m1,: ,4‘ , ..».w¢ ..4-*»;.~,- ' ==»'..';'-a=eifc‘*9' m»-1

13
_ _____,, ~ -......--F’ ' *1“ | ‘~ ,4‘ _ » ,_..».W¢ .1“ -=-~*-<7 "’ ..4...-.........*»;.~,-_' . - . |_.,_._.,,,¢; __, M1,: ~ _-- . _._ ~ , _,...*,....... . I . ,,~..-.*~ -- —_-~;~*- »‘ --4-'-f;T_,...u»¢~<~"~- ==»'..';"'-a=eiFC"‘*"9' . --1-"“" .~ _ ' . ' ».~'~-"“'..-&~':=-V, ;, " ....~~ . - - ' . J‘. , M»-1., _..1;¢.~ h-'3 ___,_»_ ---~ ~ - 1_ 1, V; ‘-1.5;-»_,_;~ ¢'!F'.""_€ _':~.~- " _ K.-I 1, 1‘ u " ' ' '7 ~' 4 .- ,1‘ -;, , . .»_ -;_,‘. r ~ ‘»' ~.~ ‘. ~ -»;'f+- “» ,\**{;,m ' a ‘V ., ,-»-*.\\: - . ~_ V . - ~ -—~"" ;;.'..1~_1,‘~ m, "d~ .' ' ' . *?~¢~' =:;~._‘1-.;1*_'_‘ ; -1’-}""’§”.;,=\-1%,‘? ' Pg‘, ' . .1 5* <3» . - . .-_»_,/-?‘.“i~*‘”_!'i~==§;._-w ;.:‘ i * A2 ,1, ).'¢\;‘,»_i;u.> ._,.; 5., an 1 f *7 ‘b ; ' hciw-°"9 ( 1;: ::.. ' " wwwxnat vi __-_¢...,\ »..- '>.- ..<,y"\ F ,- 3) ~ A-. \ ~~ ' " ‘W 4 L. . - - U‘ . I“ , ‘- ~,». .. ;;.;~ W [ Md/>~*N'l7 ’° “fwd 2"“ X »5@~§-7-*5” &.,N.J,,,,,./45*» N.;~5u4##»$$'1°’"““7” ». »>r~J~‘*tv‘””“""»3Iii3.:’:?->\ I Q . IF LO 5><*‘kD‘37>Q&7 Fm l .-- .< , . . 1* ' . F,;I»’¢/5 ._ FMM was +~=/»/ ”° 1% W P;,.5»'W'*°"" I) M"‘.-:'?|x. T;_’P 'HMM’I!F e ..J-M1 . , Y J I.F. ; ye‘ M yfo 2.) Q IF ,5 .+, Wu»-1M-*“/° . ‘>1 ~ .F= . 4-' (1*Y'>"l7:0 <”JM‘Lé ' 1fw>4”‘ *3 ..oiM5""'M »d»@~*f .> ¢m1*- “*‘°“‘> ""°“°"‘°°‘ ( *?°", f ..= ii?) ? 3) » at Lb (119 s>% <5; ‘Q T’-"*7 ~oL(fa§~3,L,) 9 ’"':i’f1%1§"* ‘? 7 -\ vehiqw 1') “L41”//Z» - '>4.+“7_ . .~a> . "‘ *7 - ? . .. ~ .-_. . .. . ,...\_,.-... A ff ;_;jf___ _‘_,__ . _. M, ._.: " W ‘~- _,_ gs-\._7 \-_- _,',. .9 . 1 ~,_:* k » . . _;: ,......-..L- -1* *1 V Exercise 9.5: Page 1 of 13 : Available at MathCity.org Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Exercise 9.5: Page 1 of 13 : Available at MathCity.org

Upload: others

Post on 17-Jun-2022

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

_ _____,, ~ -......--F’ ' *1“ | ‘~

,4‘ _ » ,_..».W¢ .1“ -=-~*-<7 "’ ..4...-.........*»;.~,-_' . - .|_.,_._.,,,¢; __, M1,: ~ _-- . _._ ~ , _,...*,....... . I

. ,,~..-.*~ -- —_-~;~*- »‘ --4-'-f;T_,...u»¢~<~"~- ==»'..';"'-a=eiFC"‘*"9' . --1-"“" .~ _ ' .

' _ ».~'~-"“'..-&~':=-V, ;, " ....~~ . - - » ' . J‘., M»-1., _..1;¢.~ h-'3 ___,_»_ ---~ ~ - 1_ 1,

V; ‘-1.5;-»_,_;~ ¢'!F'.""_€ _':~.~- " _ K.-I 1, 1‘ u " ‘ ' ' ‘ ‘ '7 v~' ‘ 4.- ,1‘ -;, , . .»_ -;_,‘. r ~ ‘»' ~.~ ‘. ~

-»;'f+- “» ,\**{;,m ' a ‘V ., ,-»-*.\\: - . ~_ V . - ~-—~"" ;;.'..1~_1,‘~ m, ~= "d~ .' ' ' .‘ *?~¢~' V =:;~._‘1-.;1*_'_‘ ; -1’-}""’§”.;,=\-1%,‘? ’ ' Pg‘, ‘ ' “. .1 5* <3» . -. .-_»_,/-?‘.“i~*‘”_!'i~==§;._-w » ;.:‘ i

* A2 »

,1, ).'¢\;‘,»_i;u.> ._,.; 5., ~an

1

‘_“*

4‘-.‘\7

f *7 ‘b %

; ' hciw-°"9( 1;: ::.. ' " wwwxnat

vi

__-_¢...,\ »..- '>.-

..<,y"\F ,-

3) ~

A-. \ ~~ ' " ‘W

4

L. . - -U‘‘ .I“ , ‘-~,».

.. ;;.;~

W [ Md/>~*N'l7 ’° “fwd

2"“X»5@~§-7-*5” &.,N.J,,,,,./45*»

N.;~5u4##»$$'1°’"““7”». »>r~J~‘*tv‘””“""»3Iii3.:’:?->\I

Q

. IF

%

LO 5><*‘kD‘37>Q&7 Fm l

.--.< , . . 1* ' ¢

. F,;I»’¢/5 ._ FMM was

+~=/»/ 2° ”° 1% W P;,.5»'W'*°""

I) M"‘.-:'?|x. T;_’P 'HMM’I!F e ..J-M1 A

. , Y ‘ J I.F. ; ye‘ M yfo2.) Q IF ,5 .+,

Wu»-1M-*“/°

0*;av

ii?

. ‘>1~

.F=

. ‘ ‘ 4-' (1*Y'>"l7:0 <”JM‘Lé

' 1fw>4”‘ *3..oiM5""'M

»d»@~*f

.> ¢m1*- “*‘°“‘> ""°“°"‘°°‘ (

*?°", f ..= ii?) ?

3)

‘ » at Lb (119

s>% <5;‘Q T’-"*7 % ~oL(fa§~3,L,)

9 ’"':i’f1%1§"* ‘? 7 -\vehiqw

1') “L41”//Z» -

_'>4.+“7_ . A

.~a>%

. "‘ *7 - ?

. .. ~.-_.

. .. . ,...\_,.-... A ff ;_;jf____‘_,__ . _. M, ._.: " W ‘~- _,_ gs-\._7 ‘

\-_- _,',. .9 ‘ . 1 ~,_:* k» . . _;: ,......-..L- -1* *1 ‘ V

Exercise 9.5: Page 1 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 1 of 13 : Available at MathCity.org

Page 2: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

S

V . . r. _; "

i,_ » 7' ‘_"~;"'." _,'.;'

>7 . *~.'""'~ ~"\ 1

‘: 7}-I ~‘. »-;, M

Q19

QM};-' @ if?(L_‘__x_\1)d,,(-Q-7(5"yA'===O

1

,~_ ¢= <..f- '. _ > ; _~:i-_%_-- . ,_ ‘ ..- @.~...;-.~ . - - '_>_ .-_,.,_.v-..._._._-__.-:""’~;|,; '§£;;'_;':‘4?Y‘j?;“§;_,s_“;-“f§‘,>'-2

. .- -_-_ -. 1- .~., " ' ;‘ -—p-an¢;—4-un~_____ .. T~ . _‘,__ -‘ ., ., _..‘.;,;,..._.¢p\n--~»-~--=~‘-----' " . - ' ' ‘ ‘-, > * '.'»~-1 »~:"-"Q . . - I - >- ._\_.~.. .,,;_>_-- ,-5 ' v_ . ‘-vI_»==~‘. sq» 1 -- ‘ __ '1

' ., - _ _ ‘ ‘;.~ v 1._+>.~,. -.~,!~\_ - .-_ . _ ;j‘_a;;_.>,_;_.c_=_ , . ..l§¢<* '

’.“‘~=4-- ,

-. '._ nv\,>‘

.\.

L A A ~ ' aw.A .. ; ‘:4 A ‘ '§3;I,.

C0 (@4773 7M»< - 157 " ° “Q M="‘L‘“*'7 % N 23$

~ . ‘ ‘-l_"q';7“.;. ‘:4-.-:~~I'~_T':2

- ' "\:;.-' ~=*r;~r- ??:3‘¢".;-"~ ‘I.A K, .l‘.‘.__

H

,,_ H

~ N =“' i ~ 42-"&1~.*~;;L.. L \ _::__-X M :2 ,,\ ‘ ' ‘K \z‘¢i’Eg»;;.

-3:31" Qzllmvc QM‘;J,,_ _ V j l ,,, =.

.Mj¥-N-5 =J~Xj+l“+1_ Nay "‘I‘F ‘fa’ ‘Q -5 (

- _{ 1e

‘ v°‘.‘,“°”"§. ~*»“{>*i'=>‘”~*>***v>¢v<*>**v-“?~%"‘=%¢-»’

Am-"1A ;2i1—» L

—*;(°‘L*"'7/>“L“*‘ aw‘?:2 ’ ""'

M’ 'X. ,1,

’ @344 ‘F’ 7,1 ~@~*A1=% % = x?. F“ '1‘ W % A %‘b M L N __|

~j;;_*1 -11., % 4,,-1 _1 7'" 12-‘ * *'

1>11-

><r\<

, -x

. A~ 7 M =N .~.»;,<<,./1-1>:gg1i=;.

b,,'fl~;;.=b.@%a7@ L1 1‘l3=,%L T /1 4

. . ‘ -:4. =-C- __.,,_ i_- , (§MJ¢+J(G.--¢%N[j“”K”M >37

¢€*~1+*>¢*.=** ~&,-J*/ =0 1

H " " f S(:+-;-Lg-,)<i-* ‘ac~_{_~ 0;“ ,3“ =0,-@

€>°f*"7) \/,_f“fA ,M0,,,L+17z =¢,/‘(ow M -_-.x+l; $1 ';*l?”'-"*1.¢@;%¢¥'"»¢*i» '

nu'1

x .

' Y ’ k ‘ " . .._*\‘;_: ,, r..,.\

. 7.'.®Ez<a~Ck'n“§6Ej

~‘*"_§-@~+ jaw M t§*""b“°"‘ W>

b(+_%>d».¢+ Nil :='-C.

.')(.L 4.1!. ?é L ‘

2.- 7' * V

__ ——w)C>s~—--—---""""’

. ..i.-_"" =- -_-‘"' == i 2‘>*?>°‘' ‘¢'*M77&Nx -.‘. Nongxf N 9'" x L E?-r

I iii}! _.v

5 . ;.~.>

‘)0 $35)‘

L-.0:, >

\(2

. \=PF‘-,_--n

. ,7

\.

1*’

l

.-

K

1

¢

. ‘_

;._,_._,,,~.._».'_..»-..,-4’)-P_ra,.~::::§_?-'"“-‘.-.='?<

-/1,.

E;-<D@;_'.~|-;-,--_‘_‘,,....."_'

%

%

- +1‘: -1 M§I=;~.-Nx N°" E"‘“”HL&’é75 _ M N K - Y kw"-I-¢,,. H

..5

i

g-i

Exercise 9.5: Page 2 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 2 of 13 : Available at MathCity.org

Page 3: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

t ~ ; ’ - * ' '1": " .,,.'.‘,;.-‘Ira-‘ ‘\"-i ""%: 1-‘f’

(* ‘L < ' " - » )~ ~ ' ~

,‘;';>: -3,11»->5;

:1‘.~ ~ Q -' '\

., {-2 _1_v if ,, 0-

}/W7 _' 1:1L‘ _ ..,.

i

‘I ‘.;‘ .

, ._ .

‘ — ¢. ‘

3I

-4

a$72‘

"K --0‘ ' ,'." @v(L“7"‘ZM’“ 7601/7,/@ V 1,¢./@

O 1’ V L X>aL»1 Z4,‘ -

M1‘:%1’ ’ 1-k_ . a°wE,¢J‘15‘5¢§€€°\'

M~1?f*N-,\-‘- ®‘#“““E"““ 5 '““17‘N‘ "W¢4°..>v_r~3L-;'~_1:<¢_;, -1_,_;_,“;£’. Eli

N

51:

<&*~*1*Q" ' ~»<

-_-__\ 1__ ‘X N ‘S "a '

;.,~'—~ 'V N Mad->~1’v.@7 ‘ ,q

' ELSU M Q 7'~

J-=Z‘ +2‘ """$“?>'* M

M “Ni s:1.,/ e»_N‘K

. X -r 4-“ "2a—':—‘”(j

IF 31”‘ -E1 G 'ii‘>Ml "5'LlXla% v(=1»~1+*-‘L).,= - _ M Q va \W%&.JM$¢q@<,,.1Fx H ;_;1Q3{L),%1_

* Na (L so-’____@ 7 _ 7(P‘) k.,\b-1

1~+»<*>%> “. .3-___J~( QM .(m"7' "-2.. LH-...x»g,>“~\ N ’“ J7 17 7 1%- >. _

M1 " A . ,¢Wv‘6w. M=Jx"fLlbO1L$"JM%® V‘ J1 7 .

M;\¢=f*\1 "’@wE ,K)0l7v;=Ac. _L.(2_'x~I“+K";\\l)t14\""1“>e'0L1 '0

., *1

Iv/\,;M+§@>"*‘1>'“b”‘f>”””‘ L7 '4 J ~°,4. <=*]~*>”='>"‘“ ' 24*’ I $

" " :1 . 7 K ,-.-ju-$~“*>~‘- Q M-;.;n@+<’.-T-~ ~~ Q,»

)¢ " " 7" _.-;.-701 +C;/>1» ff//,_/~/f 2 __g:_ N»

“Hr

M < J ?YA 3 ~-~»>4»1=*°’@ 1 ‘ Y u A J" 5»,-

@(\I"’+1\/)J»~ +¢"*‘ H7I 3 - ‘um ‘ '1 M‘\"N"‘ " 63¢ Ex Mg:\1=17+‘7 ~ ,,_ v<)”‘*[ "

=1+;_

Mg” 7 N =13—‘> §f*"*4**§@t"“"’K5N51 KWM~1"'L“13+k 7k__ . 3- lx+é:>0l/w “Md! 1:6

&D‘f’3Z£1- 7 on. " 4 kw"®U)! (Tn ‘

3 \~ .-6 ,-f;

~,~—M1 .313-¢.-:1~a ¢-:3‘ ¢ »

‘_3gM\/A ,Q,,,§ 3’ :13 3-’ ~ §mAM+5Lt)MA,bNb/iMb;~¢~w’v\) J31 r-C.

1-Féa‘ ? 0' 2 A i' H ~3 7 ’° ' +-@IB L11:

~_..‘.-.--1-~*:*_“‘ ‘ "

-5_ N-;\"'\"_'O‘.'3LLM7’-\ 72» 7.. .J_\_(

h

..|_(‘l +?-‘I)J”"~ 'i.'J’5(7(7 ‘Q7 p JU73 7 /

' H8+.+

~1_\<“

rr-Cf A-->- j

~11?’

\'\./

9-f

P /V ==_<>. _,_ ff» —:-- C (

y + 5&3» + (1 +1‘! “ %:>>aL7 /GD X” 1'4?‘-)f Lil '

( 7

6

~__/ 7‘

- 1 \/. a»-—--7*, ;.",Jr'917‘ M 71‘?-;-221 7(\13+l)~ ( ' '.' V/\~1¢=N1\ " (Dobw W

-F

jlv =°

. 12-1.. 7- ‘-4 77-6 " * ’_ .. 2. ~~ _‘,:\_ 7&2‘ 2_v\ ; IiN°@bMi?\\_,_§L

LrLx+\; Y,’ 11* ,T'+

. ' __’_____’w_,,._.

Exercise 9.5: Page 3 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 3 of 13 : Available at MathCity.org

Page 4: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

-1.‘. . ._

;~<‘.‘_....'-35 '.~ \1 ~ »

@

> _ ,~ . f'__'_____ ‘_‘:‘_;~v'> — f L__‘__/ _> V€__F* %§§._ I,» » .. ~ ‘.--.

‘_$f__,'l?€. . "‘ _ I . I ~ ' ,4 __ I ,—" ' V 7 ;:_;..A:;. .- ‘»--'---'.““_""""'*‘*“""".,' ‘ ‘-.' 1" - \@I\;"?'; \ ~ -‘ , 4 1.‘ .. - _--ii-‘W 7 . _ - ~ * ‘ 0.. I'll-I .-,~-M.»-»-»».. -.;,\

L,¢f_'+-1L4-:_v\)<’l»< +5“! :0 ’@ @ , ,;,(f+~1" N.‘-=-"':"€\[ I H

fl‘-’3.*.* »"?.?_‘*1LJ’?nv N $ pal M 5*“! I

*':'*1-"?' .L7%:. H' J L

H7

_,,:...q_E-g 7

gt E"->1‘*

* " Q‘ x 7£:;'+‘1L.>0[M ..Q.7i‘16L"/ '—'-'0'»-®

‘ ><»~=l"Y>~5k‘6’l

*"A1=7*‘ X " V Q,L_._’r_*\g=~_=~_~_;_:iZ " M<r~1>§¥-‘”‘1».;;=_;3~£'- *“‘<1>“1>‘°7 M ‘ ""*L

t‘/\“ ")€"'1V‘1'1-1 M ,H1 __ 3__\1+L‘}'. -_g»__l(’j_ :,.2“-_

1:1-

4ZA

r " -=>,*°"1 J/' ’ —/‘ -1*“: "=.]_ -0 5,511» N -117 ‘. '1u'.1/M % M ‘1. _1_ ~,\ QM,‘ _,_

1- = a =* ¢ .~__. b;UAQ-AM,b¢,,’@:@,[email protected].) 'l§€(ks;3»¢b¢q§Dl¢-;J,~F=i7-5_

1 »=( 1._ »_ >. )J»~ e3([l-LY)?! ==° “Q9 J¢'Eq(’5b“7;)d"" '11? (mum, 1: 0%2 ‘ wk +1 .4» ‘X 4‘ » ~ »aM__MA‘1_;:.;__,_®,

\ . . -;( L . ‘.» __‘~<“,"(L,Z'+\{“+z>c)

LN='-(>97 _U*'A.l2 - L A

Ml.“ V - t Z1 M=T+:1l'A

N='€%~i '.. ¢2y %, "‘>~= 7 ‘xi’ 1-» . . . Ni: _‘_g,~;H- » ' . M»=- ~ L --.,

M A__ N‘ ,-_@wc=><»-J“D11;(€°! 1 i vb A

j rJ

\,-.-~.

’ 31*)” *4 7 ' \;>.1u I’

. 1 .

;Q;l1t,MIb~@»»@»~*>*~=¢ M @»6x~»W1A~ 1;‘ 35¢

;¢@%¢¢+»»>M '** " ° "'JM~*1<W%“W”W

‘°‘\‘=-9.

*3T’

+Y“;

‘"“r

+

u11-» .

‘ ‘ I.~F:-'-iTv]’Tb:l_Nb‘ NvlICp-~\<>* "‘* —.>¢ J

L X --‘C. T - '”"' l - \.>2 an .>' V 5;“ 2.Q»v\1L a?“ 1"

( ”0"@ . 'J:F‘= -_1Q,_'»'='e'.::7L7k __

._ *1 >-

“H -.-;<>-+5‘; » j »~' V. . 1- N =5‘¢-‘/"’ L, '___ ~ M-s ' X ' _

N 7kn Nx ".@4PE-x0~()_3},;n$ .

.

J ‘ " ? W1 =‘<'--.= A~*W"“ "M1M§L5’"”" “2>“‘b”“1>”"* .

~ .£,N\ ’ _ "_LPA+3\) ' 3 L iij ¢-C. ’»§(4n¢+3~;,'><-)02"\ + * > (

? j -2; %

"P’\w~N"‘=-€11;iI"»-.=’i3» "X 41 *3Am 1”

B

- ______.___--——--'9")‘

i__7_74\>i—7—’7’ 7

,.¢;;§¢gcm

A

‘==*""“‘Y Nip D A_ ’ » N1 "’ ®U5N°w‘a'

N ‘GM N.,.~E»<@J3>1$“'C‘7 NH 7b ' .c 3‘

3

§"<,‘-

.-k___J~’.1S‘a»:(\_I'-4;‘/»\'*"yQ:L)_.'>/.11/-1a ="c< v(

..,'¢.,¢--"'

\

J5‘/4*”-=¢ °‘,"J_*'===¢ M %x um ‘1

X

Exercise 9.5: Page 4 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 4 of 13 : Available at MathCity.org

Page 5: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

~ ~ ---_~""“""”'_"'“_'““,"f; , ' T .v»2‘.--~;§"' ’I‘ ~ - ;‘ - ' '.._..__.."”—.:nI?_‘~31'n

__ .. M I -- ’ —_uwIrI-—-,:pus,-<»--- -‘,'*.'- "H ' - ':1; \>;,w~)»_,>,;,‘:. wrw». -'- ‘ »5 _:___‘____;_—_,4pn.-, ,= -. ,.

_ -, ,~ .-1» .-_-_-.— '~ ~ V 7 ‘ ‘

._W.;¢»=- :__\5 , ,, ';- '

1. \. ,‘ -3. P4 . .

1' fr~zK‘

M = 3->\~| +7-“*1

._ Y £1 3-__ 1 ~ ,_o._@ @ ' ,

('3;-£31“?-+7-"‘7)dm +0’ XJJJ7 5% Q;-’i+~1-1)alA\

( ' ~ ' a_‘1 N -_=2'i3\)3""-L Ow 1;

;- e,\+7"/

" 1_1_'2_K (e_2'~A4_‘1.-]>0(’“ “A7 so -*6?.1-3 N 26*‘;

=12.-A1 +111 -A1-°< |" 51'")

, . ‘ ==-' 4-\”' yW » E.K0~<JhI>‘1)‘£n’ M °

~"®u)NoM5 3 ‘ M \ 7L '1 1

L \_ ' 7' Ab!“ "i

M --N1 -;. l2_~¢ji+léL"(""i"lZ("‘*6¢7— ‘ “D Nmkcx \

i V ;>_~»<37-1-7*" 72/(“‘l$"> M1?£Ni J0) .

. _ 3 1.3 y Q‘-J‘;L3 2_x?..,61J_.-101 ' ‘ M ;’;,_x'+‘*l-1 1 ‘4Ni'Ml ,-*Lé"»\~'[',:M'|ui- ‘ "* 1 ' ‘ ' ’

M‘ 3$1“+”'“Y > ”'<=3"7+L> "hill =- \,;.2 ;-_ -I =‘;.€bx., -1 "‘

’ ‘ - -:- ¢ '35‘ W5 N ' '

V. . ”1C3/$4’ % “‘l””“' . IF. ajpw »V

3:37 7 F9“! ; YM»9b"f"']b5U‘ -,5”? ‘M’

‘ J ‘I —x- _ ,.' ---1}? "H .

Q, .== Q -" Q" H E-,;(a;'~_‘_T_\>aLw--e. J"; *'°N ’ r- -2_0,,\ - :1 -1. " ~ : 9%’ ®~ 31

‘ ‘ -F ;J—_x_ H3 n7 X A @1014 “LX°l7="‘O

/

1

1

I

3

\

1

I

K

(1. 4-<1"/' ) 7. :0 __'z( '

§_(:~.$~1“+?-~1)‘*“*‘;~<L ‘ Wk’ M¢2+;“,»Z‘ N="°J LL; 11 r;o'*"@> --‘X.

\ » ~ X' N :2 E7 .’ -:-Q. 1 +

M¢3¢;+u. »~**r%» M1%WU@”5“¢%

l

M7 '_2:';’§L N_X;~()'X‘] .-'25/%\_‘ » +J<tuw~§ %VN%b'1-L»lb)\r\u7\)J'7=C.

“W5M1=N1‘*@¢5”JD‘ J@@%iU#+~@ =¢

=W~*%»w“”“WwFQ *~***“__Q_ Q, -=1 C .& dMalwJ;m§" 0-“P (ldéi

gk;1,~,~~;+°:%£)<£- 1“ >.¢1MJ1~»4?>§’3-°—’—-"":2"”‘ \@

1. ~ . V_ I

¥£$+¢— ==¢ ~¢ *"“I

L QL \]

-—-I-—""_‘-".-‘y%? 1

V » % ‘J55 $45 ‘WP

\/\/all

“IOT-

Gaf

'7+

'3

L/§— ?L\x

LA

“£4

/\+%r*

7+

L_.;~rfrw~¢¢<JLS

/n

-1’!-3 ,_

r‘'73G.’-

x+/\

~&

\/

O

YS

+'_‘f\’-1

rm4=

;L=j1

)(+_‘W¢_‘l\_n‘fx+/\

\L,“l.

ii?n

x\"i ,2:

3.4

. V1

/.7‘,4'

~wf(L1¢

“W0

"W

“.

/’1%

-P

1I\

434+!

OiLy

I

r

.1_ Ls 8 Jr; P1 _

#\< 1?. \ -°:\§- <§. K ~ \ \1' ( » ;\

I 1 » \-a~1_1'=._ _-

W.-.,,,-' u.-vasnif-"“"»">T~é“'~?m"~""~ ‘T 1"ma__,.... ., ,._. ___ *.

1.»‘...-1"‘

‘L;5

O : .

(

1

1

~_...-L.._..».;.~:-.¢

\

1'.

s

Exercise 9.5: Page 5 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 5 of 13 : Available at MathCity.org

Page 6: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

.

_\.- \

_______........,..:. - . " —. '

,_,___-,—»--— 1", , i_,-W, _ __ _ __-Q"- "L <”',, ~~=¢.,‘ Y "r i, - -> —- " "‘ ' v‘

. -’~» -’ Quack . ~- ‘ ~ Y ~- “*. \ V _ W, .. W, - --i_=__~‘.\ .,., .1,. .- U '

1;; ;~' —=~:>-

V; ,_.»_-_¢-\--».~"”'" “'"'“"""

>;_ . ~" ' vw --- '_ ' ._ ‘“*'.Z'.;"

-,1 1‘. 7,

W; .L .4 ‘v .

A. , '..\ if ,

\, , ‘

'\,t,., .

. “Vbl‘ . . , .

I‘*(;[L.¢ A a"' flu‘ L‘-2* V 0Q(‘I*~+'x‘f)o3i~/~ -T><°L'1 =0--@ @ <31.~mv~1- +<-‘*>~*/>0“/’”*'?’

; M w'“+><*;¢ N~=-XL ““~°>*v+v’* “’=°‘§"’°7

E M1-.~.l1‘1+'>< L L Nx:~zX H1c2)i+L7 L7 N,‘= 1“? Ll V

» ' N .1. in e~/\E‘*J( L M~17=N'»L .t@>I/¢No~»~,EmJ.DIt6'(E7 M17" *7 Q) N» Y my

' M‘V v N

1: "’*___374j‘3:j~=,-7_§-§'3;[ = H.

, 3 ;.~_U>¢+=-H, N~"f 14 3'-7 ="’:?“"51 L " ,Y N1 » -><" -M V 3W‘1+‘1 79*”) I57 J7

Qi_"§:.fk--;..>_v~»<--2. -*4 N1, M'NM

- - % 1)-;r ,1__l Q .3=~+°~j_ 15* 7,_=~ 4_?Si' 1

5:217 NV :— X1+,~.1? . ,xQ<+1) -7:...

?@F‘?“*“~=1;*-.~"“'*""Z1>"1’5"*é>’*”“L“‘" ‘((1- AM

.'-*v'cM +\yN= av/"+3,“**f~r(-\/75’; IJL.-F = =='~ "5

A _ ' Y IF,I J__ L_»_\J(.!.\.\'.<.J.>¢ ~rbc‘-»7@)Ala~1'l.T K ',._

L -V ~ L dtyvy-+-‘1N v*- ‘” L

,.E] %

' 0. .

. ' i~

:M.¢L&PQ7vkAJA'&9[,¢.b@g7_L-F;LL Q ‘/+1/7) Y

§LP‘?

-F

ixiit 2~

7k

"N

T 1. 1- V“A L ‘ ML-:-_3m.}~1+7‘~"~l ' 7

4'-7£\1)ol'M ‘J’; 7('a’-A130 1.Lxxik ,1 1

F97’\_Y co

. L. 1 ‘

h =="_5v\L4-1 L Nv£""37"+ ‘K7am Y“! ?%

7% M,,m .-.@1»E><@~@*%:”'1- *

N /v1=~'-WL NV in .

-5/W.

,M‘ QM‘ @;@eWJw'~;4fw [£3-7t'\1{-‘)\_TL)AA.\’\Lml :,.¢ , -

=-W»»~;r §u:»»~%~W*“>’*“ ‘ “~§’ ”"”-3 ’ C.

3 L\_

:-__€, W" _

. _ /-_. . ~.. _..

,‘7‘ _' .

‘ :

L EM $1 ‘§‘._

' $3“ 73"1,4- §_?>,>_;

¥\&xr1-Par

' “ :\'/t’§"+‘\-.4 O, 3;?

!~f"J

,-

-

A1)Wf

.-_/

I

gr»

T .

1/6*)""}M;

/\"FL

, . 1 \_I~_

__

34

W-Q’/P_

+

L.-\ 3 <

P

1/w

—r-FT

<ff_§+1

-,¢

k-——\ ._.

.¢/¢,/

2‘ ’-_§13-3*?

s

/)5

7¢¥

'25“1

Q-;v.""34(

4 '(L/\+

~;"(—r\7

'u/\+

y_—\4~

(D_,%’Ag\¢+/\:.,‘

@’_,Y./\‘fl\

(13-f",~2<1-H'

v(kf‘“7

~B?

.-

)/PM

<0/.

T~<

,

\

3

\

___},-r...

.+.

L/\_‘

v

..:11-f§7\§

_‘”Fr\

;"""_’;;{":.

-/""":“\2:

+71Z

A7%:

.5_‘°-A-Z~_;TgH

H xZS;‘¥,-R'

-,\§/11,l=’~.¢—¥\@

*AM-A_,,¢.>¥(

><\x

Exercise 9.5: Page 6 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 6 of 13 : Available at MathCity.org

Page 7: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

~-pm~,md$!=§

_#.__,,__,...; "* ’_ _;1gI'rk=-»-'*'“““”""‘ "'0" W ' ' '

' ‘ \. . 4 ._;mf —, -~ ~-3 ~- V

...‘-\-1 ,

@.

J1‘r,.

_ .,;._N,.. .~~.-~.-- ~ ' K;.4: ,1 . -~ "

% I- ;_

@ 1?

_ .1 ‘L ~~0 @ 4/"\*"(5"‘7'¢)M

. 0

J

I

.,Z7/

_>Vr.2.=:—;:;r;@1='-""’

‘ \

. I

- L Y W~=>- ‘I . , . <1-7 '

__~;_~,\f-.1 4-7 )J/»\+(v.+‘{30k7L . N:;_-My-Q.

,‘_. 3 N}, '2¢»"'*1

M.=»-1‘+&1*+1*”1 * A -\% ~,;==-1 iM7»1. N -.=2-X ‘

*- +3 7Lm=i'»"~ fl" 7

~ ; 1?{ M1%m @v>“"E"“M“m

M\‘+NX' ‘._M®{_o ‘I\lOv~l;7‘0~‘£DA6b£°] . N N4-$M%‘m¢»}1>~l

- ¢

yé ._‘1’/1"‘-'-"'l‘?1N’ ;»,»t+z‘*3;1l'.:;~< N W14"';a""_ LI» >. ,-$1“ I».-**1 ( NKM1 L»,-1 -;?—*l,‘b“7> ~

pQ‘+‘1L) J7~

‘ IF QM" 1-‘! '-(-L) ”\ I

1 .(34- —-21+ 15¢ ej 7 "2"" =

. .37‘ "‘ . 1

IF, ; a =' - IF, 2 ’—‘1," Q

:2’-—"' . ..,:=?_3 #330.

m>..§

*1:3'4

11—¢*1,»-

. 1 ¢

Q .

1

~_.-..,<'1.-»»;_.~_

fn

u1

1

71

1];

¢\

.¢7@*~; M“p;;f>l7a>h~,;£-F=@.,_7q>‘l7

M =-~*e~>»l~ ,_ ’*’.m»1-Z *

@»a:*+11W@ W“ ""11 Z-*7 W * “ 1 .@&N e-qt‘,-1 7 ’. l7)J'7;‘°

5 31 ‘>1

.. Y 1.31 3”‘ g.‘~ N =“°":*”*“*‘37 ¢~/1-3;“ """"”"'~§M ,3-‘,1, 4-lxz. 4- 7 1*

_ - ’ ’C. L1 -N: L‘-‘"0.{~11 .-.@w¢>‘_‘“*’’$?f(‘7 M1=w¢ * H’

),,b'~»-* ‘ I§1<r>~°H>"@\g7 -

9

L37

>31

1~M1 '9

I

4.

P8»_r.

(“u#-

>1

7" >Er' ‘< T’

L Jr’ V F F?‘ Fr"

\\ u U \\H

'_,».'-1'0 - ('\ :19 xx?-‘ Q6I} X&‘1i_’,'#\ . Q

j>1?‘><,.U\P,‘,’{(‘:2

§“

31 33"‘ 2.vx \ ,-_ “i (L

Jaw‘?-AM] +2”/ixb +725’ C :7 7”’ ' 0M1 >13

3x QJ ‘AM

. ‘ -,:_ . ’ ,,,\,_';gA15(/

<@;a:uw,:**1*i‘>d-+“‘ ‘" "J-»»J@@»-W~*@ 1 %

J 3 ‘ '

+2-‘1jxe..vL-"'Y L --L =>;;:u-§~#*~1 cI

' .. ~ >1 C :-63

%.~\4~\-+§Q?M ‘t N 5”‘ b”‘"“ “*1 9°“ “D

{ymj L4-ii}-:;,X'=C.. . ~§?"""V"-_-J‘ ",-1>7<’331

s""""""""‘)‘.._§

' .2

-oh“/1’""

$‘>~

qi

£Z‘+~1@;..¢cL

(-)"=~,<

17/

Qr~'1

(xv7"’)

A-

___'::/I?/\’{-~

1'1;f,5?/Q:

\.-.J.1»,I=r"‘

'7*.».;.'

1;?:2‘\'li,

31',-,.‘»

__-_o

./F

L]

0-<:.

L’-'—~.

_ .

u_

\/$ v\~\,\\ N Q‘) <_\

\ K Q1

. '- - ‘ I .. . -. _:.~ F"-"""' "W" -._ >_'l__‘ .

~Qp“"

“+Av3-F

'3’)-—»;,%><,+/\:;$

Q__/~W\=L~T"d

M1

A_—-‘gL"?/nfl’

'*_\

4/\

\\ _

\*

Q

r1:~

1’.

if

<_

Mr

~:»%I.; '“s4.

.I_/""1,"

r"-'‘Y

’/.\_..A1

/WK“

17/Q‘"71

y.‘/\_~»4'7

<2”-Y

s , '

1

1

1Exercise 9.5: Page 7 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 7 of 13 : Available at MathCity.org

Page 8: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

. : "’ ,1-1‘ V ’

é ~ . _1,_ .> 1 —=»= '" - y ( ’, ' 4 —u+—.~:..--_.;;.~.__.'* ~ W--'" "" . —— ..._ .- --- -;.*‘;~,_~r=_» . I ‘

- ’- _ 5 1. -‘ ‘ ‘ ” ' * ‘ 1 7 ' .'» -'7 . ..-is-¥{>, L-‘ H‘. .af_ r-.7 ' ’ ’ »» ‘ ‘ ¢ ¢_,_f . »~,~‘- - v- ('9-.y-. » \

, , _. ’:d’:_,.:‘,-,f...._A,__Y_\ ,"' I .

.. *1-Q.

Q3 *3“ +(<3¢¢~’< + ’-‘I¢”>“’"7>"”Y“° *9. 6 1 M ¢ ‘§'”:"7( N"‘x—‘

\ v ‘in-\._ -

(‘Q 69

"g axan N: Q::ot7+2.Y CM“. Y M :- ('><+L)h6Y-5*). '1

D »A I

M1 , G‘ VV

Ni;"1 ‘

-‘ "36) V \

M . ' N E»: _M“\ if X _ J” L" ' E0“ (_'H_2>G_,7N't_N1~ M '

o_@g;,t7( Nw{‘5-Z1<°°L"“’ "',T'i @¢+2.)$~'"* +"'137 \x

* é‘o¢7*l7¢"*“7 % - wv? j M M1 = <°&*:>£'*l?

%

@.i<;».¢1.;#§. , ¢»¢1b"25Y°"°“ /‘F *‘~'?Y

;1;~F _ gbtva’ =%$m7 =?l"‘"j=<»<;,_*_2-_.—;Z€ei>’»=-*'=".i;~.'<+ -/a9=*‘_</ '7‘

- V

N -"1 '=* "1’: *’”‘?> » 9;!» @1»1-F=~<~"-*/ -“—- L L

MWQMQ7 bu 3 1 5» CJ"$"(-\D‘;’7-0 FM }Q*+~>4*A " *“q’“i"h ' *¢Q’* ib,;;A1;‘;,u>\+<$»>»wi’@~*1+=*Y ‘ 1 4 1}‘ “¢I if-"F;

§;;§@1‘:;,..+<£‘¢¢¢v+@17)@*/;.=-;~1{/2 f. ‘ ‘ V _ 'Y\_ " ~\ 1

% ( _, .* ~+ 51,0;|\l*-.1-€.{G=$74 >(g:K(x-§1.)$M»~(ci-+1<¢fx(l:'>~:

é x *

AM =~? %-.@¢E>ml~D'7S3f“7 M=>w(“*‘3§“*7 >""°"’C"’7 '.7-"*' " W 1 .4-“.,"‘c.‘~»-in»/¢*J@W~b”b**1>‘"“”” ”‘° %“=\>*¢“+> 1**i>‘~*1)’L~‘é““ "'1 ?~\-

. _____ "2 1 (~65 V (

V ¢9~"‘7 .5

' 4 A. . AM‘]=Nx'3®"2’EX“‘JD;65]Ea,'» ‘V

‘wk . “2,- -=c_. L

5

‘ ~'j&’i“7 * 71’ V 2 C 5‘, Y »-"'Jé%¢;&'ny+21o_&¢§Jf>t_+<N '-=¢'f S

.,‘ "

"\_"‘ ' 7‘ ‘ :2 ‘ '

))§?I$:»1>~)y¢£-Z2,-4-"»'%-1_<i“!<g'%"71»i"“‘ C‘ .

"‘r“z'~

3?

7\

~§>%%’*w*><(J"i*“>°*“[f."?’;'

'>tLQ»§"’;“] L

_»-L--- >4

Exercise 9.5: Page 8 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 8 of 13 : Available at MathCity.org

Page 9: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

aW41,-:.

(P ué»

'”;F" V »

._ "—-" “

. 1m \ L “%@K1-W>’7M‘UJJ0w 0% 4» @?\‘7'+3:)0l:“* +@‘ “"w/)"‘/7 ’O9 ~1—*§E= °‘ "lial

5};/_ Z ..Qs»~+1 +51) --~@l Q

1.~‘I+(°°*‘?7'§f‘\ ""'° “ .4“ '»‘*“"7,’-'@7 3‘ _° ,.@ ~ ,\/ 1

AM c1*~\)4*1' M ‘i qtL%"‘1) * V * ,\/+*~J"’ ’/'49V1

M

N-;x-+1 ‘ £ z 27;

I30

N :\-uh: 1. 1 '7 "I ‘A x \/4-M0!/V -.= -L3liY_i'-if?)

9

in‘t.

Z/T» 1-+1 \/

*it_N_2‘_=—__-I-' '“"*b“‘b“‘”Q°“ n 1 5

N1/_: (J3\/+\/>

,1.“ 7%M 1-7 Z “'

'°”@'u>-\-=\'o-~° $°l""Tl'I?T\T “iv \/- K”'°”’ "* =~§1;.:/_:N'_~

__ I *7 ' ’~ I4-V

-"UT~—1—_X(1—‘1)'*Y(**‘Y) "'>>fZ7(+7 L1

_ , Ow = —P~(>::’_i"_Mubbflj QM —‘—'F";‘r:~7~ ’“a /+v

TIf

= 4/1:-n."'*"1

‘Z‘ii?

1" ""'- \.“~L“*‘1" 3* H ‘L 7»/-W1.4 ____ \/>1"KA’

, ",L=*:.*Jl}-‘1‘..i.-./~ <7_+2»‘/)z1~"' ~<W~> % <=~**% "»%lW@ ' 1}"; *

(fill AM + $3‘;-“ll‘(‘/"" ® §!+v A»/‘= ~Z»J“’~

M1

5<

5

£5” 'J-2»

AA 2. Qua '(13.‘__71.>‘- (3**‘1 ) L QMQD/+\/J 7' ii"

_11.’_.x_“_3_->0] ' (_’--1; .__=, D

N L ‘+gD?»BE""'J:“;l€q' K - lvhl 1,-’ ‘Z;-'1.

. z “S2 , ~1r*t>”“’“*>"‘** ‘L. ‘T’? W” ‘ ~*W"" Q” x ....

._."-*-A-1“<*:'

k/~¥"\

vC'*‘1"

0ML»¢+~1‘) '

\

1M =4 1+ 3 cfLH» -)g_"+‘1u J7: _T>'(-2‘

‘A

Q-L %~%v2—.:*.11= CL- ,;

9W‘-\+E“

\/Qyvv) -.1. =._-=¢,

an-‘i J» +N"L '::sI;»'7 % T ¥A**%> '*

;,%1~'%~ *2 } ” ‘. '»<_ L -

1+1“ '>’Z@— “a+‘1) 1' 0¢\ C C/L‘ A-ué= 1_“_|.\1 3 Ls.

"l:§:';P’“ 1“1*"7xY , .. .. . ‘-~_---.»_§;J=.

:: -L\\/"'7*\j_________,___,

l~%"\/2.

CL *

A |______--"'“9‘ Q

1* ,1

r’

7..

\/

,\_

P0it»:Pgtv

.1H1:

1, * '

us;\4._- '#'

Exercise 9.5: Page 9 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 9 of 13 : Available at MathCity.org

Page 10: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

F_

“V‘M

_'“

H;Mwe‘_'

_

xH‘1b__(my_

_>v\%A__3).

‘QWG

I_4:‘

Exercise 9.5: Page 10 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 10 of 13 : Available at MathCity.org

Page 11: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

;}; * *

' ;—1»—.—-_..._>:\»¢=='#‘\'\“*_ .

=- ,H‘ .‘z1-iurw. 4__r:_..., , ' ‘

2— ‘..;,__‘ '=g;_~-»».‘.~~;-_-.~ '1"" ' "r ,_

~++'.-,.! '_ "

:21‘ ' ’’ 2.

\

.'~ l;¥‘{_~Z'!1'»<5 ."“3'E“ ” \> ~34

>7 I v ‘ IN”: ‘ML!-“ ' ~ ‘X

ré H

. ',\

, . . (P-4

‘Q " I '2. Q —-""6

L¢~>"1?eU=-l”"*W] 6 + ‘Jfl Q9 @LTw7)JMpn Q’ =- ‘ ’

X \1aMY A M=\1LTW1L .{[i;=':g2_~A l

, _ Q _ ‘ £9 - ‘ M 5- ' X 3

M1:-'~" M *

cw-—w>4- * ““‘WA

V M\’-N1 , ~»,1_».~.1’:»@1<? '*'"‘"B“‘3>”"’Q°

mc 1-~1 Nam " J5” '”"'

? N =¢\+» * N _M1 ,; »v~ ~A~,5-‘b1’~‘°*‘- j .-‘

V;/)Y~,_0._; ,\ > _;~/NT. ¢.-3-_2\_:'.Jf-—~

?if_"l3<_.-.-_—_L:.'_ ~»M;~~“"~* @@b»»@--@5»-»>*1r»"1‘b’““5‘ LE}.N ~,<+1 -: _,_I,F =_L - ;.L,_ L *);;'.§

*:"*"*1

V .,. N ->01-%-7’{ 7 »

N —m‘1 Q "" 1‘ N5 $‘1‘*l°"' "“M ‘t .F=.L-

't¢~7\'_' '3-:‘7 if‘ h=7_’*$»J-"”})_@L’“1l 417*V./_\ F‘”'”"'-J‘

~»~@»»w~» * ~LW+%>~1>(1’-~—‘-,:"L”L/

i- A .1» 1 .

»A1":L'?'Lf,<(:¢_~,>+vL»~~w> *“'>%YZ?’/(‘*7 & 4_J_)J- ~ ~’_‘~;‘*7 ’° ""0 @

. L L» N::--J*""'

_.£.>l

\’

&_ v~ v _

M»“*f’1 M ~1 ~»b63'2"” _- =kw °‘ 1'7 7

('7'-"12 10L“ .+ ' '.'M‘1-2 Ni .‘ .

_y~1,P7» '>\

w~s@»-b ~W**>’*‘%

1 ()€.+7\.)3’ (n+1)x. L " L.._l~>g--3-*1

="f;;{‘;-3.tl-1} > ’i=’:*l-—/1*‘ ~

.. _ m. , ' L F)

\,--\

r‘~13-

‘\"

.c\"'\/

cl,v\+_(\l\'{L:C ’

. <_L1_P_7z_> L->14-1 Q/Wv‘+_ 7'5; -;-_: Q

‘L’ ___]_1g\{ ' - ____ .»

H = *j:;°:;’rl7- M “--5'-:'»”' »--'""'” ”

1 2. \-)1-'V

(x'+7_) ~ ' -

» P“ *1 _ - -_- '» ___M_1.,,A .\,'®2,b'b1‘0~(l. ‘M Q »

4 ;,.§+1"*

;-l

N -.=Q=

\_,\p.“-\

W“Y‘,__,_

@_4r\>

J__zL§*_~-"'n"~‘*1L

iJ*»*>’*:/ - '"

"Vin-L*_‘1 , C

tamv’-*1) ’ E” 1

-¢-i'-""""- _-{--__)(

_ ,__,, . “.4 "‘-"' ' ' r

,,..__--nun!-it-""'_""'_'“-u~

At""=*°""£7“"' o;—0Ah" “L*"\L>

Exercise 9.5: Page 11 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 11 of 13 : Available at MathCity.org

Page 12: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

' _' '>_v_____ _:m-Qawzi7' *1. , ______‘_-1, __ _ » __~ . - ,.-;-2-»~.‘-"-2". . " *

E‘§'-ii‘ " J» L1, _,:=;g,P;_ '_ _'_j T _- ....~ -' " .

3.~§“~.i\»“,‘;-;.'.L..'~*_; _~l‘_‘_:\_-_--__'§_"_"_'_ _’_’_—__,‘ 4 -- ' Q5 \ .. _~

,.»-7~--.—-- - ---:f-" - ~ -‘-.' '- _

\v_ '\ . -

._.‘-.. ~. -_~ .

\ Y .1

,

~.x.

' » » XE’-xi ’

, , »-\

Q3L374-1w<‘1L)ol~\*(Z~><+l»"¢‘I)"L7’“°""@ h A

M1 MW ~_,,M», pm» +Jw»»~‘>~r~&~1>*#=¢J . 0 “A"~X IL l '

§‘“*“'“‘“‘ = ;:~_;§;:1:*::fi2 = l+?—”‘”7 71+“ %

11+$'~ N L7 ~»r(2,+3"""1). 3+ x2,i_Zj%;H,-1’?/3{~[;c

' V S +1“) " ' ~'

N -"*1 = 6 ~:-W-: ~\__:..€i ’“'A 7 ' i %

‘}"**""' *<1‘>*“”“‘> :»j@MI»‘v11+§$”“’

_*\5\gL\’=o .1‘ -\t,§(“,1>@\,,,\+wx‘a( ., . . :._ ..

CTQQ 1/D 7) W - , _. ;- -_ é

@@~ ~:<;M»~\><1»A+>~<P»*3**1>’“ ? %

- .4: _L.‘1 + -Z§<=\.v/.-56’-L:i____;l4‘_\} 7:. _l__ :3;:]L_~_-;_-,;1.;.l;LT)-L 3} x +j|+'7L‘I‘ K

H XM’ 3X7+ T" F 130 vL +4 9»»\('+**7>*'*‘:A-*Q_‘f.7’_-»~*“*"~t' " §

?M~J»§>17L,JA:¢£w5'“7@‘**1l"7T~T§.1E§“ ~ A

.v 3Q/v§,,L 9M(_l+'w1>+@11):¢\&

=~ 9:25;-W '*'Q"3~‘—“‘3-l'-*r73»' G O P»~3<\+~>/9“ =~@1@“ '

V GU‘ +-£1) :> , CW1+M 1 {M 'W3(.‘!+x‘I>‘/1’ == £~1€.c'. UL“ E1-3'>\ }}/~\ :0 '

. C

*1?§1§>:“_L-2;‘) §1~»r ~"@ “*9 'i<\~"~‘/>Y = ‘i' j L 2 *- =

% M ;<»<+~:@_<:1»£>'f3**>s1><>¢>¢<1+=~»1>7 C

W ‘ V <.MxL7> “.2. MW 1/ ’ *1”; . 8”{ *’ = Q; + ii - .1. N @ 1+2”?/_ %

% W ’> *"*"**> -_ ~ == --L-— ., == 1+ lmj 4- W7

/% W L » <'*”“3 ‘1(1+><*1>-1

f;~1;L ¥—'K#t*lLlé‘;’?);}%13“M‘U‘ ‘ u h = >.(_;4/1<y))‘+)/1‘?-/—__*) ,

I , »""‘"<M ¢“"“’’ ' L " . 1. 3_’(/3 ' '~' I _.

~;-_ 37 -44 »3y(<’Q" ‘Y "/A ‘Ii —; ff A ,_ '* *: 3:; +______°(’, .1 7A T

_ C_/_HU/L)-1. ;f/<1-;~ xj) AI+

A \ \*’*@‘"“_“‘1=N»<-'-@L>>-’>><@~°”“{§“é"“r%-_ '~;».=..=J,-A

Exercise 9.5: Page 12 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 12 of 13 : Available at MathCity.org

Page 13: M1,: ,4‘ , ..».W¢ ..4-*»;.~,- ' ==»'..';'-a=eiFC‘*9' M»-1

_' ’__“_j|,_,_ ,,_ <~--~-a.---~ "N" '

L;¢%@@<~v__’ a ,f¢f; ‘

1»."" ,,1. .

@%%<v-xv) 4

_ - 4%

C)

L (1/v\'+ ~1+~/~‘1“>*1’@W9 012

‘ 1-171. N =' 1*“ 7 '

maths

M1: t__2_X7 N1= )+;_.,\,/»_(

‘SL5 =w_»1-11:‘.-_1:‘1l'¢-1;<J_-.1i?~*@£» A

u ‘ "1.1.'K'T")47 v<.(I+1u/)

\\. ' ' - A‘ _.

§Tl*v) $7

._=_ L{~2_'n.;i-I-t~7—7§’1__ 6*

M 7» (

@wM,,7,;\; 7d/$4-‘7(.71-‘>J,,x1‘-1-7\J7-{-:_1‘“]:.0‘f7"-=0

7-::Ȣ>

,<-4--*_»h7x_ ~1ol,v<+-;<.J»/ — ';‘/L[9-£_3(Y;~>*x7ol7$o

*m;+v~1"7 ~>@~¢<@ -*~> ~

4- "K-\""‘ "1L“ é:*,:i.1t~_%‘zZ‘:§~‘*1)="*7» ‘ “(,1 4%”' ‘ $304

,_;__0M11/+7 =<_ }

@91-

I‘

Y‘

,1» =@4(-,5) - -‘-"=,%*'

*1 ;-W’ *-9°s(—— _

“*1-v=¥?»~_ =(1‘**77a”‘ "*@L'>3“+1“+*1><*~*A"é°‘”l”/ ¢‘ °M1: :>_~I+\ N ‘

§¢MYfNx}uW¢®¢W*

N\x’M‘1 -.= ‘-1 -iii N‘~,&+*1“+7 .

tr-i'~1¢>“ w‘*r~v”‘"* ‘=L£‘“‘ W(ix

>~-+7

tinw =' "*°

I

69¢}

Pb?

MI-NX .: 2v+g+1 N-\'b-‘b*N -—’7\.

L%> ="‘“§°‘*‘> ".1‘<~>

Y X, = °l"~L--_~@i ’

Exercise 9.5: Page 13 of 13 : Available at MathCity.org

Chapter 9:: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin

Exercise 9.5: Page 13 of 13 : Available at MathCity.org