SlideShare a Scribd company logo
1 of 51
Download to read offline
F*-~¢J;>- 4 ---1 M
5% 1 = ’§-Km‘->3 ‘
1‘L|...~?.'v»Q--LVML o-%,.o-§'l1»-
MAi¢-L)-n6,;.
A’_“__M___,_____(_ -._ - __ "M
Aida; ‘Q ¢k
Pi-:.§k‘) ‘ "3
V x
»uA'v»~>~Q~.-Q ’u..:->~.L..1.J_,,
x43. '
'5~l-'~1-»‘—» '4,
1=§.U,a,u)
h~..,~-'¥.'v~ Q-ink <>~f--Q Yiw. :¢..L..U,,>,3¢w
"-1
uh v-1~....-~!( 0 ».».=,t..~3..1.~ >..~._q1.,o_,w,‘,_,;_
»-i-**<L>-».1».;.n ~A,;.),1'v>
J=W;1
»~»'-~%~~+**-~ II
W» g.. ‘z
~l‘Awz~¢9. ldu'.J~lI-0
Exercise 2.5: Page 1/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 1/51 - Avaiilable at www.mathcity.org
~& =~?:~¢-"-
A 2=§(~A>~>) 'v> J>¢Q_, ta M. ‘t. Q
L,-._,;3: J1 wsxm)-5 (<1,,)
*'~£{>*~--~;€>o>m.@ ww, cxS>u ;»~a~w.x
fh,~>)_l L Q wJ~n~.w.u x-¢4_Q ,5...,L§
{A an ,x.,-(up) <>w-<,.1.....(<>.,,,)
/~11 widn ick 01>
-QQAA §t;‘)) =- ‘Q-
(>)) '-QKQ vk )
."ii
ag L. ~°-'- {(M5)
(‘|"b)'-§£6)
»~:e<3¢_,k't»..~~"M’—'-¢9-i-Hv-.J< v¢.0....»,a/>
(x a"))—5(¢ 2“) d-10¢-1 '.,.,,,
'Q~*~‘ §-b>">) A-0.», -)C GQLM: .
(1:3)-'olmo) u
‘Ha. (<>>o)-
~__-ii-ii--q
Exercise 2.5: Page 2/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 2/51 - Avaiilable at www.mathcity.org
Paid
Lu: 1‘ = §~A>~>3
‘Io
1%,; = §-b+%» >‘o
$1 =. S-(‘A-$s*>‘>§'§b">‘9)
.,,,,.J p/W ~94-o'r 1"? 8*
2%. ._ w~**>~>>-%“>%>2.
_L;___ it i_-’'&‘-3-'%‘>">)
SK-90 8 SK--30 S“
3____*- .&~§l'_<>-§ '
Wk M *
mm 9~.-$- Qsks °-’ °* 4'
Lu-)-'_-X~-‘v:
So E.‘-_ = 9»-' f %u*%"’) ':‘swV”1'
M 51-» $5-,
$.19
b¥ Lb“ 7')'"%'>§"
_-;“)_ - 8'p—Do
%*:<=~¥~
.. =. l~'-Luv D
Av §>Q>,»§ r- :8-::° ‘S:
O
3‘:
§§M_)_ §y(»,~)
Qu,Y_§- &'(°HO
V~
Exercise 2.5: Page 3/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 3/51 - Avaiilable at www.mathcity.org
-gr ,;3.,,,, .,.;,,¢,_
hi %=§(x,>) n_.,,
Mm AMJML-,.». ~gf:,1>->> W
-3:.-A-‘-§i>= £5 = %.Hn = %*>,_ = s“ i
E52. _ ‘ -'%;K )x§ " 31%; E =K§Q., =81“,
I t
>,~;@-i;> =l*- =%<%-> =¥»>,. -axhm) '
%i:,K%E> = if), =§(s~.. = <&..>b = ;,,
°*~>‘*~1*
A § -if -b... :¢..L.L1» 4; vu {AW
§(¢>§=o
New ;vv~ Wu
<i~1.=__l%~._
a* AL
‘I~>
,.._.*_>;...
“Q3 s,
,1~~-;§-.2 ~
r‘”'{."a1'.I’»‘f§.ifa
~
fy‘, -
Exercise 2.5: Page 4/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 4/51 - Avaiilable at www.mathcity.org
ivo~L-JL N. (?~hLh~.J>._.§);
£LLu,_(} 3; 1- 5
(1,-,3.;g.,.) '***‘)
E
£
1
$_-_!-¢1.u.m.-V1-;~Jm~.
km '5-x“ Eu
J.
1.
SI‘:-q--
.<Jc
1.
u,“-a(.,q ‘ + 1+")
1-=-~ (9-1")
9"‘*l"9(';:.) W
1-.-'-~
(‘:'5‘ 4b pa) *‘+5‘)
Y-O
K-Q-O A-0
.2.
N
<3,-1-1.-M 3:"
Q‘)-J)
QQ
-10>
1»... €.
hm‘)-o 0,45
(-)(-O
8-
U
:8.
-l= C.
'Exercise 2.5: Page 5/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 5/51 - Avaiilable at www.mathcity.org
Ga Lu 3:” “*5 7';
($;‘Q-0 (920,
$4‘-
X‘)
1' , L2.-,
l,,.§(o,o) xs‘
I. $:-an 3
- Um)-(~r') *5
=- En» “*1,n-mm ‘W-1--> *5 "
o
r. C.-
:.-I
-1 *
'5 '5
Q_‘~_ L-.:.... _*'__...5
hm)-1!-»-7 f“'JL
SJ»
. - J“Mk L Ll “_,_ -L-~;' “"-"~
'5 3
L 2»... 5:2-’ L1n)—9(-.~) Xta-Y
pd = AC-b0 l
3 : -‘$3-“Q
=1) ,3“; , g M u»»>- (~--) , *—=» °
s. d-:- 1~l-#3‘ -'-'~‘-'*
1 L“ 136:0 -1;-‘$;2o_
A-90 A,‘
Exercise 2.5: Page 6/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 6/51 - Avaiilable at www.mathcity.org
1 2.-... ,0kcJz_s£.@ 1
A-00 J_*- --“M i
- 9.4.. ‘ ‘ i
- Jun .J.(<-so-'$¢..o)
X
* >
- 0(€»n-Q:-~6>
.9.=°
3
9,; 1..-... x- 11» + at-1‘>_%
‘l»‘>-obn.) qt‘) --H‘; -‘It -H-‘‘)
$_-__=- _._g .0. L1 in J.n.g,- L;..$.$' “""*
x
1 UM 1...i1.1‘a~-3;.-2‘:
(‘1‘$‘.(3>3- £5 +-; -uf ..2_~,
1;... (~,:’._u~, *'.nQ‘ -1-»)
= _(‘oS-I“-94
1.;- 7- L 1
1,,)-;tn.)K1 5 *‘3 " cl 4'1"")
9-:-n-n.-
_ z+u._u-at
'-= LKi
1:}-L
s~»~.u..;» a-., Akwibdc m
QM w-; ¢.ai.v$¥ '
Qg 1.2.» _.._1.‘Z_
._ (1£7) -Y (0,0) “'_,," —
Exercise 2.5: Page 7/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 7/51 - Avaiilable at www.mathcity.org
§£"4,k.l
w s‘ '
1 -, -La“
(‘>13-o(°:¢) 7"*‘)t
i
5% W‘ ')>“‘~‘ “"3 %‘l>‘9) = i.-__‘:, o»;».¢du.>s ‘E-
1+)
loL.m on (1,;)_.9(¢,,) M *
d.i:u.<I;-A u...uv.A~, -‘,4. Q--kA_6__M* amt
Lek u”>*'9(°>¢) 41,0», “.0. 1&0. j=~x u...
Q = 1.2.. _}&l‘l!_._ '
hr»)-»(-,.) q@.“}‘.
=_ -L:-.. __"‘_.2}E_...
(‘Ia‘))-illqo)
= 1~'- k_“___;___)
hm)-al-,» +-~
WM va.(L.v,~@~v
S¢ M L44} <1-M Md Q-X3-?>1'
1 1 '_"-""""'"“""
Q1 1.~'.- _}.i:lT
_—_ ‘M‘:)—o(~n) ‘L -Q-‘1
_p_ , 14» _}‘;1‘_'._ .
kw»)-» kw") "-1‘
9% bu-L -A‘~.u rm.-Jr {um = -3;;-2;; ~=»>»-»-M vi
"°‘-L-41> M Uri)-—a(<>>~) M
c1.L.|.f-12nd '7~4-Lm. -/>0»-¢N’~mJ -[L-<(.I( Auomsk (AC1-AK
Exercise 2.5: Page 8/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 8/51 - Avaiilable at www.mathcity.org
.1, =
"IL
M ‘,,,) ____, 9,°) Q-'.--3 “L »(~v-I. ‘j 7- VMJL VKA-~
-. .
Q 1-‘NVL
[*A1‘>-oh») W:'-u-51$"
1;.“ XI-k-YA“) _
1
(1,»_’(4,.) i '~})
IJ_,w_,, k-N 3
hm)-1 luv) ‘ ‘"‘k
u.=.LuJ- 1» “M X- ‘5““""** "°"'“'-"¥‘“
§» M ‘§3-M 1....-Ji‘' $4» *3 ""9," l
—iQ‘ 1;,‘ 0~"4' ‘Q
kw-u-.-1 11-,‘ + A1
1 = 2;... .._§£.'_*.h?___
L
(‘,Q_‘(a,0) §'A
9* wan M-V.» M ’§b>'>3 = 5-‘5:_—*-EL “’’*'°“,"‘*
' Q5 +<lx
£2 JnL»1 M §‘*>>)--aha) €-
A;;,|_¢‘I_',,,,3 Ron ha-I. Am») “J An") wui
¢»;.M:.
- ax‘--»-
1. = ‘-- ( )
ln-aln ¢y}{'-Q A1
>
Exercise 2.5: Page 9/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 9/51 - Avaiilable at www.mathcity.org
1 1_;_,_ (u-->m ) -,1
L“)-¥l'>~) Cwnu +11
0 +nw >
Q c—-i.____..______I.1
0+4
-Q=L"1.
0L
¢...~..3>....1;...~.x A-u~.&uz,;£"
Q 1:... K1‘-*3‘;
(‘*>'$-eh») 1" *3‘
$_-3» Lu: 1 um M
Q k‘?'~')‘-)L
(‘M-l'»~) *':"‘3‘
k 1 L)‘
5f w-1 J>-.» 'r..3c §£»‘>) = ‘kw 3 "'W-¢~d~n
X4-j
h v..!...v, M (ma)--> Lo») fu,“
oL.uI.;.~.» _....L..u. J>¢-9 “ml. 1£~.a.k cl-u»'»J<é_x;4t
LQ k:“)§-—-);q) Q10“-J ‘KL 1-v'~.l. 5 =n MIIL +YV§1t)
‘§a‘!)—9¢:0) ,* ,* W? £1
. ' 1-
= 1»- i‘§‘*.-~_‘..>...,.
&,s_,L-,0 Q (H_Ma)
2 ‘L;~ (“'Y“")t
kw»)-»»,~> H. ,,T"'-‘
ml.-<s.'~»dL“-.-.)<{-»~<H!--~7="~'~'*'~'%~v
4
4
1
§
i
Exercise 2.5: Page 10/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 10/51 - Avaiilable at www.mathcity.org
v§;4;",,,,_g%._¢9.;“,_‘_,¢u¢.Q.-.n!>~§~.v ‘vs K
s. m. 3;.“ A.» "rwk e.x3d<-
,.-1-__-_---Z-1-_{—-Q
<32 11¢» ___.°“>‘
(3:5)-5(':s ‘I--3“
$3» Q3 1 1.1 V44, A-4, :.;...."..x “M
.1 = °-'-~ _‘_*_>.‘__
um-.1-,-> 1: *3“
sq“; »~ 1..x gm,» = 131.. ,,,_,,,,_u ,0%
cl!-QQ»-..& vo»9»-0, 01> (u,,)_,Z,;?) LN “A d.wx_M
W“ ‘*""‘ A"-5 "vii ~U--Lt dun; -“.,- e_“;_‘.._
£‘a‘$)-9 (9)0) 01-“, K‘ Q. 3 H‘,
A Q - 1Yv‘."
L.~>)..,(,,,, x‘--wv‘u“
MA
i-i______
("53-l°u)  --‘n:'>Q-
$0 ~R*’OO (IA (x,|,)__.(.’.)
“KM” °"""‘§""""*' At-1;-A M '
$§‘*>‘1) —-5 (6:0)
Nude
§'+§~s~. (~,~>>—-»(=,.3 “M1 1:31
ll - -L1-~ 3"-Q‘
Lu.-.;..(_.,.; 3‘~__31
(‘D5, -Qt‘;0) 2')“
Exercise 2.5: Page 11/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 11/51 - Avaiilable at www.mathcity.org
1= I--»' —‘- “(lg)-y(in) L
S. 0'5 Q.‘))~—)(0>o A1p,~j ‘=31
W-~u ‘M. -L§w.Li <1-u. moi €-x.'~¥-
QB Ll-Q €('l)'5) 0 ‘SL (‘£9 *(°”x
X‘--~33
‘—‘- O L‘. (‘£0 2(0):)
$~4w A-“k § 54 ‘NJ ax “L
S33 G3-- A
-f(>») = §_E3:;s H’ £‘”)*("'3
4u ' Kim) =(°.v0)
Rum $0») 1 O —-()3-4.‘)Nay;
-'4» gq-my .. 2.-.... _l‘_‘l__.
(‘>33-I(I ‘Y (o§—0(0; 0 } 1;1")‘
~.xu.~>>-=,~.~ Q1...‘ h-. 1.2.». 5-~. it...
Lg“ § (X?!) : 1‘kit I
(‘h5)_,(0, Q) (‘A Pi -9(0)0) xxQ’ W}‘Q
__ !L.:.-_ M1
(~wa)~o(-,. “"~‘ _
v'1 W ‘A W “duh *Y“
s. L4- §(x,~» dw. Mk ¢>(»’<-
(‘>33-o('>~ 
.¢,,,,¢_._ ’Y0k Qi (°>o)
waila§3.§»@ at
.. x 3: rg
I
E
Exercise 2.5: Page 12/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 12/51 - Avaiilable at www.mathcity.org
(2-E. F;~A 0. )>uU- M ‘I-
-§(*>‘5' = 3*‘, 5* (‘As‘>) -.1: (_°:°)
1
) s
a_ 4 (aw) =(~,-
U> G1 UH‘)-
Qiup» L‘
' K >  (U!)& 1:23“; qt *1 ==
"4°_ ' Kt») = (~20)
‘As-0. z§(~,.3 = <>~ (3%)
3*»;
Now 1.-M W” = 1;-.._. ----(~m3-.k->-1 lg (‘>53-» U») *''
¢_xLx>;_>,L=»,») o.9.~..§ W4. JL;-.1 *j=-v~ WM.
(‘.”_,‘.“) Q53)-5 {up} K Xt
' Q; '5Yv‘L
(>‘:)—§~>') X  -I» wq‘
S‘ 25*“ §k~4 >5) = 9
(‘NS -Q (IN)
$5-»u §K>">) 1» C4-llbuuus mi (°>'3
$, Li.» §-(1,5) = §5(°>n)
(‘HQ -0 U2‘)
:=') 0 =' a
A Q-an
1
1
1
3
i
Exercise 2.5: Page 13/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 13/51 - Avaiilable at www.mathcity.org
x
Q...“ -U. §(1>‘a= }__"_'__‘}:_ (,,),y,(¢,,
my
O __
(19)) = (0:0)
e,.,,_,_;_,_,_ kn <'..L',~L.tq ~§ §¢.>(¢,.).
be €_‘(°>0) ‘X 'g$(°)0)
9:1» c..:...,. g,...a.~.. 1,.
'§(‘Aq‘-Q : & . (Jab) #10103
u -§. ( -1 )- ' ms) (0)0
-Ru. §[o;o -.-. O
Nuw .‘ .5
_Q-W‘ gbh) = i* 3
(‘“)_,’(,’°) QM?)-!l@) "ii-3;
hi k‘>">——'>(°)) M “A. f)=.M1
3 3M €L‘>,) 1.1”“ X3‘? M1
(m»)4-,-> kw»)-,1-.-> w‘
, IL-_.,. +~§’*~
Q»‘>)-sl.'»3 --w~‘
2 JLL... (--vv?)*
(‘4a‘))-5 ('9')
Sh"... ..
(‘$05)-g [o;)*(‘,D _ O
$~'-u ~Q~i-- §-U»*a = {-9°")
(*»‘>)—ak~>-3
S‘ gh-»">) 'o C-CL;-.>4-.v» £9")
“~4-.
Exercise 2.5: Page 14/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 14/51 - Avaiilable at www.mathcity.org
Ni!-3
H.» - 1.~.. €<‘~>~>-f°'"‘
‘ -50 y‘
_:_ Lu» '-°
-no y‘
=9--'» 31>.
-'00 h
-_-_ 2.4.-.
‘H. £
S0 §x(O;b) = 
*-
§”(.’.h _Q_-____ ‘('2 '~§ — fin1)
Y~-Ibo ;
.- 1.-la-A 0@-
_ 1--1-n
K-ac K
.Q:..- Y~
K-30 K
: 
K-30
§,,(~»Y= 
S‘ -gxkoyu) t ‘$’°)03
. @
Exercise 2.5: Page 15/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 15/51 - Avaiilable at www.mathcity.org
P
13
Q1! L._* &1,)) 1: —--‘I--I‘ (‘$25) #(°)>§
1+3
.-Q Qua) -
. =2)‘Q~I-.~»4H)’d'*£°
Do §_x°>v§ 5: ‘S',,°>v) €.;.»)>¥
$_3_Qx- 'vs
x“: ;..;_ L*A>> -4=(~>~3
§>(*>~>3 = vi‘--3‘
(1,5) =.(n
-3-bu. §§'>'§ = °
Nwu
. vi“ ~>
'Q~'vu -SKXQQX 7' L“ X‘ L
(1‘$)"9 kn) (‘v’)-a k. 7 .1 *3
Lu<(>~>3-e b») Q1»; Bu. LL-Q ‘j=‘~* ““~
1~'- '§(‘A;‘) 1 _}EA:l__
QM») -a luv) QM)-akm) X“-w MR’ X‘
-_-Q.;..,. ‘~*
(xm)-5 Ln») X1--~"
.Q..:.- %(‘4>‘>§ = O
L*>"'§-99*‘)
QM); Q~m~;)--ab») <>Jl.~.-3 Rn. Q»-1w.1 7::-.)
M K
9*-'* §b»~>)= """‘“ *3 M
QA.a)-vb») Q,))-oli) 1 *7~
L... _3§1_.
1 L,~))-st‘-O 7'1“
Exercise 2.5: Page 16/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 16/51 - Avaiilable at www.mathcity.org
Q1? *&*>~>> = =3
bl?!)-9 ‘ux
-L2, §'(‘l~|; '-'- -if l
("am-,1-,»)
Q‘ -__._ ;,.,,',",g _.Q.',,,,.',,k An-IA moi Q.‘>'-J:.-
-¢.,.<. § Us 'v~Ji c..t.-........>. ¢u<L~,.)
Nnu
L; 'S'(>b)— ‘§(°)°)
§*( 3‘) M --—-C-‘————--—
-90
1 .Q.:..-. 0-°
—9u 
= Q
—!u
1 O
= - .vW-... 4“ *>-‘s'=°‘
¥~»~»~>- k... 5-~——’<
-_ .Q...:,- °—°
K-)0 K
.=l.;..-O
‘L40
7,0
Q» ~»Q-.o“- '§‘Ko;v') §, .g,[o;q
FM N ,4_,_ ,,,;r,-,1 Awmd.-.~» 4, m
3%“ QPJ»1J.....», $-v_>_)-
QR
Exercise 2.5: Page 17/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 17/51 - Avaiilable at www.mathcity.org
m “§."‘L~‘ -_’:~> »;f-_>- ;%,,,,:' "3
 85'2.-¢_.,
¥'A =
§(*A>‘)) "
1.
5
- x
at
.. ,,. -#~, ; ~. ,"
M‘, u-,.£- amt‘:
I.
-
g‘, ‘-'- Lu. L‘)
35*‘
§
£.
§~,=
git §L‘l >5)
Q‘*»‘)) :
mg. ;~.n..c.., ~»-»~-’=- x -xv
_—_,_._-_-11-:-
X
‘1Q'~'3"
':. 7. X Q
'1 2.‘).

‘$3 - '* Q,‘*)'L‘ M
1‘)
iiiiiiiQ] f(~A>~>) = ‘h=I.2(»),U
$3,.
G‘"‘**‘"~ §b>~>) = ’..:.!(‘>),Q
‘Hi ,.».11.u., u-1-k- xv:
3'—Q’lx)
Exercise 2.5: Page 18/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 18/51 - Avaiilable at www.mathcity.org
----L-__. _.2_
1+2. 1‘-‘iv
xi. __: é
Xt-3" 1"
¥=§-"~5,31.
*§ =_.__)._.__.)._(»;)
3 "*("h)")’ *
-_.__.___.. ..L_
~ 2L *xiv
: ‘U’ II-"""i 0 _'
X1*3; I
¥" -A =‘~*>”
___,_---_-----k-a--m
Q .
*2 ‘§(‘*‘>) = s'.')~(1-*0)
S3’. Co»-3-u-»
€(*»">) = 'tn:)¢(X-k‘)
'~g;.>v.1:-1A, u-A.‘- xkb
.§....§ 8
"---3)‘ M ‘M,
‘ .
-=. .._.____---- . 
--(‘A-wgf

‘H ‘ H (‘A-~9)"
Exercise 2.5: Page 19/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 19/51 - Avaiilable at www.mathcity.org
§ £7 ,_ ____.__.-C --:;(+
$1:
5:81-
§Q>‘>‘
RX
1%
Il
L = gr-C->»>5. o
=.>
ftwo‘)
5‘-N -
<- ~~5
___.____. E
-
- (M-‘>3

-- K1--3)"
<53 fa»; - ‘é‘s;..~,
G.»I»A~
=
m;_“__ u-A.:- xi)
1;,‘ = u: - <=~u»-...~>>
Q‘
1 -$.=..>~9
Z‘C»»~a
_________--———--
Q-ii §u,~>> = 12,.g,e..,,~)
533" Gui-AM
1. ~»Q~§»€‘+~j") »
->.»:n.m, L.,.¢.#=- X4»
= -‘--um
x‘-Ivy"
3
$1 >
4
s
E
4
‘
!
Exercise 2.5: Page 20/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 20/51 - Avaiilable at www.mathcity.org
§*
¥1.
.¥_& -, _2'l'_..-
, Ȣ~;-
i
gv‘“'§;""='-'(X 4-))
X"-+‘)" I
=‘-‘>
at-*3"
Si" G-Alum-
§£>~a) =. ~Q-K
<§(1,->3 = ’°“"K *6
_._._._.__
(S1‘~T>‘-*3
i
_.____._.."-‘)
-_-1»-_-1-ii...
Q...“ §b>») = .Q.,&_§§{~~2‘ -1
S$Q‘a-3" '' * X
T‘-x§ -3-U‘*-3‘+‘I>
5;“. .,.;.k- x<‘)
‘- 
 _K-7-.-A---'l‘A->  _(_.1....__.":.x *-
.. ----—-——---' F-_l ——-Q-——~ 1 1, L
’ Kg‘:-‘) -1)
"v)
*1‘) K:-S
)---‘_-_ <";iI.T~**>(mm F3
Q 1-/S xx‘--‘a‘" Q >§ 7’Sx‘--;‘-)
(SE1-*3 wr'~,~>
Q m¢ms1<;~ >
-- _ __.L._--- -=. - _7;__..
':. 1--—{>l X X1.~31. $56.‘. 31.
Exercise 2.5: Page 21/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 21/51 - Avaiilable at www.mathcity.org
_L__..*' £9 : _-l--—-—--'&1Fkf‘:>,_7~‘)} _____________$.z§T‘,‘:} X
-'4-X(F1? **) ( yf"r;
:2 -—-——-—-—Q V -' 3 ’ I
4;:@:;-*»u:~:;~> <m=~»~sLI»I=-l;~>
V 5   -
2
" .F>*~=~
= ‘>.___.._ Kyzzbi +1 - .i¥*‘)t ‘** V X
51!-...,)'¥ &y;1_*‘)L __x KS~k._~). __-*9
=2&Sign ..
1.x‘)
'2 "--""""':._~_=-
ISX ‘> ~3‘
Zhk____,,
iaif-*5“
~:—¢—
 _._.
(Au >">2= -_= -~
- ‘* ’ >
gr ‘I
' L
I L
§b>))2§ ____ -.: §x’*».~)-»%.§
,§X1‘--3"--:1-L
-3/_'_
gx _i‘_-k_£__‘5w.__-;L1§ _ Q8_k_K‘£“—-‘)1-'%_ 3
_ ____:l________ ~L
'- -;_ 1. 1 3,‘2_§x--3--1)
Exercise 2.5: Page 22/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 22/51 - Avaiilable at www.mathcity.org
Nan ._'_
§~,='
1cȢ~,uw"~
.___.__..-1--_-—----

_ » ~- &
81 " -,_ x -,_ 311.
Lu.--‘)-wt)
_.-|
‘£7 T. _-_:_T_~ 3h.
(X--5 +1‘)
11) . .3; Qx‘--5*-v ‘
.13
_ 3/L
+ gz = _¢{@e..5*~m>-~_>E§»¢-;‘».;;'~.
£1“
..}/L
11) . ‘L1
___E__._._
y_ ‘L 13,1bx.--§ +1 )
=_-__,1 N J;~.»_¢,,,_; .uh.~. ¢11l-~‘L:Mu
k?.»,.&.1-....2» 1'5-1;)-.
Q13 E‘,
5.-3» M 2.
mg.
1%.. =
in
B11
‘K-“>
@_ G)____.-_--—--
6) u~>-A.':- ‘Ix
'1-‘9
Q_.
1-‘D
____-=5,-‘bk!’
Nu-.» B1:
‘A-‘Q
E3./‘ma -.'. -- E
___$_; ¢_
i(—?Zi>77”

2. 1)
I
s
;
1
i
Exercise 2.5: Page 23/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 23/51 - Avaiilable at www.mathcity.org
Bl1 "K-3 is M
-- = —¢ -£- <‘
53 .
Mm»
ii. = .::§>;§~)
bx»; R
= -3;-*4-1i"> 5
V x->
-: -—-9..-
*-
_b,‘__._% T. - &‘
Q-1}‘ X-+2 ’
.._._
SJ»
Ldr 2 = 1*-“i’-- V ---—-~®
*-3
mg. ® Lo-A . 'k- X
bid QK-Z)__-_ ?‘§-kb)-‘T
7* K1-5)”
= >.(-~>-7K-‘a
(1-*0‘
>1 = _ i‘>_
M U-~>)"
._.. ‘L
s
bk»)
*&1= jl>____
M1 £1-*1)“
NM <>'~q§.® >»1;.1s., Q»-¢.:.~,
ii -= -1.‘;
),1.-
Exercise 2.5: Page 24/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 24/51 - Avaiilable at www.mathcity.org
R g_~,).  - (§>)- (-0
3.9 ' ' bx-w)" i
1 . 1
‘-
(1 ‘>)
2--5- 1%
,,,) u-~>>‘"
E
>3» (1-5)
1- _ _,____}_..--K 2 % “
'3} £1-~91’
Na.»
1 2 33:.
>»~>¢
3 xx
'37. K kx-5)‘)
-= 2.‘, §‘*'T°3‘i" ‘**'}&‘JLK
k bx-‘:D‘
'_ 1' :6-116+ ‘J"—'-§'--”'{‘>
n (X-‘=)“
= -LF ‘J“"L LS
L x-~o)“
___.LK,L__,)1..
_________________._.
K1-*>>“
-1.L-‘>3 ""°3 _
bl-~>)“
Y‘% ':.
Em)“; QM bf’
_'__;.-_-—-v-
Exercise 2.5: Page 25/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 25/51 - Avaiilable at www.mathcity.org
Q15
95;.
Lek 1=
5-Z M
@-
m._“.@ <.¢~)--- *
2?..=
2»
$-
2}. = ‘$1. - E
3* s

3
s-
X.
4 y=_ =~,K~.-.. e.-‘av. +e..a»->x
N’ v; V
)0
New
bi =
*6
75‘
1 L1
‘D
‘I-L
Q; ,[5:;:‘.: +‘9-)~'$- '
‘ -i ‘L 5-‘L
>Z_§__-= E:&')- at: +>L~»-0-* ‘X
w-»..t- 5
‘O
. *-‘lml
>23
‘O u
s ~, x
1-L.a~- Q. . {Lax
£5; = --
New
#1 ,__
any
s #2 "“-X __.,.Q.1.,.u.ax + 1--°-~-&-‘>1'~
1
' Us-
-- ‘>1?-9-~x + ‘Pk --9--‘*3
s
2 an. ‘>-
Exercise 2.5: Page 26/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 26/51 - Avaiilable at www.mathcity.org
"

Qli 'b~'~‘~I-3* -vb:-‘H
3*.1*
La 1 = 1"-.Lh>2‘.* 4-*1-.:.‘.~;
oh -L ?z,..U-':),Q+*i...W=2‘ca _
_-....u.;~.*> . ’t¢...U-$23 ‘E
K
2- 1+‘? -@
-X‘) 1
m_“_® ‘,,,‘_g,;,__q,q,,, w-,.¥.-1.
R u-»~,>“>-k~5~~>>-<—*>L
‘M Q-xv)‘
-2:‘) +1» +5‘
Q -xv)'“
_§_23_ ._ __-xi.
M (v-*3)‘
37'___2'- -:. (M-‘:"Y '7‘ ('5)bx’!-
U-xv)’
31% -L5 (u-9")
me u-m>’
u:-.“,.® §.,.1.-.1», ¢,,.,,.+¢- a
EL *($-1»)-->~~hL:"~3-
*9 Q-10)"
-sg/; -wl“ +‘AZ§_
U-uh) "
>2. = .1112;
5‘) (-xv)‘
1 K*i). ._.-L?-_-----a‘ (“*3
(-aw)
Exercise 2.5: Page 27/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 27/51 - Avaiilable at www.mathcity.org
Ndw V
we _ I9... 8
“ii "
x",_ _§_ K __1'__._
31 (-aw)‘
L-xvi Ix -U *193- 1 §"*")Pg
L -xv)“
zxh-u») +1» Kw-x‘-)
L -us)‘
31-1% 4.9: -5-I.~Q() _
Q-xv)‘
78% fz.Qa--~>)
any (-ma)‘
n-i
,1: un~$" -.<
*5‘ V L-M3‘
I
5 1
Qv» “»‘-n~.~,..), '11- 31 , V44.-(.45 Kui 51 = }-‘S’
‘$059) ‘ 2’ QMKML--L) -———-G
“'43-Q u-A-‘L ‘AL
{L = ‘§”__;=_u~q.,+c»g»~<.>.Z'- 1
1».
g§_ = ‘§’&~;c.»,Q.~¢_ _,s;_».».<)}
2*
.§"_§__=é__ EL
)5,‘
= ;q_ ,§’'~ac.»&s+¢-$$;..{.~o]
7")
W3) B5 bk
Exercise 2.5: Page 28/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 28/51 - Avaiilable at www.mathcity.org
‘§ ="~2_'C-'>(1.-»c§+‘»_‘:4'-»U»~n+n ->*$‘~U""“ '—"" ® 1
':. ~€,{_c¢6-Iv ¢.§ ''&'5¢A+<. - $;*u"‘“"‘3 ' 2*‘ Y‘ ti ‘
haw
N,“ .5.-.g;.@ >~.1.-..u., u-..*.» 5 ‘
EL ,_ X ‘Q?-CnU»+ L3
5)
->z%_321
an», "‘
D$~)5
53.-
§(=,-D = Lké ""2
‘AL
,_ C»U»x+ Q}
aw ‘"1
_ 12”’. _s:..~.~¢.» +1?-»£~¢-Q--s -- ¢ -Q-L‘-‘*‘3
X‘)
1 Q &c.,u.~¢ ,,~»,c.,L~.¢ -»$:.U»-~u} --®
FM» ® < ©
__?1. = ZLuh bu -
¢_,E_;_ §q*,~,> = 1.~(e~<?
Gin)-on
w&.@ ;.,.1;-.11.-, w-»'~"°'*
‘X
_.e.7* K8.-r¢:)
2*} ,______,___
1»
N04)
Exercise 2.5: Page 29/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 29/51 - Avaiilable at www.mathcity.org
>’-§- ;__ Q
__m ,,, K ‘H
X
= '3?
Y
: i___._"' . e- '
(£3-0:’ )1'
1'
‘M.-‘Q
ii. = _ _¢.__ ________ @
1
>7)‘ (e.“+é’)" |
Nwu Q to-A-'2' 3
ii - ._l___ - €?
D‘, L‘+2§
b§» _ Q’
-£7‘ _ Qt.‘-#2)
New
-Li}; = 3w1'Qé;'»>)
_ a
- DA (an-9:’)
v __ '*
"-L Q - --——-'-" I: tQt‘--2)
11¢‘:
bԤ -_' - K e _
M, wm‘
'Q"""‘ ® k ,
3% is .
**7"> ”‘°z‘*
Exercise 2.5: Page 30/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 30/51 - Avaiilable at www.mathcity.org
Q__1' §u,~» = .w.i~=_._:3)I)
g? G£ww A‘
Qb5)"‘&“£!:st6-~>
§(*,_,) = 1..(¢.»§-)-1..u~~>> ----'
-.;,.@ >.~x,=.u., ->-1~-*' ’~
5  ,,zx--L---'5
% - 1%)" N’
1 2 -ii“ - L“
3;: 1‘~»‘ ‘“
_°_‘i_.-_a_ 2%.
bbh _ Wk“)
_ ._3.-l‘~....._.L.
' Q8‘. "¢~>" A
= v_x.:_----"-‘P
29-; ,___‘1.b.2.._
,_ -—-——--—— ®nu b‘+>‘)
NM» A-'-0,.® >~cb..u., w..a-t- 5
Ei =  __.z~; __L_.X
)9 fFf' *3
§§ : z§ 
3'; 1‘-0‘ "
_BiS__,>§.>.§_)aha»z .3.-2.. _.1_
7' -7}: 1‘--3" "
13 _ 11
be-a*>‘
Exercise 2.5: Page 31/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 31/51 - Avaiilable at www.mathcity.org
in
b"£ : Q1‘; ©
>5 (*‘+a‘>‘
Q»-»®+
>1; 2?;
M»
<32
_ D55‘;
(_‘L>‘)) -; )2
$_~l»- Gu-'u~
fc»,~>> = 1”-»5‘ _----CD
§.'.“_.® L»-A-i-‘K
9%‘: : 351.‘
.33.. = :;;;-‘$9
35%
z‘;
bah
‘ 5 75:‘ +‘}1~‘o3
1 ‘J-K;--1-*) +33‘.
x-
La. "M;
1 ~:‘§‘>!.-.1-- ~+ ;'(--x!..~,) -___
?.§_..M- ‘> x-
7;-9--‘|L -- "IN;
.>“1.- =;_ EL
‘omx, Mk M)
) '
= 7~,~*-' § -3 .
‘  X-
5-
— 33-l—-a-9.-1.‘aX +7‘-5-"L‘”3'*‘7 "" x
Exercise 2.5: Page 32/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 32/51 - Avaiilable at www.mathcity.org
‘S
_ 1- —
QC‘ -vi»!-‘9rL‘ -"i-*5 'l”“3 ‘*5
._._ 1"k+;l-x -N1?‘ k~*'Q-‘>+
8'8’ .:_ ‘;:k5.!-~x+§+;-‘§+Xl~;) ———--6)
7*)?
&-~®+©
$5 ,Ԥ
hr. )5 Z‘: 3*
qii-n--—---i__
Q2 $(‘*>‘1§ 1
sin Guy“ ,
'$'§“>‘9§ = §*:K‘I;Q ---""“ Q
‘>4-N-Q >w1.w.9.-, ‘-°-’*-"-'*
N,bc
El
>1
B“;-
_____....-=—--
>~>>u.
 4
§-Q‘|'=)‘ 5
_ __L.__. . L.
' ‘9
i9-x‘-
5
, _.?__.
5'1’
_ .)_.
‘9
"' .---_—-II'1-1
T--.--_ Q1
-3/1
Exercise 2.5: Page 33/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 33/51 - Avaiilable at www.mathcity.org
‘M
an (>‘-9)"
um AR!‘-Q w--‘~-‘K’--*3
1L = -l-—-- ‘L
: ‘ _________.® ' ~{
1
s
I
1
1
i
7‘) i-Ufa)‘ 5‘
1  I ‘L
' |_ x73» 3‘
‘a --‘A
1_;yi_i__;._;:
3? = _ _‘S_.___
av 5551,‘?
_3lL= -L 951-
M015 “K M)
= g_£__-_2.>.._ }
hg 5S,_‘L
I
= -*;~%rA)
(-1.1)
= - *~;S”"“' " "B‘-1L"
L‘21"iL)--XL X
5 U5X91 >'"-x
1 _ .L. £ ‘$"
3 Kn‘-wC~)"‘
I
ii”2 - _-L‘-111 __'___ ®~ 31$;
$15
BR
1
Exercise 2.5: Page 34/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 34/51 - Avaiilable at www.mathcity.org
Q.§3' -$L'l>‘)) ':- -------—-M3 “L
g_,§_,.
i -~1C‘~~)"'
G.~.3¢-A.»/ - '
§u,~>u = { 7*"? — ~@
w.~® ‘v~T-*”*> M-‘<-*
____Z-._._
%~i: = “~-%
Pi
N.
z‘%
bah
 .11
F - -*~ ‘I ; ]
= 3
L §~~i“~3‘*‘>
. , ____1l:_._._-
= 51 _S""&"'3 “, ,J-;-:¢$¢‘z!-Ax
K L—'¢-1‘--3")
=5 F +~£{--3‘-><t X
L Q--i."+3")u"'
3+3}= i'_ 3!.
(+1f-§'§ "
..____§5_-;,>
;_ _§‘9--33) X
2"’& Q--uh-§"')t I_L .
u*_£__‘_3,-;‘_- (H351>_(’*)'5)_ _%§--§Q'...)'-) .71.‘)
" '* ” gJ.¢+3=)" ‘
(+1‘-5") t §,‘*3‘J’Il"3(~ 5‘? 5“ L
- Y (-nC"-3")‘
M ya; /3%
-@{*‘;*?8*3;~‘3 "'i?“ 7 ( —1
Q j i V L+w1."'+~;“)&'
Exercise 2.5: Page 35/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 35/51 - Avaiilable at www.mathcity.org
-31-; ‘%"‘3*>‘*3*>’“, - ?-@ vs
‘ 9 “’ ‘Ia
‘I
353* (--7Z‘+~j“)3
“N 44!--Q wd.<..QJl.-,_ u>-.~£- *3
25.-. 2
>»
BE.

= ‘IX
_-__l‘
-..-~>-11$.~""
x. AK ------35 _§+1§~f'§
(-1"--*3‘-)
‘£‘""'3
(->< x‘-w 3‘-)
*- “::‘:3i;€‘ K
=__ —‘:L3
D” U--x-‘+j‘) h‘
Na.»
‘ - _i..12.... - ;;0,,>
B17»;
3
_ A 1--‘L
' "" =1
hi U--~»'“+~j") t
-. ~. ~,-
*1
>1 J1
(M-x"--j’-) L- (--31") - §+‘2)- %~ "'*L“*f) ) - ‘Lx
7 ,__
_ M Z1 (-x-Q‘-n-*J"-)
‘L 1.3,1' 3 ‘L LV7“_ (+x+3 ) - (_+'$vE' — 3X(-~1§U-§1+))
mg
* H (+w“C-vj‘ )5
L+*.§"-»~3‘)(+'$1‘i)_ 3xK1+x3 )‘
Y W 1.33/1.
(—-1!‘-P5
i
!
“> 1
Exercise 2.5: Page 36/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 36/51 - Avaiilable at www.mathcity.org
‘ "
}"§- i+~£.‘+‘)L+'§/3:.-'*3b‘:*3:_‘:-'3L'?‘7A':~ "" ( J 1
Sm, g».»e».~,=3”*-
31$. i+~ft+3" +*'5i5'“ ’~"‘**"> k -v~3’~ )3"
F~A-a ® 4,
w>‘~% _ _.__.-WY
“.3”; ' a~_~,2>u
S~»+..-J: ~»~+“- ‘(*“*“*'3 PMjsokbivus L“?b~u,;, u,- £95 . Plygi = o(’~!-1-~ 3':-an)
Q32 fiim) = $‘~'~*-i"“"‘5
%(x,'>3 = $5-*-c"‘;"‘“3 """_'_®
, u).).£'*
*0‘; 1 C)>'»..$$~»~‘6
'31
W B“: =_ -S~"»x~$*~‘J """'_‘®
"L
‘»LNu~> M»-® ‘="*'**"** “*"‘)M
‘_bi_ : 9,,-_,.~1~C’-*>r‘*)
1")
% 3,1 1 ;,;.,@,-.~> @
EL '' §2L"z. 1- O
~ 7,.» *5 .-.__..
Exercise 2.5: Page 37/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 37/51 - Avaiilable at www.mathcity.org
Q-it fvlf) = -Q}cr‘)
539 Gvlva»
W,» ‘ 2% .___ CD
5"“
EL.>~
B‘? - _'¢l-~>.c».~,
T5-
§j- ~:. QC»;3,}.
New
‘zi
>3
?i : -_Q‘c0$‘j
hi-
AM--;®-®
Pl~!'_L'-Ome z-,~
' -Q Lo-A-‘-
-36$»
---—-— Q)
g,.,n_u., <,.,.A.+.~,
.;iQ}§ {um =
34- 6.1»... Y
§(*v> =- km’
{(1,3) . L(=..3~§"‘
‘$(‘l>5‘ ='
;.“.@) ‘>¢.1=,.JJ.1 w-2..-bx
lb}: , .L__..L_..__. 1*
Q1-.-.
R
"'. x‘-v)
* é
~»--—-@
Exercise 2.5: Page 38/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 38/51 - Avaiilable at www.mathcity.org
31.9: ‘—L~&'~.~§').~*L7"’
‘ *2»:- £"->‘3 R
L ‘L ‘I-
=‘:_j*_>:_’:1“_-%
K‘z~,5'L>‘
‘LQ, 3‘.-it 7® I
M‘ b¢~>‘>
1. 1
N... J--w -»Iw- -»-*'*"’ é
__§__ . _L--‘_. 13
2;; ”' 1 Q34-3)
2. = -9-. N 1‘-v)" '
NO-9
w Ȣ~:*>
1"--)'“ - ‘UL
"-''i')L
*2._ ‘)1.
"E? _" *‘~a‘)"?
ML‘-»g®‘
E3---3-‘-§':‘=°
21‘ “J _'_______,____..
5
Q3 §-um) = ‘MILK _-:::3»3
six-' ¢,_;,,_,_,,_,, 11» _) ,6)
gum = ‘Y-ilk 16-3 { j
w.® k-~1>»”*» “""1"*
Exercise 2.5: Page 39/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 39/51 - Avaiilable at www.mathcity.org
Z1‘)
=&%
N-
 ___.__
: _ - £._’x)
ilk‘) +--—-$5‘
' UL‘-i).- 10-‘O
:~. _Z_‘___.;_:-_ . 7-5 k‘_)._“
+ §I'_§_..
ha‘-3‘)
N/5)‘ 1., ‘-:"—'-"
' w-~:>‘~w>* W/>*>‘
1*: (-‘- 5‘)
1“+3‘-‘l"i§'-¥ ‘&")'
-7-‘) Q1‘-W3‘)
~i‘~3“+1~|L‘3"
_; -7-‘J 1'"+ 2‘-3
(‘xI.*>)"
3_§'_'.:._"'.'__‘.".‘2._-_
Us
N»
b"§ 1-
-gr‘!
‘~)")
vs’ = Q-15). _T_‘_-- - L1
(1‘-v3‘)
Rx 5
1; _- @
310- (If-)‘)
"°"“‘ ‘MVQ w-»-V ‘9
Pi-.
=5
' 1.$.f2§
> 2'-
if-3*). §- *5 (f7-5*)
' + ._.>__*~** w-»~>*
t ,,d_'.1~.-‘H... .,,, ....,,.

gs @155»,  1“? 5,._ WW. _
,5 ;'5%
, ...., .
E L
§~’1(-I“
" LL“.t:':..
§ 1
3 »
Exercise 2.5: Page 40/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 40/51 - Avaiilable at www.mathcity.org
_; L»eA>~f* 1% *_
(x‘-';‘§z--
'11 K1,“--5‘)
£49- 1"kj+‘tXzj‘
1% K1‘-3"
X“--3“ +
{Lmy §
_. 3~__*£::il_
aw)‘
_>_._§_=_2z~_.....
>0 ‘)"‘L-‘r
gi. :11 _.
(X +3‘>>1» '-‘
'2. ‘>
W/J‘)
153- = = —“‘-3 “ * ”"®
M‘ h~‘+>‘)‘
RAJ;-Q ® <
?L'.'5_».3’3-_;
51¢ >5
:.O
(§_'g1 ,4; .§u,~>>= ~l*<@=;~>m -~§’<~=W""») '“- "="““’ “J
)“r A ,. ,
an
‘L.
‘Ma % **‘J"
532‘ G.~'u~lw
M,» = »&ww=~> - >‘*~=1“'~>‘
B-4;‘, v,,,§,_,u,, u-A-’c-“> L‘
16% ;___;__;___,__X_,*,._i_.‘.>_.-:§’..-L A-:.W>).1>
--5/1" x 3"
1
K
E
1 3"--1.3"} ; ‘°‘ ‘
-
l
'2
|
§
§
E
Exercise 2.5: Page 41/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 41/51 - Avaiilable at www.mathcity.org
= ~£.____‘*"' .... ..&-J--“‘ +1*>t-3' (‘IQ “‘ %
‘*>,  )"*‘
= ‘>9 _,.*v>‘ = _z*;‘Yp.‘:.}(‘I>)
3}»; 1‘-Ar)"
-_ __}:_'.*_L - 151374 Q‘/>3
X‘-Iv)"
1 ‘* K1“-‘>"3 _ 24125.‘. HI»)
§1‘~>")
EL 2 X - 13142 (‘[5,
*7
SҤ _ z Pi
Ex)‘; >5)
= sjiix--qw&w»]
_~._
- -1: ‘*3: 5
SK
: - ..__.7T_——-—
-+31>-
Y 7.5“
= - ‘_
‘$-xx‘
=f_>';?_1c“_'l'3:-
5"- x“
)1. 8 xi. DL
x*§‘L
-—s——z--z-_-—-—z-—-—i-
Gig. 9* §(1>~>)= 133$): *‘*“‘ “""‘
k¥x‘ %~:)L = ‘*0’ §1"§‘>)
Exercise 2.5: Page 42/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 42/51 - Avaiilable at www.mathcity.org
‘ii:
’§
>;.(;,. m.».{- - ‘A 40 ‘3
5‘
‘Q
New
§>
Ԥ~,
Nw»
G.~l.u-A
Q‘! >5) : x-_-——l*51-
1--‘;
Q;-»~';).7.*A-i-(*:@'=|-)")~‘}
(+~>)‘“
____ >_1?»n-w -1‘— u“
bx +'a)L
{+11%-3‘_ ______________
K-W)‘-
QA,,~,)_ 1‘; - MC‘-x-5‘) -
-1
b*»>"
L
11‘: -w 15‘ -- X7“-3- .._.._-Q--._..---¢
,-nu-
--_
_-
Lx--‘a)"
- L1--~a)"
wk’-+ um - 3‘ 5‘-r P-‘>~ 1‘
gx-S‘) 1' _ K Z
‘x--5)" b~b)"
»¢+=-24» -3‘ — 3‘-=->0» +=~‘~
L+~a)"
?_~(’“...'z.§’*-
(‘A ->91"
1 (1-~>)h+~a
(‘A--*2)"
D
Exercise 2.5: Page 43/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 43/51 - Avaiilable at www.mathcity.org
_,,._~,
£25
lkx v) 
'2 ___.__'.-_-—-— ;,’;’ },§.,%’_i".
;I_ s‘) (‘*3’)
_€-y-Q~¢‘=~
U1 - §‘2)1 '= —---—-—‘(Q‘-’)L
(“")>L n
New
64¢“ "‘§1"§3
; i3Q"~L'>‘J~‘JL 1 ?*ziw3“*1<
(X _,,_,)'*- L1 ~*:)L
L~M.~,)‘._{‘.. 1109-3‘) - ?‘>"- xx‘; -X‘)
U*9)"
géf.-L7(‘3+§_;é-17(‘>+)ji_X€_1‘2+X‘
Q+‘9)L
._; x"-PA‘: + 5"_i,_1,,__-i-—-i—?
(X--‘9)L
U->>’*'2 _,_______._.--.-L--~
U~>)
S~:L‘Ksxd§>>
1 git.-LX~~>>'“
“Mu K%"'§‘>$L 1" ‘0'§“'S")
Q-50‘ gym “A vb, >»§= 5*-»~(1‘>} /50¢-'~
£§t_‘ --315.33 :'. °
§
L F
Exercise 2.5: Page 44/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 44/51 - Avaiilable at www.mathcity.org
H7.
Sir
§u,»> = %».~u»» ------65
>=nco>-t¢~v», -~-’~-‘<~ *
8* 2 COQQXW3-3
st —.: ‘jcL*"))
§-wk = ‘j--8‘-~(1~">3-‘$
§“ = ..~3"9.~,..&~m
d__4_ ® ;?a_.1_,_,_U,.’ u:.».-k- “5
S’ : cJ>(‘l‘9~*
g 1'. c4nU"))
5” = 1.-$L.-L1‘a-‘*
§ = -~19:-4 WW3 A
W
NW1
39),“ {Q1 - ‘Jx §~,~>
Q-§_~}q,;_..Q1~, - ~j"Q—wZ‘$:..L‘»~~@)
._ _;~,;-,5[<',,_-,.u~, + £2;/%;~L*“»)
1. o
= 0 ' Q1») =Lv>=~)
<32 M %<‘,~,>=
ha-:»1*>-~ »**-=:w»> '4 W» +<=»~>
*2
%- *u:k 3'-_mL<>>'~) =i= §'>£0>~3
Exercise 2.5: Page 45/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 45/51 - Avaiilable at www.mathcity.org
§&- Gu]M
New
¥1
%(‘A>‘)) : x.LJQ:'‘(,h _‘)?.*._:(x’ )
‘LO
Z
= X-___._.___ . =_. -H2: K1-.3 *1?‘-("la)-In -3? _
I
5
-7Q-"~ :1." “T-T xi) +2u'c.2.(~.~;,3 _ 5_ ‘:1
'~'- —- ~12-— +7-x'L'.'l(b; ) ‘:3‘aw’; 1 - -—--—
-.~. 'n'T4:I.(by.‘, __ __3___ X x1431}
1+3
X.
$49»
% U‘ = "~=¢<~'1_l§*»m - §§
‘New
* 9» = 11,_._‘.___._..-3;; +’'¢:',1:¢;.-Q}
3'? (X-'5) ‘-'- (°>0
3"--x" *9
fag‘
+ ii + 5..
XI bl
L
=-__._.l‘.._..._+.l‘l__. ___-Mai-,;3,_
1 ‘L1. ‘9-
5+1xi-
__ 3 1
- —_’-“-——- + —--Y -- 15%»? L
‘£4-3‘ X‘-v3" “’
= ~-1-' k“¥*a") ~ 1-War) 2*;
@9453
v» “"=*‘"=*%
New
; ,,,_ §,c~,»> - M»,->
1» = B-In v
‘° *~£ bu») ¢(.,.§
> } ,
._ E
Exercise 2.5: Page 46/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 46/51 - Avaiilable at www.mathcity.org
2: -—k-0
§-)0
= La.
M-an K")
¥xb(.,.)= -
NM»
<1;
.9-r,_.. §'2LK’°)*'§”§'5"l
bx = " ” * (
$1-D» K
=_ .04.. ’~-¢>
¥~-->0 y_
»$L‘..-
_- ¥.--to &)
§vuL"°> Z 
$1:
-F‘-5£0>°)
5‘: 'S,.*L°)°)
____________._.---1--v
Q__Ԥ}_ ms
bur §-_L~,»,%.3 -.—. vP+'>3¥. +%¢-(1‘a1)
P-hum h¢k
gx-,1 2' gray
§£>‘w,?:) = X;-u-‘5§%. -- $;..(v,,1)
nu 1
§* = 3x+‘)iCJ>(151)
£5 = ii‘)--%¢-L~»~>+_).u +0-sk~A»2>_s]
.§“ = ?-C-abb2:)-x;£'<5.-.,.~,~;a_) V
,-Igwoi
-;, '1. ‘*5 '"  _
Exercise 2.5: Page 47/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 47/51 - Avaiilable at www.mathcity.org
§ = c.§(~.~,e.) -x>$.:.t~:i> -151
§ = ¢»u»-as-hark-£»*>->‘v*">“>"
"191
l
N no
'§;_ = 35 -'>‘) C-wvai)
-ax = ‘:[X--$¢-§*‘>?-)-‘a-1 -Q,(x51).
it
{H = 5?-Mwsl) ->~,‘z S.a.(1~,z)
Una) -1x~,1&:..(x 5-1)
gun = 3.-$.a.(1‘>-l3.xi+Q(1b?.).
-IIKELQ-Ls1-xi +$2~(~;1).1a]
= -15%$:..(‘1U+ ¢-.(1» 13 - <1-(um - P->>1%=~k-a1
‘Y = Q,b~,?. -3'1*;%$.;..(~A~;1.) ~ 7L'“5"1"<;.,@~,1) ____by
PM @ ~x ©
§'*‘ai = ¥i‘A‘)
__..___w sg §Lx,'>,=L>u) = _.1i">_ ,,s~M '-ok
?.-1-ho
_g,
1.. ii-§X.*~) (1*u)';
Si» G-Q-AM
V
'1‘?
.
'§h",’%’u ‘ 2.--u
54;. Lu-A-''.' X
‘$1 =‘-521?:
$ <
® J
}
1
Exercise 2.5: Page 48/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 48/51 - Avaiilable at www.mathcity.org
$3,, = G135 K
_ _.!._..
g1» _ 1+“,
gxul = K51») 1
_ -~ 
%“‘>1 - (1--no)"
“IMO
&‘,1L_, = 13?. X,
k-) K-17
K1-v ‘~31
_ _?=____
(Q-v w);
Qw iu1J4~..Js N1-5 v -‘$2;
Q~_‘L'1 ')"‘--".Q~) --obi‘ -.= o
S_~§»- ~
LA-§(1>~>) = 3"-ni‘~9+°~“ -—-—-—»
Y,‘ ~; zx-,+k¢x”
gs " 7'°*x
N.».§_~_._,____*:._.
ch $5
Exercise 2.5: Page 49/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 49/51 - Avaiilable at www.mathcity.org
3 .
<1» bx‘;--‘-e.~A. ' n1
A‘ '1-‘>--x‘-
-Ii>-@--_i___
QQ3 1. 3
"” "3 --X. = °
Q3!»
hi -§(X>">§= 37:“-31--13 -__.____@
D3-{Q--® m-A.‘:- *‘)
5;‘ -; Gx--’>x'"
S» 1 ‘D’
*“""é:>..=.__2cL.
<11 gt,
(n-»'sx"
_.7_,~)
ex-+315:
'7-‘D
E "3‘~-*9 +5‘--cox —-o_‘ = w
9,33-
Vi §U>b) = 1'“--3‘3-vjw“ -*-QX-+>) 1“ __-A<
W?-® >-»~Iu».Q1-,- m.;,_.‘E:- xx»)
£1 = 11+‘)--0.
¥., = ‘A~-1~;-->
“~ é:»_. = _ .11.
A1 g.,
.. ’-‘**‘>f*!“.. _~u- ‘
1+1‘) +> ____m_._____-._
4
!
s
i
Exercise 2.5: Page 50/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 50/51 - Avaiilable at www.mathcity.org
@ Q-w-1; +93»; -Lu
s_._w.
‘A
S»
Na»
Lil §@A>“>) = ‘E-'1§ --$~'~'*‘) *-"Q
uw-® >-**'~’~°-» “"’*""”““’
11-+5
= '2.‘A‘j --<‘»‘o
<;2=__i=L_
61 9»
L
rx+b
Q12... : -"
An 1->~>~ 0»;
E-nan ‘Q C-""L
TYl»~Ju> T» “*3-3""°$ “Q“°‘L
_?_,_,-_-Q-@—@'_"'
1
1-
Exercise 2.5: Page 51/51 - Avaiilable at www.mathcity.org
Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore.
Exercise 2.5: Page 51/51 - Avaiilable at www.mathcity.org

More Related Content

What's hot

Aparichithulu 01-02
Aparichithulu 01-02Aparichithulu 01-02
Aparichithulu 01-02
venkatesha9
 
Hsc math practical 1st paper 2015 wg
Hsc math practical 1st paper 2015 wgHsc math practical 1st paper 2015 wg
Hsc math practical 1st paper 2015 wg
azaharkdc
 
College raging-1
College raging-1College raging-1
College raging-1
venkatesha9
 
Aeman dee ekkadunnaaru
Aeman dee ekkadunnaaruAeman dee ekkadunnaaru
Aeman dee ekkadunnaaru
venkatesha9
 

What's hot (20)

1వ యోహాను వ్రాసిన పత్రికా 1-john-.pdf
1వ యోహాను వ్రాసిన పత్రికా 1-john-.pdf1వ యోహాను వ్రాసిన పత్రికా 1-john-.pdf
1వ యోహాను వ్రాసిన పత్రికా 1-john-.pdf
 
HSC Registration Card
HSC Registration CardHSC Registration Card
HSC Registration Card
 
Piano lessons-book-1-kids
Piano lessons-book-1-kidsPiano lessons-book-1-kids
Piano lessons-book-1-kids
 
Zed Attack Proxy (ZAP)
Zed Attack Proxy (ZAP)Zed Attack Proxy (ZAP)
Zed Attack Proxy (ZAP)
 
Collector 01
Collector 01Collector 01
Collector 01
 
Aunty help
Aunty helpAunty help
Aunty help
 
Ruhani Khazain-vol-18
Ruhani Khazain-vol-18Ruhani Khazain-vol-18
Ruhani Khazain-vol-18
 
Dondoo dondae
Dondoo dondaeDondoo dondae
Dondoo dondae
 
Divanam 01-03
Divanam 01-03Divanam 01-03
Divanam 01-03
 
Anaithikam
AnaithikamAnaithikam
Anaithikam
 
Amma manasu
Amma manasuAmma manasu
Amma manasu
 
యోహాను వ్రాసిన మూడవ పత్రిక (3 john _three persons.pdf)
యోహాను వ్రాసిన మూడవ పత్రిక (3 john _three persons.pdf)యోహాను వ్రాసిన మూడవ పత్రిక (3 john _three persons.pdf)
యోహాను వ్రాసిన మూడవ పత్రిక (3 john _three persons.pdf)
 
Aparichithulu 01-02
Aparichithulu 01-02Aparichithulu 01-02
Aparichithulu 01-02
 
Hsc math practical 1st paper 2015 wg
Hsc math practical 1st paper 2015 wgHsc math practical 1st paper 2015 wg
Hsc math practical 1st paper 2015 wg
 
College raging-1
College raging-1College raging-1
College raging-1
 
Addeillu
AddeilluAddeillu
Addeillu
 
పాల్ vs పేతురు
పాల్ vs పేతురుపాల్ vs పేతురు
పాల్ vs పేతురు
 
Aeman dee ekkadunnaaru
Aeman dee ekkadunnaaruAeman dee ekkadunnaaru
Aeman dee ekkadunnaaru
 
Paddy pests
Paddy pestsPaddy pests
Paddy pests
 
యోహాను వ్రాసిన రెండవ పత్రిక (2 epistle of john.pdf)
యోహాను వ్రాసిన రెండవ పత్రిక (2 epistle of john.pdf)యోహాను వ్రాసిన రెండవ పత్రిక (2 epistle of john.pdf)
యోహాను వ్రాసిన రెండవ పత్రిక (2 epistle of john.pdf)
 

Similar to Calculus ch#1 (1)

Chap02 solutions-ex-2-5-calculus
Chap02 solutions-ex-2-5-calculusChap02 solutions-ex-2-5-calculus
Chap02 solutions-ex-2-5-calculus
khurram shahzad
 
Structural analysis-5th-edition-aslam-kassimali-solutions-manual
Structural analysis-5th-edition-aslam-kassimali-solutions-manualStructural analysis-5th-edition-aslam-kassimali-solutions-manual
Structural analysis-5th-edition-aslam-kassimali-solutions-manual
DIANAHUERTAS14
 
Yarn 2/1- To study the material passage diagram of the carding machine
Yarn 2/1-  To study the material passage diagram of the carding machineYarn 2/1-  To study the material passage diagram of the carding machine
Yarn 2/1- To study the material passage diagram of the carding machine
Mahbubay Rabbani Mim
 
Salam barmuhammdwaaalemuhammad
Salam barmuhammdwaaalemuhammadSalam barmuhammdwaaalemuhammad
Salam barmuhammdwaaalemuhammad
Muhammad Naqi
 
Greg D'Auria Intern Performance Evaluation
Greg D'Auria Intern Performance EvaluationGreg D'Auria Intern Performance Evaluation
Greg D'Auria Intern Performance Evaluation
Megan Donahue
 
Brand Marketing Portfolio
Brand Marketing Portfolio Brand Marketing Portfolio
Brand Marketing Portfolio
default default
 

Similar to Calculus ch#1 (1) (20)

Chap02 solutions-ex-2-6-calculus
Chap02 solutions-ex-2-6-calculusChap02 solutions-ex-2-6-calculus
Chap02 solutions-ex-2-6-calculus
 
Chap02 solutions-ex-2-5-calculus
Chap02 solutions-ex-2-5-calculusChap02 solutions-ex-2-5-calculus
Chap02 solutions-ex-2-5-calculus
 
Chap 09-solutions-ex-9-4-method
Chap 09-solutions-ex-9-4-methodChap 09-solutions-ex-9-4-method
Chap 09-solutions-ex-9-4-method
 
Chap 09-solutions-ex-9-3-method
Chap 09-solutions-ex-9-3-methodChap 09-solutions-ex-9-3-method
Chap 09-solutions-ex-9-3-method
 
Chap 09-solutions-ex-9-5-method
Chap 09-solutions-ex-9-5-methodChap 09-solutions-ex-9-5-method
Chap 09-solutions-ex-9-5-method
 
Chap 09-solutions-ex-9-6-method
Chap 09-solutions-ex-9-6-methodChap 09-solutions-ex-9-6-method
Chap 09-solutions-ex-9-6-method
 
Structural analysis-5th-edition-aslam-kassimali-solutions-manual
Structural analysis-5th-edition-aslam-kassimali-solutions-manualStructural analysis-5th-edition-aslam-kassimali-solutions-manual
Structural analysis-5th-edition-aslam-kassimali-solutions-manual
 
Yarn 2/1 ----Study on a draft calculation of draw frame
Yarn 2/1 ----Study on a draft calculation of draw frameYarn 2/1 ----Study on a draft calculation of draw frame
Yarn 2/1 ----Study on a draft calculation of draw frame
 
Lecture 11 state observer-2020
Lecture 11 state observer-2020Lecture 11 state observer-2020
Lecture 11 state observer-2020
 
Yarn 2/1- To study the material passage diagram of the carding machine
Yarn 2/1-  To study the material passage diagram of the carding machineYarn 2/1-  To study the material passage diagram of the carding machine
Yarn 2/1- To study the material passage diagram of the carding machine
 
Salam barmuhammdwaaalemuhammad
Salam barmuhammdwaaalemuhammadSalam barmuhammdwaaalemuhammad
Salam barmuhammdwaaalemuhammad
 
Salam barmuhammdwaaalemuhammad
Salam barmuhammdwaaalemuhammadSalam barmuhammdwaaalemuhammad
Salam barmuhammdwaaalemuhammad
 
Excel prectis Set (Sumit_yadhuvansi).pdf
Excel prectis Set (Sumit_yadhuvansi).pdfExcel prectis Set (Sumit_yadhuvansi).pdf
Excel prectis Set (Sumit_yadhuvansi).pdf
 
Greg D'Auria Intern Performance Evaluation
Greg D'Auria Intern Performance EvaluationGreg D'Auria Intern Performance Evaluation
Greg D'Auria Intern Performance Evaluation
 
Nicapp~3
Nicapp~3Nicapp~3
Nicapp~3
 
Virology Notes 2020 #26: Therapeutic viruses
Virology Notes 2020 #26: Therapeutic virusesVirology Notes 2020 #26: Therapeutic viruses
Virology Notes 2020 #26: Therapeutic viruses
 
Bioassay and Microbiological assay Manik
Bioassay and Microbiological assay ManikBioassay and Microbiological assay Manik
Bioassay and Microbiological assay Manik
 
Ufo part 6 of 16
Ufo part 6 of 16Ufo part 6 of 16
Ufo part 6 of 16
 
Brand Marketing Portfolio
Brand Marketing Portfolio Brand Marketing Portfolio
Brand Marketing Portfolio
 
Ufo part 5 of 16
Ufo part 5 of 16Ufo part 5 of 16
Ufo part 5 of 16
 

Recently uploaded

1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
AldoGarca30
 
Hospital management system project report.pdf
Hospital management system project report.pdfHospital management system project report.pdf
Hospital management system project report.pdf
Kamal Acharya
 

Recently uploaded (20)

1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
1_Introduction + EAM Vocabulary + how to navigate in EAM.pdf
 
NO1 Top No1 Amil Baba In Azad Kashmir, Kashmir Black Magic Specialist Expert ...
NO1 Top No1 Amil Baba In Azad Kashmir, Kashmir Black Magic Specialist Expert ...NO1 Top No1 Amil Baba In Azad Kashmir, Kashmir Black Magic Specialist Expert ...
NO1 Top No1 Amil Baba In Azad Kashmir, Kashmir Black Magic Specialist Expert ...
 
Bhubaneswar🌹Call Girls Bhubaneswar ❤Komal 9777949614 💟 Full Trusted CALL GIRL...
Bhubaneswar🌹Call Girls Bhubaneswar ❤Komal 9777949614 💟 Full Trusted CALL GIRL...Bhubaneswar🌹Call Girls Bhubaneswar ❤Komal 9777949614 💟 Full Trusted CALL GIRL...
Bhubaneswar🌹Call Girls Bhubaneswar ❤Komal 9777949614 💟 Full Trusted CALL GIRL...
 
Online food ordering system project report.pdf
Online food ordering system project report.pdfOnline food ordering system project report.pdf
Online food ordering system project report.pdf
 
Jaipur ❤CALL GIRL 0000000000❤CALL GIRLS IN Jaipur ESCORT SERVICE❤CALL GIRL IN...
Jaipur ❤CALL GIRL 0000000000❤CALL GIRLS IN Jaipur ESCORT SERVICE❤CALL GIRL IN...Jaipur ❤CALL GIRL 0000000000❤CALL GIRLS IN Jaipur ESCORT SERVICE❤CALL GIRL IN...
Jaipur ❤CALL GIRL 0000000000❤CALL GIRLS IN Jaipur ESCORT SERVICE❤CALL GIRL IN...
 
Computer Networks Basics of Network Devices
Computer Networks  Basics of Network DevicesComputer Networks  Basics of Network Devices
Computer Networks Basics of Network Devices
 
Signal Processing and Linear System Analysis
Signal Processing and Linear System AnalysisSignal Processing and Linear System Analysis
Signal Processing and Linear System Analysis
 
PE 459 LECTURE 2- natural gas basic concepts and properties
PE 459 LECTURE 2- natural gas basic concepts and propertiesPE 459 LECTURE 2- natural gas basic concepts and properties
PE 459 LECTURE 2- natural gas basic concepts and properties
 
Hospital management system project report.pdf
Hospital management system project report.pdfHospital management system project report.pdf
Hospital management system project report.pdf
 
FEA Based Level 3 Assessment of Deformed Tanks with Fluid Induced Loads
FEA Based Level 3 Assessment of Deformed Tanks with Fluid Induced LoadsFEA Based Level 3 Assessment of Deformed Tanks with Fluid Induced Loads
FEA Based Level 3 Assessment of Deformed Tanks with Fluid Induced Loads
 
Basic Electronics for diploma students as per technical education Kerala Syll...
Basic Electronics for diploma students as per technical education Kerala Syll...Basic Electronics for diploma students as per technical education Kerala Syll...
Basic Electronics for diploma students as per technical education Kerala Syll...
 
Ground Improvement Technique: Earth Reinforcement
Ground Improvement Technique: Earth ReinforcementGround Improvement Technique: Earth Reinforcement
Ground Improvement Technique: Earth Reinforcement
 
Design For Accessibility: Getting it right from the start
Design For Accessibility: Getting it right from the startDesign For Accessibility: Getting it right from the start
Design For Accessibility: Getting it right from the start
 
Computer Graphics Introduction To Curves
Computer Graphics Introduction To CurvesComputer Graphics Introduction To Curves
Computer Graphics Introduction To Curves
 
Thermal Engineering Unit - I & II . ppt
Thermal Engineering  Unit - I & II . pptThermal Engineering  Unit - I & II . ppt
Thermal Engineering Unit - I & II . ppt
 
Online electricity billing project report..pdf
Online electricity billing project report..pdfOnline electricity billing project report..pdf
Online electricity billing project report..pdf
 
Introduction to Data Visualization,Matplotlib.pdf
Introduction to Data Visualization,Matplotlib.pdfIntroduction to Data Visualization,Matplotlib.pdf
Introduction to Data Visualization,Matplotlib.pdf
 
School management system project Report.pdf
School management system project Report.pdfSchool management system project Report.pdf
School management system project Report.pdf
 
Linux Systems Programming: Inter Process Communication (IPC) using Pipes
Linux Systems Programming: Inter Process Communication (IPC) using PipesLinux Systems Programming: Inter Process Communication (IPC) using Pipes
Linux Systems Programming: Inter Process Communication (IPC) using Pipes
 
Theory of Time 2024 (Universal Theory for Everything)
Theory of Time 2024 (Universal Theory for Everything)Theory of Time 2024 (Universal Theory for Everything)
Theory of Time 2024 (Universal Theory for Everything)
 

Calculus ch#1 (1)

  • 1. F*-~¢J;>- 4 ---1 M 5% 1 = ’§-Km‘->3 ‘ 1‘L|...~?.'v»Q--LVML o-%,.o-§'l1»- MAi¢-L)-n6,;. A’_“__M___,_____(_ -._ - __ "M Aida; ‘Q ¢k Pi-:.§k‘) ‘ "3 V x »uA'v»~>~Q~.-Q ’u..:->~.L..1.J_,, x43. ' '5~l-'~1-»‘—» '4, 1=§.U,a,u) h~..,~-'¥.'v~ Q-ink <>~f--Q Yiw. :¢..L..U,,>,3¢w "-1 uh v-1~....-~!( 0 ».».=,t..~3..1.~ >..~._q1.,o_,w,‘,_,;_ »-i-**<L>-».1».;.n ~A,;.),1'v> J=W;1 »~»'-~%~~+**-~ II W» g.. ‘z ~l‘Awz~¢9. ldu'.J~lI-0 Exercise 2.5: Page 1/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 1/51 - Avaiilable at www.mathcity.org
  • 2. ~& =~?:~¢-"- A 2=§(~A>~>) 'v> J>¢Q_, ta M. ‘t. Q L,-._,;3: J1 wsxm)-5 (<1,,) *'~£{>*~--~;€>o>m.@ ww, cxS>u ;»~a~w.x fh,~>)_l L Q wJ~n~.w.u x-¢4_Q ,5...,L§ {A an ,x.,-(up) <>w-<,.1.....(<>.,,,) /~11 widn ick 01> -QQAA §t;‘)) =- ‘Q- (>)) '-QKQ vk ) ."ii ag L. ~°-'- {(M5) (‘|"b)'-§£6) »~:e<3¢_,k't»..~~"M’—'-¢9-i-Hv-.J< v¢.0....»,a/> (x a"))—5(¢ 2“) d-10¢-1 '.,.,,, 'Q~*~‘ §-b>">) A-0.», -)C GQLM: . (1:3)-'olmo) u ‘Ha. (<>>o)- ~__-ii-ii--q Exercise 2.5: Page 2/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 2/51 - Avaiilable at www.mathcity.org
  • 3. Paid Lu: 1‘ = §~A>~>3 ‘Io 1%,; = §-b+%» >‘o $1 =. S-(‘A-$s*>‘>§'§b">‘9) .,,,,.J p/W ~94-o'r 1"? 8* 2%. ._ w~**>~>>-%“>%>2. _L;___ it i_-’'&‘-3-'%‘>">) SK-90 8 SK--30 S“ 3____*- .&~§l'_<>-§ ' Wk M * mm 9~.-$- Qsks °-’ °* 4' Lu-)-'_-X~-‘v: So E.‘-_ = 9»-' f %u*%"’) ':‘swV”1' M 51-» $5-, $.19 b¥ Lb“ 7')'"%'>§" _-;“)_ - 8'p—Do %*:<=~¥~ .. =. l~'-Luv D Av §>Q>,»§ r- :8-::° ‘S: O 3‘: §§M_)_ §y(»,~) Qu,Y_§- &'(°HO V~ Exercise 2.5: Page 3/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 3/51 - Avaiilable at www.mathcity.org
  • 4. -gr ,;3.,,,, .,.;,,¢,_ hi %=§(x,>) n_.,, Mm AMJML-,.». ~gf:,1>->> W -3:.-A-‘-§i>= £5 = %.Hn = %*>,_ = s“ i E52. _ ‘ -'%;K )x§ " 31%; E =K§Q., =81“, I t >,~;@-i;> =l*- =%<%-> =¥»>,. -axhm) ' %i:,K%E> = if), =§(s~.. = <&..>b = ;,, °*~>‘*~1* A § -if -b... :¢..L.L1» 4; vu {AW §(¢>§=o New ;vv~ Wu <i~1.=__l%~._ a* AL ‘I~> ,.._.*_>;... “Q3 s, ,1~~-;§-.2 ~ r‘”'{."a1'.I’»‘f§.ifa ~ fy‘, - Exercise 2.5: Page 4/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 4/51 - Avaiilable at www.mathcity.org
  • 5. ivo~L-JL N. (?~hLh~.J>._.§); £LLu,_(} 3; 1- 5 (1,-,3.;g.,.) '***‘) E £ 1 $_-_!-¢1.u.m.-V1-;~Jm~. km '5-x“ Eu J. 1. SI‘:-q-- .<Jc 1. u,“-a(.,q ‘ + 1+") 1-=-~ (9-1") 9"‘*l"9(';:.) W 1-.-'-~ (‘:'5‘ 4b pa) *‘+5‘) Y-O K-Q-O A-0 .2. N <3,-1-1.-M 3:" Q‘)-J) QQ -10> 1»... €. hm‘)-o 0,45 (-)(-O 8- U :8. -l= C. 'Exercise 2.5: Page 5/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 5/51 - Avaiilable at www.mathcity.org
  • 6. Ga Lu 3:” “*5 7'; ($;‘Q-0 (920, $4‘- X‘) 1' , L2.-, l,,.§(o,o) xs‘ I. $:-an 3 - Um)-(~r') *5 =- En» “*1,n-mm ‘W-1--> *5 " o r. C.- :.-I -1 * '5 '5 Q_‘~_ L-.:.... _*'__...5 hm)-1!-»-7 f“'JL SJ» . - J“Mk L Ll “_,_ -L-~;' “"-"~ '5 3 L 2»... 5:2-’ L1n)—9(-.~) Xta-Y pd = AC-b0 l 3 : -‘$3-“Q =1) ,3“; , g M u»»>- (~--) , *—=» ° s. d-:- 1~l-#3‘ -'-'~‘-'* 1 L“ 136:0 -1;-‘$;2o_ A-90 A,‘ Exercise 2.5: Page 6/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 6/51 - Avaiilable at www.mathcity.org
  • 7. 1 2.-... ,0kcJz_s£.@ 1 A-00 J_*- --“M i - 9.4.. ‘ ‘ i - Jun .J.(<-so-'$¢..o) X * > - 0(€»n-Q:-~6> .9.=° 3 9,; 1..-... x- 11» + at-1‘>_% ‘l»‘>-obn.) qt‘) --H‘; -‘It -H-‘‘) $_-__=- _._g .0. L1 in J.n.g,- L;..$.$' “""* x 1 UM 1...i1.1‘a~-3;.-2‘: (‘1‘$‘.(3>3- £5 +-; -uf ..2_~, 1;... (~,:’._u~, *'.nQ‘ -1-») = _(‘oS-I“-94 1.;- 7- L 1 1,,)-;tn.)K1 5 *‘3 " cl 4'1"") 9-:-n-n.- _ z+u._u-at '-= LKi 1:}-L s~»~.u..;» a-., Akwibdc m QM w-; ¢.ai.v$¥ ' Qg 1.2.» _.._1.‘Z_ ._ (1£7) -Y (0,0) “'_,," — Exercise 2.5: Page 7/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 7/51 - Avaiilable at www.mathcity.org
  • 8. §£"4,k.l w s‘ ' 1 -, -La“ (‘>13-o(°:¢) 7"*‘)t i 5% W‘ ')>“‘~‘ “"3 %‘l>‘9) = i.-__‘:, o»;».¢du.>s ‘E- 1+) loL.m on (1,;)_.9(¢,,) M * d.i:u.<I;-A u...uv.A~, -‘,4. Q--kA_6__M* amt Lek u”>*'9(°>¢) 41,0», “.0. 1&0. j=~x u... Q = 1.2.. _}&l‘l!_._ ' hr»)-»(-,.) q@.“}‘. =_ -L:-.. __"‘_.2}E_... (‘Ia‘))-illqo) = 1~'- k_“___;___) hm)-al-,» +-~ WM va.(L.v,~@~v S¢ M L44} <1-M Md Q-X3-?>1' 1 1 '_"-""""'"“"" Q1 1.~'.- _}.i:lT _—_ ‘M‘:)—o(~n) ‘L -Q-‘1 _p_ , 14» _}‘;1‘_'._ . kw»)-» kw") "-1‘ 9% bu-L -A‘~.u rm.-Jr {um = -3;;-2;; ~=»>»-»-M vi "°‘-L-41> M Uri)-—a(<>>~) M c1.L.|.f-12nd '7~4-Lm. -/>0»-¢N’~mJ -[L-<(.I( Auomsk (AC1-AK Exercise 2.5: Page 8/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 8/51 - Avaiilable at www.mathcity.org
  • 9. .1, = "IL M ‘,,,) ____, 9,°) Q-'.--3 “L »(~v-I. ‘j 7- VMJL VKA-~ -. . Q 1-‘NVL [*A1‘>-oh») W:'-u-51$" 1;.“ XI-k-YA“) _ 1 (1,»_’(4,.) i '~}) IJ_,w_,, k-N 3 hm)-1 luv) ‘ ‘"‘k u.=.LuJ- 1» “M X- ‘5““""** "°"'“'-"¥‘“ §» M ‘§3-M 1....-Ji‘' $4» *3 ""9," l —iQ‘ 1;,‘ 0~"4' ‘Q kw-u-.-1 11-,‘ + A1 1 = 2;... .._§£.'_*.h?___ L (‘,Q_‘(a,0) §'A 9* wan M-V.» M ’§b>'>3 = 5-‘5:_—*-EL “’’*'°“,"‘* ' Q5 +<lx £2 JnL»1 M §‘*>>)--aha) €- A;;,|_¢‘I_',,,,3 Ron ha-I. Am») “J An") wui ¢»;.M:. - ax‘--»- 1. = ‘-- ( ) ln-aln ¢y}{'-Q A1 > Exercise 2.5: Page 9/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 9/51 - Avaiilable at www.mathcity.org
  • 10. 1 1_;_,_ (u-->m ) -,1 L“)-¥l'>~) Cwnu +11 0 +nw > Q c—-i.____..______I.1 0+4 -Q=L"1. 0L ¢...~..3>....1;...~.x A-u~.&uz,;£" Q 1:... K1‘-*3‘; (‘*>'$-eh») 1" *3‘ $_-3» Lu: 1 um M Q k‘?'~')‘-)L (‘M-l'»~) *':"‘3‘ k 1 L)‘ 5f w-1 J>-.» 'r..3c §£»‘>) = ‘kw 3 "'W-¢~d~n X4-j h v..!...v, M (ma)--> Lo») fu,“ oL.uI.;.~.» _....L..u. J>¢-9 “ml. 1£~.a.k cl-u»'»J<é_x;4t LQ k:“)§-—-);q) Q10“-J ‘KL 1-v'~.l. 5 =n MIIL +YV§1t) ‘§a‘!)—9¢:0) ,* ,* W? £1 . ' 1- = 1»- i‘§‘*.-~_‘..>...,. &,s_,L-,0 Q (H_Ma) 2 ‘L;~ (“'Y“")t kw»)-»»,~> H. ,,T"'-‘ ml.-<s.'~»dL“-.-.)<{-»~<H!--~7="~'~'*'~'%~v 4 4 1 § i Exercise 2.5: Page 10/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 10/51 - Avaiilable at www.mathcity.org
  • 11. v§;4;",,,,_g%._¢9.;“,_‘_,¢u¢.Q.-.n!>~§~.v ‘vs K s. m. 3;.“ A.» "rwk e.x3d<- ,.-1-__-_---Z-1-_{—-Q <32 11¢» ___.°“>‘ (3:5)-5(':s ‘I--3“ $3» Q3 1 1.1 V44, A-4, :.;...."..x “M .1 = °-'-~ _‘_*_>.‘__ um-.1-,-> 1: *3“ sq“; »~ 1..x gm,» = 131.. ,,,_,,,,_u ,0% cl!-QQ»-..& vo»9»-0, 01> (u,,)_,Z,;?) LN “A d.wx_M W“ ‘*""‘ A"-5 "vii ~U--Lt dun; -“.,- e_“;_‘.._ £‘a‘$)-9 (9)0) 01-“, K‘ Q. 3 H‘, A Q - 1Yv‘." L.~>)..,(,,,, x‘--wv‘u“ MA i-i______ ("53-l°u) --‘n:'>Q- $0 ~R*’OO (IA (x,|,)__.(.’.) “KM” °"""‘§""""*' At-1;-A M ' $§‘*>‘1) —-5 (6:0) Nude §'+§~s~. (~,~>>—-»(=,.3 “M1 1:31 ll - -L1-~ 3"-Q‘ Lu.-.;..(_.,.; 3‘~__31 (‘D5, -Qt‘;0) 2')“ Exercise 2.5: Page 11/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 11/51 - Avaiilable at www.mathcity.org
  • 12. 1= I--»' —‘- “(lg)-y(in) L S. 0'5 Q.‘))~—)(0>o A1p,~j ‘=31 W-~u ‘M. -L§w.Li <1-u. moi €-x.'~¥- QB Ll-Q €('l)'5) 0 ‘SL (‘£9 *(°”x X‘--~33 ‘—‘- O L‘. (‘£0 2(0):) $~4w A-“k § 54 ‘NJ ax “L S33 G3-- A -f(>») = §_E3:;s H’ £‘”)*("'3 4u ' Kim) =(°.v0) Rum $0») 1 O —-()3-4.‘)Nay; -'4» gq-my .. 2.-.... _l‘_‘l__. (‘>33-I(I ‘Y (o§—0(0; 0 } 1;1")‘ ~.xu.~>>-=,~.~ Q1...‘ h-. 1.2.». 5-~. it... Lg“ § (X?!) : 1‘kit I (‘h5)_,(0, Q) (‘A Pi -9(0)0) xxQ’ W}‘Q __ !L.:.-_ M1 (~wa)~o(-,. “"~‘ _ v'1 W ‘A W “duh *Y“ s. L4- §(x,~» dw. Mk ¢>(»’<- (‘>33-o('>~ .¢,,,,¢_._ ’Y0k Qi (°>o) waila§3.§»@ at .. x 3: rg I E Exercise 2.5: Page 12/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 12/51 - Avaiilable at www.mathcity.org
  • 13. (2-E. F;~A 0. )>uU- M ‘I- -§(*>‘5' = 3*‘, 5* (‘As‘>) -.1: (_°:°) 1 ) s a_ 4 (aw) =(~,- U> G1 UH‘)- Qiup» L‘ ' K > (U!)& 1:23“; qt *1 == "4°_ ' Kt») = (~20) ‘As-0. z§(~,.3 = <>~ (3%) 3*»; Now 1.-M W” = 1;-.._. ----(~m3-.k->-1 lg (‘>53-» U») *'' ¢_xLx>;_>,L=»,») o.9.~..§ W4. JL;-.1 *j=-v~ WM. (‘.”_,‘.“) Q53)-5 {up} K Xt ' Q; '5Yv‘L (>‘:)—§~>') X -I» wq‘ S‘ 25*“ §k~4 >5) = 9 (‘NS -Q (IN) $5-»u §K>">) 1» C4-llbuuus mi (°>'3 $, Li.» §-(1,5) = §5(°>n) (‘HQ -0 U2‘) :=') 0 =' a A Q-an 1 1 1 3 i Exercise 2.5: Page 13/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 13/51 - Avaiilable at www.mathcity.org
  • 14. x Q...“ -U. §(1>‘a= }__"_'__‘}:_ (,,),y,(¢,, my O __ (19)) = (0:0) e,.,,_,_;_,_,_ kn <'..L',~L.tq ~§ §¢.>(¢,.). be €_‘(°>0) ‘X 'g$(°)0) 9:1» c..:...,. g,...a.~.. 1,. '§(‘Aq‘-Q : & . (Jab) #10103 u -§. ( -1 )- ' ms) (0)0 -Ru. §[o;o -.-. O Nuw .‘ .5 _Q-W‘ gbh) = i* 3 (‘“)_,’(,’°) QM?)-!l@) "ii-3; hi k‘>">——'>(°)) M “A. f)=.M1 3 3M €L‘>,) 1.1”“ X3‘? M1 (m»)4-,-> kw»)-,1-.-> w‘ , IL-_.,. +~§’*~ Q»‘>)-sl.'»3 --w~‘ 2 JLL... (--vv?)* (‘4a‘))-5 ('9') Sh"... .. (‘$05)-g [o;)*(‘,D _ O $~'-u ~Q~i-- §-U»*a = {-9°") (*»‘>)—ak~>-3 S‘ gh-»">) 'o C-CL;-.>4-.v» £9") “~4-. Exercise 2.5: Page 14/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 14/51 - Avaiilable at www.mathcity.org
  • 15. Ni!-3 H.» - 1.~.. €<‘~>~>-f°'"‘ ‘ -50 y‘ _:_ Lu» '-° -no y‘ =9--'» 31>. -'00 h -_-_ 2.4.-. ‘H. £ S0 §x(O;b) = *- §”(.’.h _Q_-____ ‘('2 '~§ — fin1) Y~-Ibo ; .- 1.-la-A 0@- _ 1--1-n K-ac K .Q:..- Y~ K-30 K : K-30 §,,(~»Y= S‘ -gxkoyu) t ‘$’°)03 . @ Exercise 2.5: Page 15/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 15/51 - Avaiilable at www.mathcity.org
  • 16. P 13 Q1! L._* &1,)) 1: —--‘I--I‘ (‘$25) #(°)>§ 1+3 .-Q Qua) - . =2)‘Q~I-.~»4H)’d'*£° Do §_x°>v§ 5: ‘S',,°>v) €.;.»)>¥ $_3_Qx- 'vs x“: ;..;_ L*A>> -4=(~>~3 §>(*>~>3 = vi‘--3‘ (1,5) =.(n -3-bu. §§'>'§ = ° Nwu . vi“ ~> 'Q~'vu -SKXQQX 7' L“ X‘ L (1‘$)"9 kn) (‘v’)-a k. 7 .1 *3 Lu<(>~>3-e b») Q1»; Bu. LL-Q ‘j=‘~* ““~ 1~'- '§(‘A;‘) 1 _}EA:l__ QM») -a luv) QM)-akm) X“-w MR’ X‘ -_-Q.;..,. ‘~* (xm)-5 Ln») X1--~" .Q..:.- %(‘4>‘>§ = O L*>"'§-99*‘) QM); Q~m~;)--ab») <>Jl.~.-3 Rn. Q»-1w.1 7::-.) M K 9*-'* §b»~>)= """‘“ *3 M QA.a)-vb») Q,))-oli) 1 *7~ L... _3§1_. 1 L,~))-st‘-O 7'1“ Exercise 2.5: Page 16/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 16/51 - Avaiilable at www.mathcity.org
  • 17. Q1? *&*>~>> = =3 bl?!)-9 ‘ux -L2, §'(‘l~|; '-'- -if l ("am-,1-,») Q‘ -__._ ;,.,,',",g _.Q.',,,,.',,k An-IA moi Q.‘>'-J:.- -¢.,.<. § Us 'v~Ji c..t.-........>. ¢u<L~,.) Nnu L; 'S'(>b)— ‘§(°)°) §*( 3‘) M --—-C-‘————--— -90 1 .Q.:..-. 0-° —9u = Q —!u 1 O = - .vW-... 4“ *>-‘s'=°‘ ¥~»~»~>- k... 5-~——’< -_ .Q...:,- °—° K-)0 K .=l.;..-O ‘L40 7,0 Q» ~»Q-.o“- '§‘Ko;v') §, .g,[o;q FM N ,4_,_ ,,,;r,-,1 Awmd.-.~» 4, m 3%“ QPJ»1J.....», $-v_>_)- QR Exercise 2.5: Page 17/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 17/51 - Avaiilable at www.mathcity.org
  • 18. m “§."‘L~‘ -_’:~> »;f-_>- ;%,,,,:' "3 85'2.-¢_., ¥'A = §(*A>‘)) " 1. 5 - x at .. ,,. -#~, ; ~. ," M‘, u-,.£- amt‘: I. - g‘, ‘-'- Lu. L‘) 35*‘ § £. §~,= git §L‘l >5) Q‘*»‘)) : mg. ;~.n..c.., ~»-»~-’=- x -xv _—_,_._-_-11-:- X ‘1Q'~'3" ':. 7. X Q '1 2.‘). ‘$3 - '* Q,‘*)'L‘ M 1‘) iiiiiiiQ] f(~A>~>) = ‘h=I.2(»),U $3,. G‘"‘**‘"~ §b>~>) = ’..:.!(‘>),Q ‘Hi ,.».11.u., u-1-k- xv: 3'—Q’lx) Exercise 2.5: Page 18/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 18/51 - Avaiilable at www.mathcity.org
  • 19. ----L-__. _.2_ 1+2. 1‘-‘iv xi. __: é Xt-3" 1" ¥=§-"~5,31. *§ =_.__)._.__.)._(»;) 3 "*("h)")’ * -_.__.___.. ..L_ ~ 2L *xiv : ‘U’ II-"""i 0 _' X1*3; I ¥" -A =‘~*>” ___,_---_-----k-a--m Q . *2 ‘§(‘*‘>) = s'.')~(1-*0) S3’. Co»-3-u-» €(*»">) = 'tn:)¢(X-k‘) '~g;.>v.1:-1A, u-A.‘- xkb .§....§ 8 "---3)‘ M ‘M, ‘ . -=. .._.____---- . --(‘A-wgf ‘H ‘ H (‘A-~9)" Exercise 2.5: Page 19/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 19/51 - Avaiilable at www.mathcity.org
  • 20. § £7 ,_ ____.__.-C --:;(+ $1: 5:81- §Q>‘>‘ RX 1% Il L = gr-C->»>5. o =.> ftwo‘) 5‘-N - <- ~~5 ___.____. E - - (M-‘>3 -- K1--3)" <53 fa»; - ‘é‘s;..~, G.»I»A~ = m;_“__ u-A.:- xi) 1;,‘ = u: - <=~u»-...~>> Q‘ 1 -$.=..>~9 Z‘C»»~a _________--———-- Q-ii §u,~>> = 12,.g,e..,,~) 533" Gui-AM 1. ~»Q~§»€‘+~j") » ->.»:n.m, L.,.¢.#=- X4» = -‘--um x‘-Ivy" 3 $1 > 4 s E 4 ‘ ! Exercise 2.5: Page 20/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 20/51 - Avaiilable at www.mathcity.org
  • 21. §* ¥1. .¥_& -, _2'l'_..- , »¢~;- i gv‘“'§;""='-'(X 4-)) X"-+‘)" I =‘-‘> at-*3" Si" G-Alum- §£>~a) =. ~Q-K <§(1,->3 = ’°“"K *6 _._._._.__ (S1‘~T>‘-*3 i _.____._.."-‘) -_-1»-_-1-ii... Q...“ §b>») = .Q.,&_§§{~~2‘ -1 S$Q‘a-3" '' * X T‘-x§ -3-U‘*-3‘+‘I> 5;“. .,.;.k- x<‘) ‘- _K-7-.-A---'l‘A-> _(_.1....__.":.x *- .. ----—-——---' F-_l ——-Q-——~ 1 1, L ’ Kg‘:-‘) -1) "v) *1‘) K:-S )---‘_-_ <";iI.T~**>(mm F3 Q 1-/S xx‘--‘a‘" Q >§ 7’Sx‘--;‘-) (SE1-*3 wr'~,~> Q m¢ms1<;~ > -- _ __.L._--- -=. - _7;__.. ':. 1--—{>l X X1.~31. $56.‘. 31. Exercise 2.5: Page 21/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 21/51 - Avaiilable at www.mathcity.org
  • 22. _L__..*' £9 : _-l--—-—--'&1Fkf‘:>,_7~‘)} _____________$.z§T‘,‘:} X -'4-X(F1? **) ( yf"r; :2 -—-——-—-—Q V -' 3 ’ I 4;:@:;-*»u:~:;~> <m=~»~sLI»I=-l;~> V 5 - 2 " .F>*~=~ = ‘>.___.._ Kyzzbi +1 - .i¥*‘)t ‘** V X 51!-...,)'¥ &y;1_*‘)L __x KS~k._~). __-*9 =2&Sign .. 1.x‘) '2 "--""""':._~_=- ISX ‘> ~3‘ Zhk____,, iaif-*5“ ~:—¢— _._. (Au >">2= -_= -~ - ‘* ’ > gr ‘I ' L I L §b>))2§ ____ -.: §x’*».~)-»%.§ ,§X1‘--3"--:1-L -3/_'_ gx _i‘_-k_£__‘5w.__-;L1§ _ Q8_k_K‘£“—-‘)1-'%_ 3 _ ____:l________ ~L '- -;_ 1. 1 3,‘2_§x--3--1) Exercise 2.5: Page 22/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 22/51 - Avaiilable at www.mathcity.org
  • 23. Nan ._'_ §~,=' 1c»¢~,uw"~ .___.__..-1--_-—---- _ » ~- & 81 " -,_ x -,_ 311. Lu.--‘)-wt) _.-| ‘£7 T. _-_:_T_~ 3h. (X--5 +1‘) 11) . .3; Qx‘--5*-v ‘ .13 _ 3/L + gz = _¢{@e..5*~m>-~_>E§»¢-;‘».;;'~. £1“ ..}/L 11) . ‘L1 ___E__._._ y_ ‘L 13,1bx.--§ +1 ) =_-__,1 N J;~.»_¢,,,_; .uh.~. ¢11l-~‘L:Mu k?.»,.&.1-....2» 1'5-1;)-. Q13 E‘, 5.-3» M 2. mg. 1%.. = in B11 ‘K-“> @_ G)____.-_--—-- 6) u~>-A.':- ‘Ix '1-‘9 Q_. 1-‘D ____-=5,-‘bk!’ Nu-.» B1: ‘A-‘Q E3./‘ma -.'. -- E ___$_; ¢_ i(—?Zi>77” 2. 1) I s ; 1 i Exercise 2.5: Page 23/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 23/51 - Avaiilable at www.mathcity.org
  • 24. Bl1 "K-3 is M -- = —¢ -£- <‘ 53 . Mm» ii. = .::§>;§~) bx»; R = -3;-*4-1i"> 5 V x-> -: -—-9..- *- _b,‘__._% T. - &‘ Q-1}‘ X-+2 ’ .._._ SJ» Ldr 2 = 1*-“i’-- V ---—-~® *-3 mg. ® Lo-A . 'k- X bid QK-Z)__-_ ?‘§-kb)-‘T 7* K1-5)” = >.(-~>-7K-‘a (1-*0‘ >1 = _ i‘>_ M U-~>)" ._.. ‘L s bk») *&1= jl>____ M1 £1-*1)“ NM <>'~q§.® >»1;.1s., Q»-¢.:.~, ii -= -1.‘; ),1.- Exercise 2.5: Page 24/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 24/51 - Avaiilable at www.mathcity.org
  • 25. R g_~,). - (§>)- (-0 3.9 ' ' bx-w)" i 1 . 1 ‘- (1 ‘>) 2--5- 1% ,,,) u-~>>‘" E >3» (1-5) 1- _ _,____}_..--K 2 % “ '3} £1-~91’ Na.» 1 2 33:. >»~>¢ 3 xx '37. K kx-5)‘) -= 2.‘, §‘*'T°3‘i" ‘**'}&‘JLK k bx-‘:D‘ '_ 1' :6-116+ ‘J"—'-§'--”'{‘> n (X-‘=)“ = -LF ‘J“"L LS L x-~o)“ ___.LK,L__,)1.. _________________._. K1-*>>“ -1.L-‘>3 ""°3 _ bl-~>)“ Y‘% ':. Em)“; QM bf’ _'__;.-_-—-v- Exercise 2.5: Page 25/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 25/51 - Avaiilable at www.mathcity.org
  • 26. Q15 95;. Lek 1= 5-Z M @- m._“.@ <.¢~)--- * 2?..= 2» $- 2}. = ‘$1. - E 3* s 3 s- X. 4 y=_ =~,K~.-.. e.-‘av. +e..a»->x N’ v; V )0 New bi = *6 75‘ 1 L1 ‘D ‘I-L Q; ,[5:;:‘.: +‘9-)~'$- ' ‘ -i ‘L 5-‘L >Z_§__-= E:&')- at: +>L~»-0-* ‘X w-»..t- 5 ‘O . *-‘lml >23 ‘O u s ~, x 1-L.a~- Q. . {Lax £5; = -- New #1 ,__ any s #2 "“-X __.,.Q.1.,.u.ax + 1--°-~-&-‘>1'~ 1 ' Us- -- ‘>1?-9-~x + ‘Pk --9--‘*3 s 2 an. ‘>- Exercise 2.5: Page 26/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 26/51 - Avaiilable at www.mathcity.org
  • 27. " Qli 'b~'~‘~I-3* -vb:-‘H 3*.1* La 1 = 1"-.Lh>2‘.* 4-*1-.:.‘.~; oh -L ?z,..U-':),Q+*i...W=2‘ca _ _-....u.;~.*> . ’t¢...U-$23 ‘E K 2- 1+‘? -@ -X‘) 1 m_“_® ‘,,,‘_g,;,__q,q,,, w-,.¥.-1. R u-»~,>“>-k~5~~>>-<—*>L ‘M Q-xv)‘ -2:‘) +1» +5‘ Q -xv)'“ _§_23_ ._ __-xi. M (v-*3)‘ 37'___2'- -:. (M-‘:"Y '7‘ ('5)bx’!- U-xv)’ 31% -L5 (u-9") me u-m>’ u:-.“,.® §.,.1.-.1», ¢,,.,,.+¢- a EL *($-1»)-->~~hL:"~3- *9 Q-10)" -sg/; -wl“ +‘AZ§_ U-uh) " >2. = .1112; 5‘) (-xv)‘ 1 K*i). ._.-L?-_-----a‘ (“*3 (-aw) Exercise 2.5: Page 27/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 27/51 - Avaiilable at www.mathcity.org
  • 28. Ndw V we _ I9... 8 “ii " x",_ _§_ K __1'__._ 31 (-aw)‘ L-xvi Ix -U *193- 1 §"*")Pg L -xv)“ zxh-u») +1» Kw-x‘-) L -us)‘ 31-1% 4.9: -5-I.~Q() _ Q-xv)‘ 78% fz.Qa--~>) any (-ma)‘ n-i ,1: un~$" -.< *5‘ V L-M3‘ I 5 1 Qv» “»‘-n~.~,..), '11- 31 , V44.-(.45 Kui 51 = }-‘S’ ‘$059) ‘ 2’ QMKML--L) -———-G “'43-Q u-A-‘L ‘AL {L = ‘§”__;=_u~q.,+c»g»~<.>.Z'- 1 1». g§_ = ‘§’&~;c.»,Q.~¢_ _,s;_».».<)} 2* .§"_§__=é__ EL )5,‘ = ;q_ ,§’'~ac.»&s+¢-$$;..{.~o] 7") W3) B5 bk Exercise 2.5: Page 28/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 28/51 - Avaiilable at www.mathcity.org
  • 29. ‘§ ="~2_'C-'>(1.-»c§+‘»_‘:4'-»U»~n+n ->*$‘~U""“ '—"" ® 1 ':. ~€,{_c¢6-Iv ¢.§ ''&'5¢A+<. - $;*u"‘“"‘3 ' 2*‘ Y‘ ti ‘ haw N,“ .5.-.g;.@ >~.1.-..u., u-..*.» 5 ‘ EL ,_ X ‘Q?-CnU»+ L3 5) ->z%_321 an», "‘ D$~)5 53.- §(=,-D = Lké ""2 ‘AL ,_ C»U»x+ Q} aw ‘"1 _ 12”’. _s:..~.~¢.» +1?-»£~¢-Q--s -- ¢ -Q-L‘-‘*‘3 X‘) 1 Q &c.,u.~¢ ,,~»,c.,L~.¢ -»$:.U»-~u} --® FM» ® < © __?1. = ZLuh bu - ¢_,E_;_ §q*,~,> = 1.~(e~<? Gin)-on w&.@ ;.,.1;-.11.-, w-»'~"°'* ‘X _.e.7* K8.-r¢:) 2*} ,______,___ 1» N04) Exercise 2.5: Page 29/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 29/51 - Avaiilable at www.mathcity.org
  • 30. >’-§- ;__ Q __m ,,, K ‘H X = '3? Y : i___._"' . e- ' (£3-0:’ )1' 1' ‘M.-‘Q ii. = _ _¢.__ ________ @ 1 >7)‘ (e.“+é’)" | Nwu Q to-A-'2' 3 ii - ._l___ - €? D‘, L‘+2§ b§» _ Q’ -£7‘ _ Qt.‘-#2) New -Li}; = 3w1'Qé;'»>) _ a - DA (an-9:’) v __ '* "-L Q - --——-'-" I: tQt‘--2) 11¢‘: b‘§ -_' - K e _ M, wm‘ 'Q"""‘ ® k , 3% is . **7"> ”‘°z‘* Exercise 2.5: Page 30/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 30/51 - Avaiilable at www.mathcity.org
  • 31. Q__1' §u,~» = .w.i~=_._:3)I) g? G£ww A‘ Qb5)"‘&“£!:st6-~> §(*,_,) = 1..(¢.»§-)-1..u~~>> ----' -.;,.@ >.~x,=.u., ->-1~-*' ’~ 5 ,,zx--L---'5 % - 1%)" N’ 1 2 -ii“ - L“ 3;: 1‘~»‘ ‘“ _°_‘i_.-_a_ 2%. bbh _ Wk“) _ ._3.-l‘~....._.L. ' Q8‘. "¢~>" A = v_x.:_----"-‘P 29-; ,___‘1.b.2.._ ,_ -—-——--—— ®nu b‘+>‘) NM» A-'-0,.® >~cb..u., w..a-t- 5 Ei = __.z~; __L_.X )9 fFf' *3 §§ : z§ 3'; 1‘-0‘ " _BiS__,>§.>.§_)aha»z .3.-2.. _.1_ 7' -7}: 1‘--3" " 13 _ 11 be-a*>‘ Exercise 2.5: Page 31/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 31/51 - Avaiilable at www.mathcity.org
  • 32. in b"£ : Q1‘; © >5 (*‘+a‘>‘ Q»-»®+ >1; 2?; M» <32 _ D55‘; (_‘L>‘)) -; )2 $_~l»- Gu-'u~ fc»,~>> = 1”-»5‘ _----CD §.'.“_.® L»-A-i-‘K 9%‘: : 351.‘ .33.. = :;;;-‘$9 35% z‘; bah ‘ 5 75:‘ +‘}1~‘o3 1 ‘J-K;--1-*) +33‘. x- La. "M; 1 ~:‘§‘>!.-.1-- ~+ ;'(--x!..~,) -___ ?.§_..M- ‘> x- 7;-9--‘|L -- "IN; .>“1.- =;_ EL ‘omx, Mk M) ) ' = 7~,~*-' § -3 . ‘ X- 5- — 33-l—-a-9.-1.‘aX +7‘-5-"L‘”3'*‘7 "" x Exercise 2.5: Page 32/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 32/51 - Avaiilable at www.mathcity.org
  • 33. ‘S _ 1- — QC‘ -vi»!-‘9rL‘ -"i-*5 'l”“3 ‘*5 ._._ 1"k+;l-x -N1?‘ k~*'Q-‘>+ 8'8’ .:_ ‘;:k5.!-~x+§+;-‘§+Xl~;) ———--6) 7*)? &-~®+© $5 ,‘§ hr. )5 Z‘: 3* qii-n--—---i__ Q2 $(‘*>‘1§ 1 sin Guy“ , '$'§“>‘9§ = §*:K‘I;Q ---""“ Q ‘>4-N-Q >w1.w.9.-, ‘-°-’*-"-'* N,bc El >1 B“;- _____....-=—-- >~>>u. 4 §-Q‘|'=)‘ 5 _ __L.__. . L. ' ‘9 i9-x‘- 5 , _.?__. 5'1’ _ .)_. ‘9 "' .---_—-II'1-1 T--.--_ Q1 -3/1 Exercise 2.5: Page 33/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 33/51 - Avaiilable at www.mathcity.org
  • 34. ‘M an (>‘-9)" um AR!‘-Q w--‘~-‘K’--*3 1L = -l-—-- ‘L : ‘ _________.® ' ~{ 1 s I 1 1 i 7‘) i-Ufa)‘ 5‘ 1 I ‘L ' |_ x73» 3‘ ‘a --‘A 1_;yi_i__;._;: 3? = _ _‘S_.___ av 5551,‘? _3lL= -L 951- M015 “K M) = g_£__-_2.>.._ } hg 5S,_‘L I = -*;~%rA) (-1.1) = - *~;S”"“' " "B‘-1L" L‘21"iL)--XL X 5 U5X91 >'"-x 1 _ .L. £ ‘$" 3 Kn‘-wC~)"‘ I ii”2 - _-L‘-111 __'___ ®~ 31$; $15 BR 1 Exercise 2.5: Page 34/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 34/51 - Avaiilable at www.mathcity.org
  • 35. Q.§3' -$L'l>‘)) ':- -------—-M3 “L g_,§_,. i -~1C‘~~)"' G.~.3¢-A.»/ - ' §u,~>u = { 7*"? — ~@ w.~® ‘v~T-*”*> M-‘<-* ____Z-._._ %~i: = “~-% Pi N. z‘% bah .11 F - -*~ ‘I ; ] = 3 L §~~i“~3‘*‘> . , ____1l:_._._- = 51 _S""&"'3 “, ,J-;-:¢$¢‘z!-Ax K L—'¢-1‘--3") =5 F +~£{--3‘-><t X L Q--i."+3")u"' 3+3}= i'_ 3!. (+1f-§'§ " ..____§5_-;,> ;_ _§‘9--33) X 2"’& Q--uh-§"')t I_L . u*_£__‘_3,-;‘_- (H351>_(’*)'5)_ _%§--§Q'...)'-) .71.‘) " '* ” gJ.¢+3=)" ‘ (+1‘-5") t §,‘*3‘J’Il"3(~ 5‘? 5“ L - Y (-nC"-3")‘ M ya; /3% -@{*‘;*?8*3;~‘3 "'i?“ 7 ( —1 Q j i V L+w1."'+~;“)&' Exercise 2.5: Page 35/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 35/51 - Avaiilable at www.mathcity.org
  • 36. -31-; ‘%"‘3*>‘*3*>’“, - ?-@ vs ‘ 9 “’ ‘Ia ‘I 353* (--7Z‘+~j“)3 “N 44!--Q wd.<..QJl.-,_ u>-.~£- *3 25.-. 2 >» BE. = ‘IX _-__l‘ -..-~>-11$.~"" x. AK ------35 _§+1§~f'§ (-1"--*3‘-) ‘£‘""'3 (->< x‘-w 3‘-) *- “::‘:3i;€‘ K =__ —‘:L3 D” U--x-‘+j‘) h‘ Na.» ‘ - _i..12.... - ;;0,,> B17»; 3 _ A 1--‘L ' "" =1 hi U--~»'“+~j") t -. ~. ~,- *1 >1 J1 (M-x"--j’-) L- (--31") - §+‘2)- %~ "'*L“*f) ) - ‘Lx 7 ,__ _ M Z1 (-x-Q‘-n-*J"-) ‘L 1.3,1' 3 ‘L LV7“_ (+x+3 ) - (_+'$vE' — 3X(-~1§U-§1+)) mg * H (+w“C-vj‘ )5 L+*.§"-»~3‘)(+'$1‘i)_ 3xK1+x3 )‘ Y W 1.33/1. (—-1!‘-P5 i ! “> 1 Exercise 2.5: Page 36/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 36/51 - Avaiilable at www.mathcity.org
  • 37. ‘ " }"§- i+~£.‘+‘)L+'§/3:.-'*3b‘:*3:_‘:-'3L'?‘7A':~ "" ( J 1 Sm, g».»e».~,=3”*- 31$. i+~ft+3" +*'5i5'“ ’~"‘**"> k -v~3’~ )3" F~A-a ® 4, w>‘~% _ _.__.-WY “.3”; ' a~_~,2>u S~»+..-J: ~»~+“- ‘(*“*“*'3 PMjsokbivus L“?b~u,;, u,- £95 . Plygi = o(’~!-1-~ 3':-an) Q32 fiim) = $‘~'~*-i"“"‘5 %(x,'>3 = $5-*-c"‘;"‘“3 """_'_® , u).).£'* *0‘; 1 C)>'»..$$~»~‘6 '31 W B“: =_ -S~"»x~$*~‘J """'_‘® "L ‘»LNu~> M»-® ‘="*'**"** “*"‘)M ‘_bi_ : 9,,-_,.~1~C’-*>r‘*) 1") % 3,1 1 ;,;.,@,-.~> @ EL '' §2L"z. 1- O ~ 7,.» *5 .-.__.. Exercise 2.5: Page 37/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 37/51 - Avaiilable at www.mathcity.org
  • 38. Q-it fvlf) = -Q}cr‘) 539 Gvlva» W,» ‘ 2% .___ CD 5"“ EL.>~ B‘? - _'¢l-~>.c».~, T5- §j- ~:. QC»;3,}. New ‘zi >3 ?i : -_Q‘c0$‘j hi- AM--;®-® Pl~!'_L'-Ome z-,~ ' -Q Lo-A-‘- -36$» ---—-— Q) g,.,n_u., <,.,.A.+.~, .;iQ}§ {um = 34- 6.1»... Y §(*v> =- km’ {(1,3) . L(=..3~§"‘ ‘$(‘l>5‘ =' ;.“.@) ‘>¢.1=,.JJ.1 w-2..-bx lb}: , .L__..L_..__. 1* Q1-.-. R "'. x‘-v) * é ~»--—-@ Exercise 2.5: Page 38/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 38/51 - Avaiilable at www.mathcity.org
  • 39. 31.9: ‘—L~&'~.~§').~*L7"’ ‘ *2»:- £"->‘3 R L ‘L ‘I- =‘:_j*_>:_’:1“_-% K‘z~,5'L>‘ ‘LQ, 3‘.-it 7® I M‘ b¢~>‘> 1. 1 N... J--w -»Iw- -»-*'*"’ é __§__ . _L--‘_. 13 2;; ”' 1 Q34-3) 2. = -9-. N 1‘-v)" ' NO-9 w »¢~:*> 1"--)'“ - ‘UL "-''i')L *2._ ‘)1. "E? _" *‘~a‘)"? ML‘-»g®‘ E3---3-‘-§':‘=° 21‘ “J _'_______,____.. 5 Q3 §-um) = ‘MILK _-:::3»3 six-' ¢,_;,,_,_,,_,, 11» _) ,6) gum = ‘Y-ilk 16-3 { j w.® k-~1>»”*» “""1"* Exercise 2.5: Page 39/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 39/51 - Avaiilable at www.mathcity.org
  • 40. Z1‘) =&% N- ___.__ : _ - £._’x) ilk‘) +--—-$5‘ ' UL‘-i).- 10-‘O :~. _Z_‘___.;_:-_ . 7-5 k‘_)._“ + §I'_§_.. ha‘-3‘) N/5)‘ 1., ‘-:"—'-" ' w-~:>‘~w>* W/>*>‘ 1*: (-‘- 5‘) 1“+3‘-‘l"i§'-¥ ‘&")' -7-‘) Q1‘-W3‘) ~i‘~3“+1~|L‘3" _; -7-‘J 1'"+ 2‘-3 (‘xI.*>)" 3_§'_'.:._"'.'__‘.".‘2._-_ Us N» b"§ 1- -gr‘! ‘~)") vs’ = Q-15). _T_‘_-- - L1 (1‘-v3‘) Rx 5 1; _- @ 310- (If-)‘) "°"“‘ ‘MVQ w-»-V ‘9 Pi-. =5 ' 1.$.f2§ > 2'- if-3*). §- *5 (f7-5*) ' + ._.>__*~** w-»~>* t ,,d_'.1~.-‘H... .,,, ....,,. gs @155», 1“? 5,._ WW. _ ,5 ;'5% , ...., . E L §~’1(-I“ " LL“.t:':.. § 1 3 » Exercise 2.5: Page 40/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 40/51 - Avaiilable at www.mathcity.org
  • 41. _; L»eA>~f* 1% *_ (x‘-';‘§z-- '11 K1,“--5‘) £49- 1"kj+‘tXzj‘ 1% K1‘-3" X“--3“ + {Lmy § _. 3~__*£::il_ aw)‘ _>_._§_=_2z~_..... >0 ‘)"‘L-‘r gi. :11 _. (X +3‘>>1» '-‘ '2. ‘> W/J‘) 153- = = —“‘-3 “ * ”"® M‘ h~‘+>‘)‘ RAJ;-Q ® < ?L'.'5_».3’3-_; 51¢ >5 :.O (§_'g1 ,4; .§u,~>>= ~l*<@=;~>m -~§’<~=W""») '“- "="““’ “J )“r A ,. , an ‘L. ‘Ma % **‘J" 532‘ G.~'u~lw M,» = »&ww=~> - >‘*~=1“'~>‘ B-4;‘, v,,,§,_,u,, u-A-’c-“> L‘ 16% ;___;__;___,__X_,*,._i_.‘.>_.-:§’..-L A-:.W>).1> --5/1" x 3" 1 K E 1 3"--1.3"} ; ‘°‘ ‘ - l '2 | § § E Exercise 2.5: Page 41/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 41/51 - Avaiilable at www.mathcity.org
  • 42. = ~£.____‘*"' .... ..&-J--“‘ +1*>t-3' (‘IQ “‘ % ‘*>, )"*‘ = ‘>9 _,.*v>‘ = _z*;‘Yp.‘:.}(‘I>) 3}»; 1‘-Ar)" -_ __}:_'.*_L - 151374 Q‘/>3 X‘-Iv)" 1 ‘* K1“-‘>"3 _ 24125.‘. HI») §1‘~>") EL 2 X - 13142 (‘[5, *7 S“§ _ z Pi Ex)‘; >5) = sjiix--qw&w»] _~._ - -1: ‘*3: 5 SK : - ..__.7T_——-— -+31>- Y 7.5“ = - ‘_ ‘$-xx‘ =f_>';?_1c“_'l'3:- 5"- x“ )1. 8 xi. DL x*§‘L -—s——z--z-_-—-—z-—-—i- Gig. 9* §(1>~>)= 133$): *‘*“‘ “""‘ k¥x‘ %~:)L = ‘*0’ §1"§‘>) Exercise 2.5: Page 42/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 42/51 - Avaiilable at www.mathcity.org
  • 43. ‘ii: ’§ >;.(;,. m.».{- - ‘A 40 ‘3 5‘ ‘Q New §> ‘§~, Nw» G.~l.u-A Q‘! >5) : x-_-——l*51- 1--‘; Q;-»~';).7.*A-i-(*:@'=|-)")~‘} (+~>)‘“ ____ >_1?»n-w -1‘— u“ bx +'a)L {+11%-3‘_ ______________ K-W)‘- QA,,~,)_ 1‘; - MC‘-x-5‘) - -1 b*»>" L 11‘: -w 15‘ -- X7“-3- .._.._-Q--._..---¢ ,-nu- --_ _- Lx--‘a)" - L1--~a)" wk’-+ um - 3‘ 5‘-r P-‘>~ 1‘ gx-S‘) 1' _ K Z ‘x--5)" b~b)" »¢+=-24» -3‘ — 3‘-=->0» +=~‘~ L+~a)" ?_~(’“...'z.§’*- (‘A ->91" 1 (1-~>)h+~a (‘A--*2)" D Exercise 2.5: Page 43/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 43/51 - Avaiilable at www.mathcity.org
  • 44. _,,._~, £25 lkx v) '2 ___.__'.-_-—-— ;,’;’ },§.,%’_i". ;I_ s‘) (‘*3’) _€-y-Q~¢‘=~ U1 - §‘2)1 '= —---—-—‘(Q‘-’)L (“")>L n New 64¢“ "‘§1"§3 ; i3Q"~L'>‘J~‘JL 1 ?*ziw3“*1< (X _,,_,)'*- L1 ~*:)L L~M.~,)‘._{‘.. 1109-3‘) - ?‘>"- xx‘; -X‘) U*9)" géf.-L7(‘3+§_;é-17(‘>+)ji_X€_1‘2+X‘ Q+‘9)L ._; x"-PA‘: + 5"_i,_1,,__-i-—-i—? (X--‘9)L U->>’*'2 _,_______._.--.-L--~ U~>) S~:L‘Ksxd§>> 1 git.-LX~~>>'“ “Mu K%"'§‘>$L 1" ‘0'§“'S") Q-50‘ gym “A vb, >»§= 5*-»~(1‘>} /50¢-'~ £§t_‘ --315.33 :'. ° § L F Exercise 2.5: Page 44/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 44/51 - Avaiilable at www.mathcity.org
  • 45. H7. Sir §u,»> = %».~u»» ------65 >=nco>-t¢~v», -~-’~-‘<~ * 8* 2 COQQXW3-3 st —.: ‘jcL*")) §-wk = ‘j--8‘-~(1~">3-‘$ §“ = ..~3"9.~,..&~m d__4_ ® ;?a_.1_,_,_U,.’ u:.».-k- “5 S’ : cJ>(‘l‘9~* g 1'. c4nU")) 5” = 1.-$L.-L1‘a-‘* § = -~19:-4 WW3 A W NW1 39),“ {Q1 - ‘Jx §~,~> Q-§_~}q,;_..Q1~, - ~j"Q—wZ‘$:..L‘»~~@) ._ _;~,;-,5[<',,_-,.u~, + £2;/%;~L*“») 1. o = 0 ' Q1») =Lv>=~) <32 M %<‘,~,>= ha-:»1*>-~ »**-=:w»> '4 W» +<=»~> *2 %- *u:k 3'-_mL<>>'~) =i= §'>£0>~3 Exercise 2.5: Page 45/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 45/51 - Avaiilable at www.mathcity.org
  • 46. §&- Gu]M New ¥1 %(‘A>‘)) : x.LJQ:'‘(,h _‘)?.*._:(x’ ) ‘LO Z = X-___._.___ . =_. -H2: K1-.3 *1?‘-("la)-In -3? _ I 5 -7Q-"~ :1." “T-T xi) +2u'c.2.(~.~;,3 _ 5_ ‘:1 '~'- —- ~12-— +7-x'L'.'l(b; ) ‘:3‘aw’; 1 - -—--— -.~. 'n'T4:I.(by.‘, __ __3___ X x1431} 1+3 X. $49» % U‘ = "~=¢<~'1_l§*»m - §§ ‘New * 9» = 11,_._‘.___._..-3;; +’'¢:',1:¢;.-Q} 3'? (X-'5) ‘-'- (°>0 3"--x" *9 fag‘ + ii + 5.. XI bl L =-__._.l‘.._..._+.l‘l__. ___-Mai-,;3,_ 1 ‘L1. ‘9- 5+1xi- __ 3 1 - —_’-“-——- + —--Y -- 15%»? L ‘£4-3‘ X‘-v3" “’ = ~-1-' k“¥*a") ~ 1-War) 2*; @9453 v» “"=*‘"=*% New ; ,,,_ §,c~,»> - M»,-> 1» = B-In v ‘° *~£ bu») ¢(.,.§ > } , ._ E Exercise 2.5: Page 46/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 46/51 - Avaiilable at www.mathcity.org
  • 47. 2: -—k-0 §-)0 = La. M-an K") ¥xb(.,.)= - NM» <1; .9-r,_.. §'2LK’°)*'§”§'5"l bx = " ” * ( $1-D» K =_ .04.. ’~-¢> ¥~-->0 y_ »$L‘..- _- ¥.--to &) §vuL"°> Z $1: -F‘-5£0>°) 5‘: 'S,.*L°)°) ____________._.---1--v Q__‘§}_ ms bur §-_L~,»,%.3 -.—. vP+'>3¥. +%¢-(1‘a1) P-hum h¢k gx-,1 2' gray §£>‘w,?:) = X;-u-‘5§%. -- $;..(v,,1) nu 1 §* = 3x+‘)iCJ>(151) £5 = ii‘)--%¢-L~»~>+_).u +0-sk~A»2>_s] .§“ = ?-C-abb2:)-x;£'<5.-.,.~,~;a_) V ,-Igwoi -;, '1. ‘*5 '" _ Exercise 2.5: Page 47/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 47/51 - Avaiilable at www.mathcity.org
  • 48. § = c.§(~.~,e.) -x>$.:.t~:i> -151 § = ¢»u»-as-hark-£»*>->‘v*">“>" "191 l N no '§;_ = 35 -'>‘) C-wvai) -ax = ‘:[X--$¢-§*‘>?-)-‘a-1 -Q,(x51). it {H = 5?-Mwsl) ->~,‘z S.a.(1~,z) Una) -1x~,1&:..(x 5-1) gun = 3.-$.a.(1‘>-l3.xi+Q(1b?.). -IIKELQ-Ls1-xi +$2~(~;1).1a] = -15%$:..(‘1U+ ¢-.(1» 13 - <1-(um - P->>1%=~k-a1 ‘Y = Q,b~,?. -3'1*;%$.;..(~A~;1.) ~ 7L'“5"1"<;.,@~,1) ____by PM @ ~x © §'*‘ai = ¥i‘A‘) __..___w sg §Lx,'>,=L>u) = _.1i">_ ,,s~M '-ok ?.-1-ho _g, 1.. ii-§X.*~) (1*u)'; Si» G-Q-AM V '1‘? . '§h",’%’u ‘ 2.--u 54;. Lu-A-''.' X ‘$1 =‘-521?: $ < ® J } 1 Exercise 2.5: Page 48/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 48/51 - Avaiilable at www.mathcity.org
  • 49. $3,, = G135 K _ _.!._.. g1» _ 1+“, gxul = K51») 1 _ -~ %“‘>1 - (1--no)" “IMO &‘,1L_, = 13?. X, k-) K-17 K1-v ‘~31 _ _?=____ (Q-v w); Qw iu1J4~..Js N1-5 v -‘$2; Q~_‘L'1 ')"‘--".Q~) --obi‘ -.= o S_~§»- ~ LA-§(1>~>) = 3"-ni‘~9+°~“ -—-—-—» Y,‘ ~; zx-,+k¢x” gs " 7'°*x N.».§_~_._,____*:._. ch $5 Exercise 2.5: Page 49/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 49/51 - Avaiilable at www.mathcity.org
  • 50. 3 . <1» bx‘;--‘-e.~A. ' n1 A‘ '1-‘>--x‘- -Ii>-@--_i___ QQ3 1. 3 "” "3 --X. = ° Q3!» hi -§(X>">§= 37:“-31--13 -__.____@ D3-{Q--® m-A.‘:- *‘) 5;‘ -; Gx--’>x'" S» 1 ‘D’ *“""é:>..=.__2cL. <11 gt, (n-»'sx" _.7_,~) ex-+315: '7-‘D E "3‘~-*9 +5‘--cox —-o_‘ = w 9,33- Vi §U>b) = 1'“--3‘3-vjw“ -*-QX-+>) 1“ __-A< W?-® >-»~Iu».Q1-,- m.;,_.‘E:- xx») £1 = 11+‘)--0. ¥., = ‘A~-1~;--> “~ é:»_. = _ .11. A1 g., .. ’-‘**‘>f*!“.. _~u- ‘ 1+1‘) +> ____m_._____-._ 4 ! s i Exercise 2.5: Page 50/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 50/51 - Avaiilable at www.mathcity.org
  • 51. @ Q-w-1; +93»; -Lu s_._w. ‘A S» Na» Lil §@A>“>) = ‘E-'1§ --$~'~'*‘) *-"Q uw-® >-**'~’~°-» “"’*""”““’ 11-+5 = '2.‘A‘j --<‘»‘o <;2=__i=L_ 61 9» L rx+b Q12... : -" An 1->~>~ 0»; E-nan ‘Q C-""L TYl»~Ju> T» “*3-3""°$ “Q“°‘L _?_,_,-_-Q-@—@'_"' 1 1- Exercise 2.5: Page 51/51 - Avaiilable at www.mathcity.org Notes of Chapter 02: Calculus with Analytic Geometry by Ilmi Kitab Khana, Lahore. Exercise 2.5: Page 51/51 - Avaiilable at www.mathcity.org