»—

""1K--3'\.§L§

Z.

11")“

2.

Q6

.

1

1

"M

L

0-

°\

3 ox

o~.+LoL

1o\+\

'5 1

m

0_

"La+\.

m

i

\ \

‘

~\

<>\+L

\

3

1

\

30:

30L

\

\

\

3'9, ~__... “

MA

9-‘ L

=

<1.“-la.

u\+\

<1

7-0--H

m-H.

3

3

;\ ks:-\

I

1

L

°-

'§\o§-O

x 0.-\

an-+L-1-3

a-\

l(¢\_\§

1

‘

V

\

\-

\,*

H1-\') 1L0.-\ 3

Q O

\

ca-\

o

PM-Rx, R1-9~\q 9"$—9_q

'

\>\

3

3

\

‘\e»'i>

.

:

ix}¢-v~vL'-_-1

"

.‘

A

=

Q‘--\

3(o.l-\§

'1 Q-I

¢"+1¢_"5

a-\ I

€-v~

C-‘1

i'3(¢1-Q

Na-»)

1(<1-\)

(1-\

"

(=1-\)Lo$+a\+\\

'S(¢\-\\k¢+\)

Q1-\)LO.-K-|\

(0~+3)("\-\)

a-1

H;

-'5(¢\~I) 7-U1-\)

1(§\_|)

V

q__\

1

‘

1

\ (L411-\-\

361“-Q-V3

3 '

1,

1 (<14)

a+\

A

cx+3'

OL-—\‘ 2_

~

xwm

.

\

2.

»<£-H1-1

W C-\>C17C1

\

sq-z»

o

“

,

“k°“‘)

o\\

1

'

\

L

\

C-I-3C;

o \

‘

5

3

(°\+l)[o\-\)

l: (@—\)

3(¢\-\) .

.

(1_|

M,

g

=

=

O\~|

own.

3

\

\

"-M

MM

aw,‘ Q-1+1 _3)

(<1-\3§o\_\) _

‘

»~

.13-LQ ox-\)

c 4

-

—---Q

-

H

(_%lg:~'g%/\1*'~')\ !\,%,C.‘.,.@... an

4

,AmaM

WWW

(H

'

CM

C~f¢cL\A

’

=

0.5

(;m
=

Mix

,n

1.

-

RB

H

(N3

Cm-P\‘€

W)

\“\F....%G\

QM)

FG‘._C.\J\

(v'{\)

oufn

xmm

kG

mu

qr»

+k\:

2

CB

‘=

§A

I

all

‘

RA

+*jC

=

Q

\'\

'5

\‘I\

3

Q

s

§

-~—-

Q

A»

=

l

\

c R \

l

~

@(\c~§L)~k\¢¥~3§\+1\“§—3¥§

= ‘IL

¢1\=>c..

¢§‘-c\~L+=3k§+3\\§_<3‘\>

I

A : aha +1§\nii N

_ 0~§1'-

151$-C

am.»

Pr

:

\~\

L-\)\

\

N‘

OK

1-h

F

‘

+$F *§C*=° ~»§¥+¢C -=AY

*5 J2»

Hum.

<1>\>,<'->----Q 5-

-Q

Wmk

B(:..-Fl

=\\\\)

W1

a.»_.x\»§‘ -»§<¢

’

A

ea my

x

<_n‘u>¢_;\3

=

\>¢_§‘

1

(_\§‘(¢c_3‘)

=

<>c.~5‘

(__\§(0_'b__R"s

‘v\

1

0~\0-\‘\L'

m

-(\-\)3\_5

1».

(—\§\d~1}"_‘5\¢\§.1-

‘5\\_o\§.

.

>

-I

‘l

;,-,

i-

‘

i"

7

_\‘)""\";

‘

'

H

W}

"

(_\§‘g\~§-5\.)

=

\"‘i~‘5‘°

5

*~>

.

.

_?~;‘ 1-" ._;1_.

‘.1 ‘a =-.

,

'2 .-

H

%

,'

5;

\*.

ac

=

k-Md‘-553

.-

‘

an

1

c\

=\-~> L,

aw:

- 1-4 ..-‘:1-.-_

P.

\n.\-\§

;\r_-

I

-r-‘ ,

3*;-ck

=

%

V

gM_,=><<»~\._»¢~\+ks»~~<#&>‘

L

otkc ..<:.c\\t-<».¥3x.»“}"<\_7:7{\_o\§-\¢v.d~\§3\~

=

-

au:\r\1'-°'\\><)L _o~‘fL + 1¢Q§°>\~

=

ofkc

1

0,\0\\C, -+z§3\~. _o\§"._1"\1 -CHI»

I

'

1

‘:15

BC-FL

'3 C

'

A

5

-i-—-—->__.._.-._

I

,-

* 2!

:

CA—~€\L

w)

‘ 5-1‘

If §

-iii.

<:A._G\"

k‘)_U=¢- ‘$7 '—U~'}

(<»~\»-

'=

a\;'C- -a\\oIiL-_\\L\oC -\,\}/§t_\;"/§L _~=;\>t

=-\>(a\>¢ +1-)‘~\§ -QJYI ~

cm-Q‘

=

’-= =

Ms-\-\*

t

»k~2_J;-‘§\'\\n

Q\\Ԥ

_-._i_______

A5-HI

$3: M»- H‘ ;

')L\v ~

»*

sa,

(M)

-5H1

=

=

Cl}.

L‘ (\><;_§‘)(¢¢_=)'*-)_-(3§_kc)l 1. 1 o\\:CA.-L_<j\>AQ -5i_0.AC-. '

+3/§L-3Y§'“._cf:\\1

c‘.Ko\\@¢+L3\r\§.'_<1li.L__-51\,

ca;

“

._c;\\‘)

-1,

L3“?-C

bl

~

.

.

Si»

Gm I

c\\=- =

u\§-\.na§§-¢\> -

u=>¢-r,*>u\\-<>~%\

?§'o\\-¢-\~‘¥~\*§'§'*3°‘75“

~--/~»- *‘~‘>“i

-§

1-V!

<3~.\-‘<~~AP\F ’

=

7-fjk

=

§(o-we +?.§.3L\ _m§‘-

(Rn-AF

=

._r:%\’“§

-\>§')*

4; (D

~*r<>\\,¢!§ 1

_¢.@§$

M,

-

._ck‘)

3 b

§A

*

A

._.-__.----_--%,____

HF-Q56:

(‘U

:

¢)A

52$)’

‘”“"~‘“* I

“¥'H*~><*>‘~~@\%> —<<>\<-‘J‘><\~‘§-M»)

’

*1

"5

UV‘),

Q> Q,

1. +3\\§”_cJ3\,

.31»

PG.-CH r FA

g

»

’

”

%

+13\/\§_.c\§l'_Q\,\1--3b)

‘§(\<»\\,c

HF»

1_

39‘ -"*§')* TA" '*°‘/~§\r\~o/»§\\ +acj\> “M3 +'"§‘*~€ * 0%“: ~':<\\‘ -33$“

V

$3}

FG-CH

w

:v

=

FQ_Qn

=

--m) _(q\@-\\‘>(°s § _ C.\r\) lkk ‘A L 1 -3 ~¢ §fm%-¢y~»¢mm+M3q“¢h

(‘sh-<1§><\\g Q\3Q\\

_‘_-1})‘/:*§ ‘_d\\A§L__

‘»\Km‘\o('. —\-'L‘§\r\g.._oi'l§L_"'=;“\;

‘

-QM‘)

~

.

‘t

km .---I---_@._..._

cxG\+\»\\73+"}C

KW)

0

=

553:,

C’“G'\'~*r\"F‘Y°§C

=

O~(¥\‘§~\o‘5\+ \/\§‘3\'\-.cx§)+*)(o.\¢._\}\ _ I

“W; 20

=

_.=~;4,-;

-¢y:;

1

J.-A

...3,g\,,

_34\=

L

_.__..__..-_.___-i._.__.

l,v'\'\'\)

$55.

\\G\+\oF+!§-C_

=

Q

~

W

'5".

OQQ

H81

'

MA +\>F +§c:

'

\\U~5-\,;\ +\>\a\~_@.:;\ +s;g¢\,_\H

=

~>/:-

=»~”&-&»~‘>*~

%

O

=:.

A

=

~-‘»§

l

*'jC-\+§F+cC

3(»\;_\,¢)>+:;g5»\_.=\H ,,¢g¢\,-_\{*~)

= (-=

-

=

')k§‘_<3L\=> +7)\\§

mkc

A

]G\—v§~F+cC.»=

Q3

F7‘-\~G\L

\'\'\\

G:

um

\—\‘+\=”

QM

HKSC.

+ H‘

CLQA-\-Y>)

=

P~LB+¢)

%

-L"

?>\4>~+c\

=’

'FG\\—\

M

kw

UM.

ac

..

FR.

C.P\——G:.

1..

\

*

'

‘

&*Md\

§»\¢.~L.L

_,M>,

%

=

“A10

V

l

BC.--F

2.

as-G‘

0\' "S

Ox

=

0

Fl

cf

*

::

¢=*.,¢,'§ F1-*rG\1

Y

'

-y _'

ca

=

= =’

-‘\'Q\OQ.

~¢,\§"

Qw“.

-

'

S» -

04;‘

+;¢=)\é\§ ._o(I§L.._<3L\,‘__

A

_~_

-

€@

:-_

§.q,.

1

+<>~%&

A»

SaQ:-

Us

~»/4%

‘W

»

3G\».-1}?-vcl

UM

,

?>c+cP\ C§5"\'P\)

»

¢i(;,?> M.

¢u>

F**@}

I C(R+%).

6$*~**

=

ml.

mu

-c:@\-G‘

=

A»

sf);

AK“-*C)

Ms-H‘

+

mdk

=

m¢

0'

@>=

5,

%-

0\

C_P\v»G\L-;

'P\$.-H1:

_

O

A

.

G1

=

H‘

=

A

c.

’

I-\%

X

'

AM-my G\L—\*

H1

:

Ch

=

P\kC.~\~Q>)

1

$\(5~\-Q)

1

.

AG\*\"\‘"

¢+v‘

\W>

a\A+¢)

=

um

A).

$21»

\mM~4

ms_»\‘ EC

4

~F’“

M

\>’\-4w-1J~_

,.

Cb

=‘

pm]

_z:>

0

=

P\@,-k-\’*=.o1iA

'$.

ac-F‘ A -

t\AA;~»f

"r (KB

HI"

;

z

F‘.

Wm‘

-

=

Q

X

Ab

acx

A

e>(r\+¢)

i

Wwdi

H(>°\

M I

$.41‘

mac:

=

FC».\~\

/‘I-Mm»

Uu-L

Puk

\‘\'~J(

ac =.F‘ ‘

<'>“_59

._

2G1

CF:

1

56

.

-:

"M

**»~=l'r’-M

~v~~

&Bc)(cm(A&3 '

E

=

A

o\‘e¢¢"

‘F6-\—\;

=

____

»

Qil

1

e? W

=

ABC

.».

I-L

FG1\-\

_

Wvdl

Vxnu c.

C.

O

(L)

Ab

<1

0"

\n

\‘+c‘

1

o

s_.>_t_..

:

‘ado

0&6.

_c;\,

051$‘

Bo» <'_¢

V

‘

Q

c..

\>

1

‘

\.(.\'.A=C_O0~

bcuo

’

"¢H,c.‘».\,‘ °.@Q+¢\>

~

0+0-nu»

<>+<:~c+o

Q3-+0-\-$1

\oc+o—\-0

}.Q.\.qg+q ‘

g‘\-LL

O~¥

\q._

Clh-0:‘

Q“

C.\a

§c+o+u’

1

‘L

\'.~+o\.+0

QC

.

_ ‘

r

'1!

‘a.. ‘i <1

.i‘ |‘I

kc

I

zatk-Q‘ '

________......_,_-

H "I U

3'"

‘Mai

Ԥ\'\.wo

1.

\

Lu

Lu

\

Q‘

1»

”

2

\

Lg

\

Q”

us

U.)-LA)\J\

\4

‘

k.~..)

(Ks

up

Jpawt’

ck

11»

M

pg;

1

\

Q)

X4-"*)Jr‘AL"*’l_0$\'»LA):

0

_._._.____-(z)

Q.

\\

N

u

L4)

MM»

\

q

1.

A

1

"

,0

Lg

an

/L

be

LAJL

'\-Q

\

3

\

b-\

\\

u

LA

L»)

'3'

M

U3

H

L ‘~**

1

\-J

\

\

u

\

{J

\

3 us

L.»

L.)

'

';

\-J

\

\

[,3

(,1

Lu

T

\

L»:

\

w

M

1

\-.

»

-_

w

'-A

1% \+w~-wwn

¥

:

(A,

bu

Lu

0-Lu +u4-\.->

-

‘\

\

L

3 5»

1$"L$\L\1(.:\ . '

\

\‘

H

1»

(.0

\...>

1

1

La

i

1

+w

no

L

‘s

K4

\+w wu.»

1.

1

H

+m+w 1,

w»

I

H M

'1

'

L

~

R

5

‘HQ N

1

w*"‘~'>*‘*>*‘~> .

I

-

V

3

3

_v

“(=9

x

*-

‘dd

1

V-W-J

\+-u+w Q-1.»)

\~w+L.>+u

\

Hug

3

‘S

1

+m

\+'L~)¥—L-J

\~1..>+(.;-L.)

L1

+¢.>-rm

'

3

\+w+w+u>

us +u>

+'u.>+h-\

w+1f>=vm~m

m»}L.(\'+(:»b:; \-\~l-1*») *ruJ

\+L)4rL3+4-)

7'

‘h

b.)»i—L.)_‘\-u-3+-LJV

s'\~\11;_11u'::(

w +-u +1.; +w

L

'3 1 \+=.._a-1.-.>~—w

1'1

H

s

C

1.

‘L-.>+L.:&-L.>4-M

1.

-!\ *'L\JNa-L:\L]-3

L¢4.(,_,+w+(_,_,

L..:+l.o.,\,_,_,_‘_,

L¢~\..>+u+uJ

\+m+u_>+-u é\

'

9°

M ,

bJ+bo+Ld\-L.)

\

\

N

1;

(‘J

1

1.

~

M

2

_

2.

'1 ‘

1

*Q-

-xr

/~»..#<

nu.)

M

n_§

=

W

U)

U0

$";"'\£4.

=L

1

1

W

9*‘)

w

Q

y)

\+\,.,\ ~1..)Ȣu '\

\-+<.n-w+¢.,

'0.

mu

-t

1‘

+L.-.»+c->

H1\ H

R

*#

_g_;

-M.)

-L-0 '1

-W

"

"5

-N

Ru

:

k~)

\

\

\

\

\

\

\

--M

\

-H

\

\

0

o

0

-S’

Q

Q

-5

O

O

..€

o

o

0

o

-s

O

-S

0

0

0

0

Q

_S

...

\

\

\

D

-L»)

\

\

§

2..

-L.J

—-l.-.\

-

h

Ru»

‘L KL.»

1

-‘*3

S\

N5 1

1.

z>="‘*‘

_-,

_..

\'

..¢

\

\

'

Q‘

g.$"gl

Q""9"

gww C‘

S

.

L

Q‘)

3

50°

O

O

—:

.- §

(3-9

1 =

0

-1-

O

-

F

K

50 .

0

o

0

-4'L'$)

.

_-S .

—S

0

-§(o_L$)

[§>x.\1. 5 Available at www.mathcity.org

‘-4 7

-

(g3__r»

~

m

mm

p)\4'\AA

L -

1\\,\-QC‘

2.\|],§C} i

'\))

Mu.

7—¢3v-Q-3%}

m

4.

c\

\$|

C1‘»\

Q3-\-3-(11)

\,_,_ ML;-,;\,1,k

,,_

1&1. +3\>z..

c'1“~'1¢1L

1-‘D1-'\-C)_

(§~.D.'l_,\/$'Y\-l¢v~¢)~/vi

Q.

C1.

‘>1.

M A

an

\I'->1

Q3

. (1 own '%x A

Y

.

34..

C‘-\-la‘

1_\,,\*¢;‘

‘

la‘;-"s\o|

C.-wL»» 1-\n;q-C1,

i‘I.\>;~'1-C‘;

‘V311

C-I

<>on.a-z\n+\-cw.

on; -rib; +\-C-1

t

2JO'3+3‘,3

7-°\\ '\"'5¥*|+ocl.

'10k\-k-Db‘-N-\-cu

Q¢‘,'_7_"i§_\.(‘_‘

"'

2'“-‘L‘\'3kL

Cum.-141].

cx\

B,

c,

Ow;

51.

C-L

1‘*“'3“"+°Q’~

'5<>~»+‘<>\°1+\-CL

"Mu +<5‘<3n\.c1

'

0‘

'5

L

2*

_°

3

2111 + "U01 +°¢1-

k

VA‘

:

‘o,

(-1

0.3.

‘O1

CL

In

‘O;

C1

“¢\\

5|

‘-'-

<>\1_

\>\_

Rx}

‘M

\

\

-

.§0*3Q°_-53 +Z(1-°)

Cl

.

CL‘ Qqlr“) ¢\>

1

E

5"”

r

!

-*

1-173)

a‘

\3-

-4

B,

B;

0&1

x

.

ff},

Cu

C1

\

\'\¢-~Ul

"

U»

ox

wg

\0\1

om»

{.¢
all

\3

V‘,

Q.

“Lg

k s“1I

n.

11>

HH,1';‘\5

'5$,1$11,

Q1-\

\>L

Q. 1

,.

.a,

\-\

C\\

‘:3

‘P3

S-%,'\\L_:,

$0,651}.

~=\z,u(,q'

(1)\_1L

M.

Tkpdc

3S'z_1>_

~_\
‘B

‘\

\

L

1

0

L

5

“L

1

1

H

L

A

=

2.

$1..

‘1

H

1

Sv"\

;

Q

<=\

9

~

6

z.

5'2. .4

‘B

L8 1

1‘

$.11 Q

‘5'

Ham

L

L ,

a.\L\\-.»..\£~§11)»

I\3.

~§'

4

$‘k'\\

H

QMQ

\

N

3-§

‘

_‘\'1/>¢9/won

5

A

X

'

3

'

.

L41‘.

S

R

-V

35.141

R§-\*\°?~\1+\OU?.\;J=~|L'rmR*\-\UOia»R ;

\,\‘J~|§q’

3

.

5,“\\(.

S‘

-- g°)LSL

L

ql)\‘

u\,151,_ 5%,-nu,

4

V

_'\'5

,

4

8u~,6§2.

J»

xx

4 <=\z,um '-J»_<1

_ aJ\,n

(l»-M~»~

L‘ 7

"

.

5

k\¢:...,~c_,-,

Ԥ

1 '4

A.

1

"5

*1

$

\

1

Q

1'Hl4

1

s

wn.

Y

W

\

"\§)l_

Q

s

s

4.>..,\,

I

'

7

.

_

W

K

I).

QLL

‘

-

l

ck

'U>

‘Q

\3.'

.

Vkn\I5<

VA4-+1.

L»-nl

W4)‘

km-t>"\

gxmq

U»-an

(\._1;"

*L¢~=\§”

~

1(Q-\-)k‘»-¢\(¢_¢»u-am-£)\z-1)

=

KC-1)‘

£c~u>L

,‘;‘>JZ\.

L¢J;£>—

~

” La-ML

(»-~»>‘"

(5-av‘

U--H“

(¢—»)1

(_c-1;

(¢—>\\L

K

\

M-E)‘

('1-131

‘\*

‘(I1-IOOKJPI.‘

1

1

‘L.

of-1¢~)-r')_

\>\-“I-\>la-1‘

\o\-l\~;\-‘gt

C1-1€.1*\-‘it

c‘..>.c-;+~;'

1

(1

-16.

\

$1

-l\p

\

QL

11>.

‘1

'_

»

¥\>~»~

¢\1.HL1\\3

Sn

31

_z¢

'

\

of-'l¢1+};L g-I-\»1~T."

C.‘-7-Ci‘.~\-EL

\

\

1

‘)

1.

5"

{L

1‘

u

\

'

.

H75 |

A‘

1

'Lq_

-"Lon.

l

b1

z_\,

\

1

\

1

6.

J

6‘.

_

L

1.

-o~*<1\

~

':--'2_ ?

1.

-

\>

\»

\

CL

Q

\

l

=-?-

I

L

g

\

c\-Q

0

51¢; -'\>-c

.0

0“-C. ‘

L

L

-‘

R1 - K 1

¢

¢-

\

§x¥-L{ 1

"I--I

“M~»¢i

m~c

1

Q-L

\ »"»<.‘

\»-<_

‘ —1\a-c)(bQc)

Q

R"e‘3

-\- C.

'

__\

‘

A-4. b +C.

\

*1“

\

=

A\

—tkq-C-)(b—c)(Q‘\-¢*¥_%5 ~7*§°\-WU»-<_§(C—0u) \.

=

*

’

Al‘ \

»

\

\

7*

")

1\

5

0

w 4

12

l »

-C

C

1

'

2‘

a-1

1-1

5_

X-IL

5- 1|;

\

I

?uMJ

1’

_c

Q

L

ix§~M¢&*

‘L

4

1‘

-1.1»-1 1-1

L

Q

.

1

I.

1

Q

\

V

Q

1:.

_

%‘~

..

_ ‘Fi

k_c

‘$““MM.

3

Ry »:~

Q9

,

‘—:7é, .

\

in : (1--t)(’3~l:)\

M

u

;;,,,1_:_(v\_~»)L~;_1)k2-1) VMXL:-lg

A

\1o-Jl».v>

Q13

'

e..’,1>L

0-!‘

'3-KG-\>\k\o-L§

Ix

R“

Q)

(¢-¢)(v\~‘>)(‘o-1)\'£-13

“mu-JK

0}

L\¢-L-

(‘.1

0k

of

0.

‘

;

-

-

A.

A.

\>

"51

1¢,_\:

C}

ldlu-..c

__¢

C.

\.__

c

Q

"ck

on

._\,

.

5

-C.

C

\>

Z

I (Q}+\B+_C-'5d-\0£

¢ c \~

.1.

3

‘

on

'

L

53.. ‘

L4.>k1I».=

1

--<1C.\O

C

O.

\o

B

a

C.

ck

\>

0.

B

Q

<1--\><1 --G

an

1.

C.

"Q"

,_

5-

C

0.

__\Q/c‘H:*\/C

__Ac +?(c_*\;~

:

—C

-\»‘+c¢+<.¢

-°>X° +c_‘+‘§’6

A

-'9‘

..o,%-»a_%\-c."

’-oz"-1-\>c+\,,¢

‘1.\>-1-0:“

I1‘

\,

$

¢_\

$2

-c.

\n¢a_(-)c C.

I

R1

3

kw-h\\u_i)k~>->1)

=

5'1 c"“““"” Q“- M‘

St

'

K1-1 )(‘>~1)(‘J+/I - 1-,1

=

,

U” *1’ .

5+1

mm-E

'

.

\

L C.

1“-\§ I

a

I

-—¢(C+\>‘+q/<.

")“- *K¢ +1‘ 1.

_c+¢-\n

"

+o\\n

L

B

J lab-<.L

M

T

(177 P\-yd.»

C”-M’-KM.

O\.A\

A

2

‘)..

Qvk o\\o

B

c

A INA»

-_

<1-

\

_

A\-A1.

1

(1

\>

___._-.__@

C.

.3

A":-

.

b

Q

M

§_~,_‘”_____L;_‘

R‘;

1

»~u»-m~\»u»--¢> ¢bC ..-(L -E \ -Q-Q~¥(_

=

1.

1

M

1

Y

C.

=

'8 3 —C_3-\-3a,¥‘Q --0.-\>

=

1 1 ~Ko\"+b +c. -"$¢‘oc‘)

1

C

--0~

B1

+@<@~»-m

=-bane E

r~

I

-ckcx 1'

.

1

“"'°oK°&'\°°\‘¢K“°‘\° *\A"1.-lT‘>‘\'\>\-\>L+a\v:.\ 1 1 +¢\,< —0~+°\\oC+a\>c-c3-\> -

=-A

3

'"°'~

=

A1

- 0.-—

*'$o\\>L~

Q-1'

- \<>~"+\§’+c"__1..\_,¢)

=

.

V\’...‘k

b=(

R...

Q-‘"‘\'¥-\-‘\'C-.;-'§a~¥(s].

"

I

1;

(_. 5 f"

\-M-V4.1

1

I

‘C-0»

it c.

\.‘

\

\

.‘L

C.

‘

mu-M

J

ml

"

=

0..

LA.-c."

h

.

L

\,_f;_ ¢_

-L

:c= a.

¥ ¢_

"C 5

1*

¢i|

.c'.‘v'" x

Avai|ab!>e at '

i

www.mathcity.org

1' 3. 1 =' (Q-\.b_~,.c,>___'5c'_‘~\}t-

L

L17 S

'

'

. %_

r'\";-~A

\'> *3

-,

”nAdjA,LCA$ '.

“~11

r»-Pr

M

1.

\

\

\

7.

\

\

\

W‘ *mM*AJt

Hwkmk .’

<*
*1‘-»4L

1

Laji \.»J '&.

P‘

1

\

\

"),_

‘

L

\

\

\ X

V

.

L

\'L*k

/“h-4v»»J

59

.“‘*’>’t

=

%®

.

\@~\

2_\\

New

\~=\~

;_R\

%,,,_,,

\1_\) +\\\-1.)

2 1_K\1_\‘)._\

1("s§—£\\ +(~\§

=

L—\ -x

~.

\;.,\ Nam.»

I

1

7»

M

4-

\\

z.\\ ‘}\

L‘

Pw¢\5P\:‘\\

\‘

‘\2-

\\\ 1

\.

|

8. .}\\.

U

it

‘

1

L\

1.

\

¢,,;,b*;b

U

\\§

"1\‘ |\l\ \\

‘2.~\' ‘2. \

\ \

'1

\1

\

\ ‘

\‘ 1 '

\

"

.

I

'

$13.. l

.

y‘

\

\

_'_;

'

Y;

‘Lw"'L“~

‘HQ

-U-H

‘*~l

H—\

-L1-\\

-U.-\\

H-\

'-(1-U

=

\-L s

rx3

___\

__\

-\

3

—\

L-\

‘~\

75

=

t

\_1

$1

.

.

’1

I

v

43

I

P\J~j.P\

*

s. (X

—\

-\

3

-\

§-\

—\

3

'3

T

I

-\

—\

1

A-\

-\ ~\' _

_}‘_

—\'

3

;_-

...\_

N

:

A

‘

@‘

?.._,

-\

So

"3 -\

.

H

*1

‘Q

-_;. --

Y

H

I

i_I_.i.i_._......._-.-_._-_.

1

,3 ‘I

W --

.

,. ,.

5.1-.

if

§

B

_c ¥

L‘:

|

“.1. -.<

n

k

-

',

D

=

..

a

N0.

é

»~..-V

3‘\

CL

“

1

'5

'5

>

15

ouh

1"-Iv~¢vJ

»\

Q

q

5

¥

<2

AVa"aiT=§$ at

_‘!\’\'V\/\/,<.-¢'1A1,i=1"i§f“|cag';:;y,,¢;,¢g V

\‘k4J(

f-~. K .

H

-I

5‘

.\

1.; ,;

.x_i

r.

-2“

\».

..__-1,

\

L .,

A;M?*

(D

_

-

_»), _img. '4: 5

.;J=

Hi

1:.

-

.

;

2

"

,-

y\

3

=1

>

:2, 415" 4

'-

,..

‘: .;_,

1»

'

" I

I

~ ~!

%

%

3,

"

H30 Haul

¢f~\r\ \D\

‘MM

=

\

'55’

M

4.x‘?¢~....L'-1

1»

. uL\\c-§‘)-\~(¢-\»~')H+‘1U\§—55§ ¢\\c__aJ;‘_.C.\\L+')\\§+j\n§_'L\n as

,_

\\>\

L

.

Nev-‘

1;

+13»\§_~=~§—‘-\'\

a~\c-

x‘

_‘\~‘%\

§¢

,

Mp -1_

H1

kg

4

‘1 c

k

,\

’\¢-§

=

.'

\v\-

\-

45

1.

_.

\

5

‘Y

‘Q

‘l\‘

_\c_\\ .-13;)

ac-‘)1

\,\§__3\

..(¢\§_-1k)

+.

\\§-sh

-<¢»~~~m

'

-’(°\§ o\\o

A

-5“) -\\" 1

U <-g‘

55-0“

as-Ck

‘C-3L

\n§-')\n

1"\—°'~§

g¢,§‘

MD

em‘-*'x"’

W

L.

-

*'"-

.»~@é*, |o_

..--

"'

"'

‘- 3K‘,

1\

5

D

l

_t_

._

__'

.

‘F0 (QM)

W

11;

\-\

L..-

L -15

...\

,

3.§_c.\¢\_

3§_c~\_

QC-ah

“s,-av

¢)k_$§

K

W;-3k

’Q

1

\

u ~‘?

‘*5

‘kl

\r\§ .-5X

d\\_,\\'4.

*'

HEM

»

s.1%,w,Q)

V

be-§‘ \

.L\ 1

D

=

(“$1-1.5\\§-4>~§

L"')5~L\~ -ck‘-3%)

L‘

‘

;

W

.

,.

kg -5»,

<>\¢~‘)L

5\\~¢§

-;\\_o~§

¢\--\\.L

I

§Y

______,__,___._.._-.-Q----——-—--

{\

(\'\'\) A

-\

2.

1

\

-\

>

1"

-1

X

.

" -

\

'

\

1-

\1'cP\‘1_\——\

i

I

'sA1.~1" \,.;q_

X-.n.¢

\‘k¢J<

If

$155

as

I

\P\\

.

“M

\

\P~\

~\

1

11-1--

L

1-

.

-\

\

T

€-.,v.,.

P~\

: \(-1+1_§+\Q~‘1+3§+1(H_-'5) O-\-Q-L

2

=\ #0

-\5\\

,. Y

B

i. iv v.

~~

E

‘A. Ma‘ '

-

\::;\ --\1

I

H

QL

Q.Rl.kk»‘>‘

R‘

-\:::\\:;\ ‘ \

-1‘

‘I

)1‘ .1

-\;

D1

t"

,vJ@‘»

i

1

~ \

sa.

Ii

Q

\'\Ii-5\;

j§_C_\»

L -'L

,

1

1!

-\ l

J3

1-

5:;

H ‘<51

t

F-

"'3-’\L

_(-L\4-33

—£1~\\)

"'- -L

- \-1

_\-pa)

=

"‘A~5§"‘

0 1.

\

’

Q

L

\

~%

€1\5-~

1

‘

~\ Y

-i

h\ gu

\-n.

-3

Ԥ

\

~.»;&\=\

\

'3-5

"A

L.

1

_.\1.-+1)

\\

r’

'--\._

3

(D

O2.-I A

-

,, P‘

xly

-

.1_..§@

1

‘

{Q \

L\

‘B

Y

-Y

1

1

~\

-as

s

—

§

3

_~__*;_______

_i.

.N Merging Mzm

an maths

O9