LHEO MHEO BNTFHKI HA PC@HEBIZ^ CBS@IRNHE C\IKNEIRNHE
KIRLCKIRN@P @hkpufshry Tirt
Cxik Tipcr ,Jy Rhpn`. Rhpn`. Yucstnhe+Ieswcr Yucstnhe+Ieswcr Jhhm Rnkc iffhwcb7 : lhurs NEPRZS@RNHEP 9% _rntc yhur @iebnbitc @iebnbitc Eikc ne tlc spi`c prhvnbcb he Tioc 9% :% Rlns pipcr `hesnsts `hesnsts ha RLZCC sc`tnhes& I ieb J% Pc`tnhe I,9. `irrncs 23 kirms& Pc`tnhe I,:. `irrncs 03 kirms ieb Pc`tnhe J `irrncs :4 kirms% 0% Ittckpt IFF qucstnhes ne tlns pipcr% pipcr% _rntc _rntc yhur ieswcrs ne tlc spi`cs prhvnbcb ne tlns Yucstnhe+Ieswcr Jhhm% 2% Sefcss htlcrwnsc spc`nancb& iff whrmneo kust jc `fcirfy slhwe% 3% Sefcss htlcrwnsc spc`nancb& eukcrn`if ieswcrs ieswcrs slhufb jc cntlcr cxi`t hr `hrrc`t th 0 snoenan`iet anourcs% 1% Rlc bnioriks bnioriks ne tlns pipcr irc eht ec`cssirnfy briwe th s`ifc% RHTN@P 9% Nebn`cs :% Eukjcr Pystck ,wntl `hkpfcx eukjcr. 0% Yuibritn` Cquitnhes 2% Aue`tnhes ieb Oripl
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LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
Pc`tnhe I,9. I,9. ‐ 23 kirms
x 1 y :
9% Pnkp Pnkpfn fnay ay
, x y .2
ieb cxprcss yhur ieswcr wntl nebn`cs% ,0 kirms.
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9
∗ :√n
% ,2 kirms.
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+ Tioc 9 +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
2% Phfvc tlc quibritn` quibritn` cquitnhe cquitnhe 0 x :√ ? x -0; 4 % ,0 kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% 3% Fct ι ieb κ jc rhhts ha i quibritn` cquitnhe x :- m x -3;4 % Na κ ;0 -: ι & aneb tlc vifuc ha m % ,3 kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% 1% Aneb tlc vifuc ha k na i strinolt fnec y ; k x -9 `uts i quibritn` cquitnhe x :√ 3 x -3;4 it hec ieb hefy hec phnet% ,3 kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%
+ Tioc : +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
?% Aneb tlc vifuc ha x su`l tlit :⋃0: x -9- > x√ 9;33 % ,2 kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% <% Ne tlc anourc anourc&& IJ@B ns i squirc wntl tlc pcrnkctcr `k% Na TB ;YB ; x `k ieb tlc irci ha 94
1
I
T x `k B x `k
Β JTY ns
Y
`k:% Aneb tlc vifuc ha x % ,? kirms. J
1 `k
@
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+ Tioc 0 +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
>% Na i quibritn` quibritn` cquitnhe cquitnhe 2 x :√: k x - k -0; 4 lis i rcpcitcb rcif rhht& i. aneb twh phssnjfc phssnjfc vifuc ha k % ,0 kirms. j. shfvc tlc cquitnhe wlce k6 4 % ,: kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% 94% Trhvc i quibritn` aue`tnhe
.;√ x :-94 x √04 64 ahr iff rcif x % ,3 kirms. a , x .;√
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+ Tioc 2 +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
Pc`tnhe I,:. I,:. ‐ 03 kirms
99% Fct
a , x .;: x
:
√j x - ` & wlcrc j ieb ` irc `hestiet%
i. Na j :5 < ` & prhvc tlcrc irc : rcif rhhts wlce j. _ntlhut shfvneo shfvneo
a , x .;4 % ,: kirms.
a , x .;4 & fct ι ieb κ jc rhhts ha a , x .;4 & `hestiet i quibritn`
cquitnhe su`l tlit nts rhhts irc
9 9 ι -9 ieb κ -9 & ieb cxprcss yhur ieswcr ne tcrks : :
ha j ieb ` % ,2 kirms. `. Rlc oripl oripl ha y ; a , x . ns slhwe jcfhw ieb nt pisscs tlrhuol phnets
, 4&√94 . ieb
,√:& 4 . % Aneb tlc vifuc ha j ieb ` % ,0 kirms. 2
y
: x
√0
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√9
9
:
0
√:
√2
y ; a,x. a,x.
√1
√<
√94
b. Lce`c& shfvc o , x .; 4 % ,2 kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%
+ Tioc 3 +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
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+ Tioc 1 +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
9:% Fct z ; x -n y ieb w ; x √n y jc i `hkpfcx eukjcr& wlcrc y 54 % i. Aneb Aneb z -w ne tcrk ha x ieb y % ,9 kirms. j. Plhw z w ; x : - y : % ,: kirms. `. Fct z jc i rhht ha tlc quibritn` cquitnhe i t :-j t -` ;4 % Trhvc w ns ifsh i rhht ha tlc quibritn` cquitnhe% ,2 kirms. b. Trhvc i quibritn` quibritn` cquitnhe cquitnhe t :√ 2 t -3;4 lis eh rcif rhhts% ,9 kirms. c. Lce`c& Lce`c& aneb aneb z ieb w % ,2 kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% 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+ Tioc ? +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
90% Ne tlc anourc& i rc`tieofc BCAO ns nes`rnjcb I
jy i nshs`cfcs trnieofc Β IJ@ % Na IJ ;94 94 `k B
C
`k& J@ ;91 `k ieb tlc irci ha tlc rc`tieofc ns :2 `k:% Fct B O; x `k%
J
O
91 `k
A
@
i. Plhw tlc lcnolt lcnolt ha ha tlc nshs`cfcs nshs`cfcs trnieofc trnieofc Β IJ@ ns 1 `k% ,: kirms. j. Aneb tlc vifuc ha x % ,< kirms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%% 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+ Tioc < +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Pc`tnhe J ‐ :4 kirms
92%
,: x . x ; x
I%
: , x
J%
:
@%
:
B%
: x
.
: x
x
:
x
93% Na , x -9 ., x √ 0.; x -9 & tlce x ; I%
0
J%
√9
@%
2 hr
B%
: x
√9
x
91% Aneb tlc vifuc ha y su`l tlit tlc cquifnty I%
√9
J%
√:
@%
√9 hr √:
B% Iff rcif eukjcr cxpc`t
, y √0 ., y -9 . ;: y √9 % , y -9 .
√9
9?% Na I , x √9. :- J , x √9 .-@ ≩0 x : -2 x √: & tlce J ; I%
94
J%
2
@%
:
B%
√9
+ Tioc > +
Jy LCEZ^ FCSEO
LMBPC Cxik Tipcr 9<% Na 0 x -
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
9 9 ; 1- & tlce x ; 0 x 1
I%
:
J%
9 9<
@%
:
B%
9 hr : 9<
hr √:
9>% Na i quibritn` cquitnhe 1 x :- m x -1;4 lis hec rcpcit rcif rhht& aneb m % I%
1
J%
9 1
@%
9:
B%
9 1
hr
1
:4% Aneb F%@%K% ha x :√ 2 & , x √9 ., x -: .: ieb x :√ 0 x -: % I%
x √ :
J%
, x √9 ., x √: ., x - : .
@%
, x √9 ., x √: ., x - : .:
B%
, x √9 ., x √: .: , x - : .:
+ Tioc 94 +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
: e -9
√2 e√9 ; e√9 : :⋃, : .
:
:9%
I%
0
J%
9 2
@%
:
B%
:
e
e√9
::% Pnkpfnay ∗ 23 23√ : ∗ 3 -∗ 9:3 9:3 I%
4
J%
1 ∗ 3
@%
√1 ∗ 3
B%
√∗ 3
:0% Na x 5 y & wln`l stitckcet,s. ns ,irc. truc8 N%
, x - y .:≣ 4
NN%
x
NNN%
x
√9
:
≣ y√
9
≣ y :
I% Hefy N J% Hefy N& NNN @% Hefy NN& NNN B% N& NN ieb NNN
+ Tioc 99 +
Jy LCEZ^ FCSEO
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
:2% Na I ,9 √: n .- J , :√n .; 2 √3 n & aneb I ieb J % I%
I;√9& J 9& J; 0
J%
I; 0& J ;√9
@%
I; :& J;9
B%
I;√ :& J :& J ;√9
:3% Na tlc suk ha tlc rhhts ha i quibritn` cquitnhe m x :- m 0 x -0;4 ns I%
:
J%
√:
@%
∗ :
B%
:
hr
√:
x √ :1% Phfvc tlc cquitnhe ∗ x
0
x ∗ x
;: %
hr 9
I%
0
J%
9 hr
@%
n
B%
>
>
:?% Aneb I ieb J wlce I%
I; 4& J 4& J;4
J%
I ; <& J <& J ;2
@%
I ;√:& J :& J ;√2
B%
I; :& J :& J; :
,0√ : n .√, I-: n .-3- J n ;4 %
+ Tioc 9: +
√2 & tlce m ;
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
:<% Onvce tlc oripl ha y ; a , x .; I x : - J x -@ & wln`l ha tlc ahffhwneo,s. ns ,irc. `hrrc`t8 9
y x
√2
√0
√:
√9
9
:
√9
√:
√0
√2
√3
y ; a,x. a,x.
√1
N%
I5 4
NN%
@ 64
NNN%
Β 54
I% Hefy N J% Hefy NN @% Hefy N& NNN B% Hefy NN& NNN :>% :>% Na 0 y :-1 y -9≩0 , y -k .:- e & I%
√<
J%
2
@%
√:
B%
e;
9 0
+ Tioc 90 +
0
2
3
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
y ; a , x . 04% Ssneo tlc oripl jcfhw& aneb tlc shfutnhe ha { % y ; o , x . 99
y
94 >
y ; o,x. ,x.
< ? 1 3 2
y ; a,x. a,x.
0 :
x
9
√2
√0
√:
√9 √9 √: √0 √2 √3 √1
I%
√2 hr 0
J%
√2 hr
@%
√2 ,rcpcitcb.
B%
√2 hr 0 hr
<
<
+ Tioc 92 +
9
:
0
2
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
09% Rlc irci ha i pirtn`ufir trnieofc ns 01 `k:% Na nts jisc ns ne`rciscb 2 `k ieb nts lcnolt ns bc`rciscb arhk x `k th , x √ : . % _ln`l cquitnhe `ie shfvc tlc vifuc ha x 8 ?:
I%
,
J%
,
01
@%
,
?:
B%
, ?: -2 ., x √: .;01
x
x
x
√2 ., x √: .;01
-2 ., x √: .;01 -2 ., x √: .;?:
x
0:% Na ι ieb κ jc rhhts ha x :√ 0 x √ 1;4 & wln`l hec ns tlc cquitnhe wntl rhhts κ ι 8 :
- 0 x -1; 4
I%
x
J%
:x
@%
: x
B%
x
:
:
√ ? x -: ;4
:
-? x - :;4
- 0 x √1; 4
+ Tioc 93 +
ι κ ieb
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
9
00% Onvce tlc oripl ha y ; a , x -9 . jcfhw& jcfhw& wln`l hec ns tlc tlc oripl ha y ; a , x . 8 :
94
y
< 1 2 : x
√<
√1
√2
√:
:
2
√:
I%
94
J%
y
94
<
<
1
1
2
2
:
y
: x
√2
√:
:
x
2
√<
√1
√2
√:
√:
@%
94
:
2
√:
B%
y
94
<
<
1
1
2
2
:
y
: x
√2
√:
:
2
1
x
√1
√:
√2
√:
: √:
+ Tioc 91 +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
Ieswcr 1 : 1 : : x y x y x 1√ 2 :√2 ; ; x y ; : 9% y , x y .2 x 2 y 2 :
:% i.
0u
j.
0 x
√9:; 0 , u :√ 2.; 0 , u √ : ., u -: .
:
-0 y :√1 x y √9: ;0 , x : √: x y - y :.√ 9:;0 , x √ y .:√9:; 0 , x √ y √ : ., x √ y - : .
0%
9 : n ∗ : -n ; ; ∗ ∗ :√n , ∗ :√n ., ∗ : -n . 0 0
2%
√,√ √,√? .¹∗ ,√ ,√? .:√ 2 , 0 ., 0 . ? ¹∗ 90 90 ; x; : ,0 . 1
3% Rlc suk ha rhhts7 ι - κ ;√m ieb tlc prhbu`t ha rhhts7 ι κ ;3 % Lce`c&
0- 0 ι ;√m
,n%c%&
ι ;
√m √0
.ieb ι , 0 -: ι .; 3 % Rlce
0
,
√m √0 0
.] 0- : ,
√m √0 0
.[; 3
,√m √0 .] >- : ,√m √0 .[; 23 , m -0., : m √0 .; 23 m ;
: >
hr m ;√1
1% @hesnb @hesnbcr cr x :√ 3 x -3; k x -9 & n%c%& x :√, 3- k . x - 2; 4 % i strinolt fnec y ; k x -9 `uts i quibritn` cquitnhe x :√ 3 x -3;4 it hec ieb hefy hec phnet na ieb hefy na Β ;]√, 3- k.[
:
√ 2 , 9 ., 2.; 4
Lce`c& k;√9 hr k;√> %
+ Tioc 9? +
LMBPC Cxik Tipcr ?%
:⋃0
:
x -9
: x -9
:⋃0 0
: x √:
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
- > x√ ;33 9
- 0: x√: ;33
, :⋃00-9 .;33 0
:
x √:
;9
: x √ : ; 4
x ;9 :
<%
x :
-
, 1√ x . 1
x
: :
ß: ;1 :√94
√9: x -:4 ;4
x ; : hr x ;94 ,rcgc`tcb. >% i. @hesnb @hesnbcr cr Β ;,√: k .: √2 , 2 ., k -0.; 4 & wc oct k ; 1 hr k;√ : % j. _lce k ;√ : & wc livc
2
x :-2 x -9;4 & tlce x ;√
9 :
,rcpcitcb.%
94% @hesnbcr a , x .;√ .;√ x :-94 x ;√, x :√94 x ;√, x √3.: √3 & tlcrcahrc& a , x .64 ahr 94 x √ 04;√, 94 x .√04 ;√, iff rcif x %
+ Tioc 9< +
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
99% i. Pne`c Β ;,√j. :√2 , : ., ` .;j: √<`6 4 &tlcrc irc : rcif rhhts wlce a , x .;4 % V j. Kctlhb 97 Pne`c ι - κ ; 9 :
j ` ieb ι κ ; & : :
9 :
9 2
9 :
9 :
9 :
j 2
, ι -9 .-, κ -9.; , ι - κ .- :; -: ieb
9 :
` <
j 2
, ι -9 ., κ -9.; ι κ - ,ι - κ .-9; - -9 & lce`c& x < x
:
:
j
`
j
2
<
2
√, - : . x -, - -9 .;4
√, : j -91 . x -, : j - `-< .; 4
Lce`c& i quibritn` cquitnhe ns < x :√, : j -91 . x -, : j - `-< .; 4 % Kctlhb :7 9
@hesnbcr u ; x -9 & n%c%& x ; : u √: % Puj nt neth y ; a , x . & tlce wc livc :
:
: , : u √: .
:
√j , : u √: .- `; 4
√91 u -<√ : j u -: j -` ;4
Lce`c& i quibritn` cquitnhe ns < x :√, : j -91 . x -, : j - `- < .; 4 % `. Pne`c a , x .;: x :√j x - ` & wlcrc ` ns tlc y+netcr`cpt& ` ;√94 % Puj
,√:& 4 . neth
tlc cquitnhe& wc oct j ;9 % b. Arhk pirt `.& o , x .; 4 nkpfncs o , x .;< x : √9< x 9< x ; 4 % Lce`c& x ; 4 hr x ;
+ Tioc 9> +
> 2
%
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
Jy LCEZ^ FCSEO
9:% i. Hjvnhusfy Hjvnhusf y& z - w ;: x % j. Pnknfirfy& Pnknfirfy& z w ;, x -n y ., x √n y .; x :√ n x y -n x y √ y n :; x :- y : % `. Pne`c z ; x -n y ns i rhht& wc livc
, x -n y . -j , x -n y .- ` ;4 & n%c%& :
, x √ y -j x - ` .;4 ieb :
:
: x y -jy ; 4
@hesnbcr , x √n y .:-j , x √ny .- `;, x : √ y :-j x - ` .√,:x y -j y . n ; 4-4 n ;4 & tlcrcahrc& w ns ifsh i rhht ha tlc quibritn` cquitnhe% b. Pne`c Β ;,√2 .:√ 2 , 9 ., 3.;√264 & tlc quibritn` cquitnhe t :√ 2 t -3;4 lis eh rcif rhhts% c. Pupphsc z ieb w ns tlc rhhts ha t :√ 2 t -3;4 & tlce z -w ;: x ;2 & wc oct x ; : % Ieb z w ; x : - y :; 3 & sh wc oct y ;9 % Lce`c& z ;:-n ieb w ; :√n 90% i. Jy Tytliohrcie Tytliohrcie Rlchrck& Rlchrck& wc oct tlc lcnolt ha tlc nshs`cfcs trnieofc Β IJ@ ns j. Fct I / ieb I / / jc i phnets he B C ieb O A su`l tlit I I / ⊣ B C ieb I I / / ⊣ O A rcspc`tnvcfy% Pne`c Β I I/ / J ~ Β I I / B , I%I%I% . & wc livc 1 <
;
1 √ x
B I/
B I / ;
2 , 1√ x . 0
Rlce& :]
2 , 1√ x .
x
0 :
[ x ;:2
√ 1 x ->; 4
Lce`c& x ;0 %
+ Tioc :4 +
1
`k%
LMBPC Cxik Tipcr
KIRLCKIRN@P ,@hkpufshry.
92% @ 93% @ 91% J 9?% I 9<% B 9>% @ :4% @ :9% I ::% J :0% I :2% @ :3% B :1% B :?% J :<% J :>% @ 04% I 09% @ 0:% J 00% I
+ Tioc :9 +
Jy LCEZ^ FCSEO