Matemática - Funções - Livro pdf

lucaspk 19,070 views 64 slides Sep 10, 2014
Slide 1
Slide 1 of 64
Slide 1
1
Slide 2
2
Slide 3
3
Slide 4
4
Slide 5
5
Slide 6
6
Slide 7
7
Slide 8
8
Slide 9
9
Slide 10
10
Slide 11
11
Slide 12
12
Slide 13
13
Slide 14
14
Slide 15
15
Slide 16
16
Slide 17
17
Slide 18
18
Slide 19
19
Slide 20
20
Slide 21
21
Slide 22
22
Slide 23
23
Slide 24
24
Slide 25
25
Slide 26
26
Slide 27
27
Slide 28
28
Slide 29
29
Slide 30
30
Slide 31
31
Slide 32
32
Slide 33
33
Slide 34
34
Slide 35
35
Slide 36
36
Slide 37
37
Slide 38
38
Slide 39
39
Slide 40
40
Slide 41
41
Slide 42
42
Slide 43
43
Slide 44
44
Slide 45
45
Slide 46
46
Slide 47
47
Slide 48
48
Slide 49
49
Slide 50
50
Slide 51
51
Slide 52
52
Slide 53
53
Slide 54
54
Slide 55
55
Slide 56
56
Slide 57
57
Slide 58
58
Slide 59
59
Slide 60
60
Slide 61
61
Slide 62
62
Slide 63
63
Slide 64
64

About This Presentation

Livro de caráter básico sobre o assunto de funções. Para quem quer ter um conhecimento mais aprofundado, recomendo os seguintes livros do ensino superior : James Stewart - Cálculo I ; George B. Thomas - Cálculo I ; Guidorizzi - um curso de cálculo.


Slide Content












! "
"# " $ %& $ "#
' "# " $ ("


!





"#$#
$ '
$ '
$

( '


%&'# (
")
*+
,-" . /
' " " 01 2 /
3 0. (" /
4 5 &


%)#$*#
,-" .
, 01


%&'"#





)'## #+# (
6

(
6

( /
,- )
,- .


!
/'#
7 '
% '
/## (
5 '
8. 5 '/
5 '/
' '/
,0#
" 3
019" 3
% ) 3
' 3
1
' ( -" !: 33
'% !: 7; 33
' $ !: 33
$- ,- 1

∪⊂≠∅⇔⋅∀∈≠∩
∈≠∩→⇒⋅≤≥∴∆∉∞ ∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∈≠∩→⇒⋅≤≥∴∆∉∞
∈≠∩→⇒⋅≤≥∴∆∩∉∞≅∪⊂∞≤
" #
∈≠∩→⇒⋅≤≥∴∆≥∴∉∴→∞∩≅⋅∉≤⋅≤∪⋅→⊂≠→∞⋅≤∅∈⇔≤≠∀≤⋅≠
∅≠⇔≤∈


∈≠∩→∈⇒→⋅≤≥∩∴
⋅⇒

!
" # $
$

$ %&
%' "
()*%&%'+, #
$ - " -
-
$
$ "()⇒∴≤$≠∴≤∩≤∉≠∩
()*&.'+ $ $
&
.'/ $ $
-
()*01+ " ()
*10+2 #
3
()
∆∉∞≤→≅∩∪⊂≤∞
%4+≤*∈⇔≤≠+≤5≤*∩⇔≤→+≤∉∴⇔≤∴≤∉⋅≅∴→∞∴≤∉∴⇔≤∈≤5≤∩≤∴≤≠≤5≤→
&4+≤*∈⇒⋅≠+≤5≤*≠⇔≤∈+≤∉∴⇔≤∴≤∉⋅≅∴→∞∴≤∉∴⇔≤∈≤5≤≠
"
6≤≤∴≤≥
∈≠≤∩⋅≤∪⋅→⊂≠→∞⋅≤⇒∴≤∞⋅⇒⋅∉

$ %7 (%7*≤+≤∴
&7 (&7*≥+
≤≤8≤9≤5≤∅* ⇔≤+≤:≤ ∈ ≤≤∴≤ ∈≤≥∀
" "
⇒⋅≤∴→∞≥∴≤⋅≤∪⋅→⊂≠→∞⋅≤≤≤∴≤⋅≤∪⋅→⊂≠→∞⋅≤≤
≅⋅∉≤≥∴∆≥∴∉∴→∞∩≥≤≤≤8≤≤≤5≤≤


;
"⋅≥≅∩∉≤ ⇒∴≤ ∩∆≥∴∉∴→∞∩()⋅≤ ⇒⋅≤ ∆≥⋅⇒≠∞⋅

3≤∉∴⊂∩≅≤≤≤5≤∅%⇔≤<⇔≤=∀≤∴≤≥5&0
" ≤≤8≤≥⇔
# ≤ ≥⇔≤ ∴
, ,"


$
$
3
≤≤8≤≥≤5≤∅*%⇔≤&+⇔≤*%⇔≤0+⇔≤*<⇔≤&+⇔≤*<⇔≤0+⇔≤*=⇔≤&+⇔≤*=⇔≤0+∀
;
≤≤∴≤≥≤∴≤∴"∴∞≠∩≥≤⋅≤∆≥⋅⇒≠∞⋅≤≥≤8≤≤≤*≥
≤+3≤≥≤8≤≤5*&%+*&<+*&=+*0%+*0<+*0=+
># ≤≤8≤≥≤∴≤≥≤8≤≤⇔≤∆⋅⇒∴≅⋅∉≤→⋅∞∩≥
$ )

≤≤8≤≥" ≥≤8≤≤?@
⇒∩⇒∴≤≤≤8≤≥≤5≤≥≤8≤≤≤$≠∩→⇒⋅≤≤≤∴≤≥"


! $
∪⋅→⊂≠→∞⋅≤≤≤⋅≤→-≅∴≥⋅≤⇒∴≤∆∩≥∴∉≤⋅≥⇒∴→∩⇒⋅∉
#-
∪⋅→⊂≠→∞⋅≤≥⇔≤∞∴≥∴≅⋅∉3≤≤*≤≤8≤≥+≤5≤*≤+≤8≤*≥+


" $

A ;
B" B$ %7
*%7+ &7
≅∴→∞⋅≤⇒⋅≤∆∩≥≤⋅≥⇒∴→∩⇒⋅≤*&7+

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
! ≤≤∴≤≥≤⇒⋅≤→⋅∉∉⋅
≤≤×≤≥"
" 3
!

$ %7
&7


A$
*
+/
$ )

⋅≥⇒∴→∩⇒⋅∉≤⇒⋅≤∪⋅→⊂≠→∞⋅≤≤ ≥≤*≤≤8≤≥+
$ %&
6 $ "∈≠
# ≤≤×≤≥
(C #,
∞∩⇒∩∉⇔≤⇒∩≤≅∴∉≅∩≤"⋅≥≅∩≤$≠∴≤⋅≤∆≥⋅⇒≠∞⋅
"
⇔⇒∞ ⇔≤⋅≠
→⋅≤"
; #
(C #,
#
6∩⇒⋅∉≤⋅∉≤∪⋅→⊂≠→∞⋅∉≤≤≤5≤∅.%⇔≤D⇔≤%⇔≤&⇔≤0∀≤∴
≥≤5≤∅D⇔≤%⇔≤&⇔≤0⇔≤<⇔≤1⇔≤E " ()
#,

(3


≤5≤∅* ⇔⋅∆+≤∈≤≤≤8≤≥≤:≤⋅∆≤5≤


.F 3


≤5≤∅*.%⇔≤%+⇔≤*D⇔≤D+⇔≤*%⇔≤%+⇔≤*&⇔≤<+∀
.6 " 3
.G,"
$ 6∩⇒⋅∉≤⋅∉≤∪⋅→⊂≠→∞⋅∉≤≤≤5≤∅&⇔≤0⇔≤<⇔≤1⇔≤'∀≤∴
≥≤5≤∅%⇔≤0⇔≤1⇔≤H⇔≤= " ()#,


(3


≤5≤∅* ⇔≤+≤∈≤≤≤8≤≥≤:≤≤5≤ ≤I≤%∀
.F 3


≤5≤∅*&⇔≤0+⇔≤*<⇔≤1+⇔≤*'⇔≤=+∀

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
.6 " 3
.G," 3
%
6∩⇒⋅∉≤⋅∉≤∪⋅→⊂≠→∞⋅∉≤≤≤5≤∅D⇔≤%⇔≤&⇔≤0⇔≤<⇔≤'∀≤∴
≥≤5≤∅&⇔≤1∀⇔≤ " ()#,

≤∆⋅≥
(3


≤5≤∅* ⇔≤+≤∈≤≤≤× ≥≤:≤≤J≤ ∀
.F 3


≤5≤∅*0⇔≤&+⇔≤*<⇔≤&+⇔≤*'⇔≤&+⇔≤*'⇔≤1+∀
.6 " 3
.G," 3
& ! & ()

∞⋅≤$≠∴≤∩∆≥∴∉∴→∞∩≅≤
'/
()#, 3
≤*

+≤5≤∅.%⇔≤D⇔≤%⇔≤&∀
≤*

+≤5≤∅&⇔≤<⇔≤'∀
≤*

+≤5≤∅0⇔≤<⇔≤'∀
(&
! &≤⋅≤∪⋅→⊂≠→∞⋅
" $ "K
() )

>
()A $
93
∪≅≤*

+≤5≤∪≅≤*

+≤5≤∪≅≤*

+≤5≤≥
('
!
$

()#,>"
()
⇒⋅≤'/
⇒⋅∉⇔≤∞∴≅⋅∉3
⊂∅≤*

+≤5≤∅D⇔≤%⇔≤<∀
⊂∅≤*

+≤5≤∅0⇔≤1⇔≤=∀
⊂∅≤*

+≤5≤∅&⇔≤1∀




>' ,
'
#

'
"
"(C (C
# "()$ "
>
"()$
6 $
-"
#/)
""
" ,#
"()$
6 $ $
-"
#/) #
BB
" #(
> "

"(),#
/ $ ,
(C #)
"
" ,
-
('&)
/ $


$ )
L
"()

$
-

6 )
()#,
$

-
$
/ $ ()#,

"() $ 3
%7+
* +M
&7+
- * +

(C
"(C $ ) (C
3
&) $

5
(&)
$ K()
)
5
(')#
" $
)
3L5
$)*)' '
' +' )*
(C $ ()
"
" "())3
%7+
"
&7+ " -

+

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
/)"()) "

#+
/)"() "

∪+
N"()"(C

5≤≤5≤∅∈⇒⋅≠⇒⋅∩
5≥5%&0< L 5%&
$)*)' '
' &)
;# ," (C
#,$
6 # $


#
," ()

() ,"
$ A

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
!# #
$ "()
-
#
3
"() ,"
$ $$ $
()B B
- ," ()$
, "()
O

)"()
O

)"()
O
≅∪
"()
,-)) $.
D%
∩+ ?∴→⇒⋅≤≤≤5≤∅%⇔&∀≤∴≤≥5.%D%
≤⋅8≤≥≤*≤ ⋅≥+ ,"
#+!
≥≤8≤≤≤*≥ ≤+
,"
*># $ ≤≤8⋅≥≤≠≤≥≤8≤≤+

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∩→⇒⋅≤≥∴∆⋅

D& P# (C 9


≤5≤∅* ⇔≤+ ∈≤≤≤8≤≥≤:⋅∆≤5≤

≤.≤&∀


≤5≤∅* ⇔≤+ ∈≤≤≤8≤≥≤:≤≤5≤ ≤.≤%∀
O∴∆≥∴∉∴→∞∴≤

≤∴≤

"
∩→⇒⋅≤≥∴∆⋅
D0 *2G;?+?)
⋅⋅⋅⋅⋅≤≤5≤∅&⇔≤0⇔≤<∀⇔≤≥51EH'= ()
⋅⋅⋅⋅∞≤5≤∅* ⇔≤+≤∈≤≤≤8≤≥≤:≤ ≤∴⋅∆
≤≤≤≤≤ Q ()
3
∩+ *=⇔≤<+ ⇒+≤≤*0⇔≤E+
#+ *1⇔≤<+ ∴+ *&⇔≤'+
∪+ *<⇔≤H+
∩→⇒⋅≤≥∴∆⋅


∩→⇒∉⋅⇒∞≅!⋅∪
D< ?
5.&.%D%&0< ≥≤5≤∅D⇔≤%⇔≤&∀
∴≤≤5≤∅* ⇔≤+≤∈≤≤≤8≤≥≤:≤ ≤5⋅∆

∀3
+ OM
#+ O
∩→⇒⋅≤≥∴∆⋅
""
#$%#
&'

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
D1 *Q2O/+? *+50 *9+5& )
**89++
⊂∅∴∪∩∪⇔∀
,3
∩+ % ⇒+ %'
#+ E + 0E
∪+ %&
∩→⇒⋅≤≥∴∆⋅
8()
*⋅∉+∅',#⋅∅-∴%∅#⋅→'⋅'.'∅'∉/#0⋅→'⋅≤⋅∩1
2/3##- %#'
∈≠∩→∩ ⇒⋅
⋅4⋅)

)
∩→⇒∉⋅⇒∞≅∪⊂2
DE *Q2QRG+
" "() 5≤5≤*∈⇒⋅≠⇒⋅∩⇒⋅→+
∴≅≤65*ST+U
∩+ LL⇔≤LLL≤∴≤L;
#+ L;≤∴≤;
∪+ L⇔≤LL≤∴≤;
⇒+ L≤∴≤L;
+ LL; ;
∩→⇒⋅≤≥∴∆⋅
⊂⋅4⋅78∉93#"⋅⊂⊂⋅∉3#⋅4⋅78∉93#⇒⋅:#%0⋅∅/'#,,'0;
:#∉→'∉/'0⋅'∅⋅6"⋅⊂⊂⊂⋅∉3#⋅4⋅78∉93#⇒⋅:#%0⋅⋅∉3#⋅/'∅
∩#,,'0:#∉→'∉/'⋅'∅⋅6"⋅⊂<⋅4⋅78∉93#"⋅<⋅∉3#⋅4⋅78∉93#⇒
:#%0⋅⋅'⋅⇔/=#,,'0:#'/'0'6'∅⋅∉3#⋅/'∅
∩#,,'0:#∉→'∉/'⋅'∅⋅61
∩→⇒∉⋅⇒∞≅∪⊂
DH *Q2RG+6"#-
$ ," "()
5≤7* +V∈⇔⋅≠W3




∈≠∩→⇒⋅≤≥∴∆∉∞ !

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
*≤∞≠⇒∞⇔∩)≤A

"()

L> $
$
A
&
LL> $

A &
LLL ( ,$


73≤≤→≤∪≅≤∪⋅≅≤≤5≤7* +
;
#
! ≤≤5≤∅D⇔≤%⇔≤&⇔≤0⇔≤1∀
∴≤≥5D%&0<1EH'; "
"≠→()⋅≤7≤⇒∴≤≤≤∴≅≤≥≤∪⋅≅≤7* +≤5≤ I%P
≤⇔≤≥∴∆≥∴∉∴→∞∩⇒⋅≤∆⋅≥
# (7* +⇔
" (C
,
∞∩⇒∩≤∆⋅≥≤
7!⋅≤⋅→⋅≥
7 >
$
! ≤≤5≤∅.%⇔≤%⇔≤&⇔≤1∀
⋅≥5D%&0%H&<00; "
"≠→()⋅≤7≤⇒∴≤≤≤∴≅≤≥≤∪⋅≅≤7* +≤5≤

.%

.%
∆⋅≥≤7*.%+≤5≤*.%+

≤.≤%≤5≤D⇔≤⋅≠≤∉∴⊂∩⇔≤⋅≤∆∩≥≤*.%⇔≤D+≤∈≤7

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
%
≤7*%+≤5≤%

≤.≤%≤5≤D⇔≤⋅≠≤∉∴⊂∩⇔≤⋅≤∆∩≥≤*%⇔≤D+≤∈≤7
&
7*&+≤5≤&

≤.≤%≤5≤0⇔≤⋅≠≤∉∴⊂∩⇔≤⋅≤∆∩≥≤*&⇔≤0+≤∈≤7
1
7*1+≤5≤1

≤.≤%≤5≤&<⇔≤⋅≠≤∉∴⊂∩⇔≤⋅≤∆∩≥≤*1⇔≤&<+≤∈≤7
/ $
∪⋅→⊂≠→∞⋅≤≤
∪⋅→⊂≠→∞⋅≤≥L "()
"()>$ )


7!⋅≤⋅→≤"7
≤→
.≤%

/⋅≤∴∉∞≠⇒⋅≤⇒∩∉≤"≠→(C∴∉≤" $X

"()
⋅≤'+/
(C $ ≤∩
() "() ,

"() #
( ,$
K

"()7≤⇒∴≤≤∴≅≤
∪⋅≅≤7* +≤5≤&

I0# $
≠≅∩≤"() 7* +≤5≤&

I0

() "()
," )@
R ,
"
A# ,"$
( "()

$
( , C

,"$

()"

" $ )
, ()
>

,"$
$
#

()"#() "
# () $

/2 @
,"
$$
() @ #
() " ,"
/⋅∞∩≅⋅∉⇔≤∆⋅≥∞∩→∞⋅⇔≤$≠∴≤∩≤∞≥∩→∉"⋅≥≅∩()⋅
(C ,"
Y

/ ,
," "()
#
($
"() #

* +
$X
$
,""()
R )
()
,""()#
∞⋅∉≤∆∩≥∩≤→⋅∉≤⇒∩≥≤∩≤→⋅()⋅≤ $ ,
," " "()




;
! "() 7* +5& .%
;# "
(7* +
#
P
# ,"
K"()7* +

," "
()
;# ,"
! "()7* + "
5VW 1
&) (),"
"() 5VW5
5V"W
('3 ()
,""() 5VW

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
⊂∅≤5≤V∩⇒⋅→W

>*+

> "()$
#
"() # (),"
Q"()
3
≤)≤∩≤"≠→()⋅≤7* +

,,∀

≤∴≤∀




∈-∈∀

.∀

/∈-∈.∀

/


≤J≤

≤⇒≤7*

+≤J≤7*

+
≤)≤"≠→()⋅≤7* +⇔≤→≠≅

,,∀

≤∴≤∀




∈-∈∀

.∀

/∈0∈.∀

/


≤<≤

≤⇒≤7*

+≤Z≤7*

+
≤)≤∩≤"≠→()⋅≤7* +⇔≤→≠≅

,,∀

≤∴≤∀




∈-∈∀

.∀

/∈1∈.∀

/

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
,-)) $.
D% *Q?2?+>- ?⋅⇒⋅≤∉∩∆∩∞⋅≤$≠∴
( ,
:
"@3
∈≠∩
→∩ ⇒⋅

==
+∈≠
-
&H&U
∩→⇒⋅≤≥∴∆⋅
∈≠∩→⇒∩
⋅∩→⇒∩ ∩≤

≥∴==
⋅+
=∈≠
∩→⇒∉⋅⇒∞≅∪⊂
D& *; +6 "73≤@⋅≤⇒≤@≤∆⋅≥
≤≤

∈≠

∈≠
≠∩∈≠
∩→
∈≠
=
+=⇒


≥≤
A→∞)⋅3
∩+7≤*0+≤5≤' ⇒+ 7*0+≤5≤%E
#+7*0+≤5≤= ∴+ 7*0+≤5≤0&
∪+7*0+≤5≤%&
∩→⇒⋅≤≥∴∆⋅
A, ⇒7>
≥≠∴⋅
⋅ ⇒7


A, ⇒7>
≥≠∆⋅
⋅ ⇒7


A, ⇒7>
≥≠≤⋅
⋅ ⇒7

)
∩→⇒∉⋅⇒∞≅∪⋅≅
D0 *! O[+? 73≤≤⇒≤
"() " )
7* ≤.≤%+≤5≤

) 7*0+3
∩+ D
#+ %
∪+ E
⇒+ %1
+ E<
∩→⇒⋅≤≥∴∆⋅
A,.8.,7'B'#0/', #8 1
00%7

)
∩→⇒∉⋅⇒∞≅∪⋅2
D< *Q2RG+Q"()73≤≤→≤$
7*1 +≤5≤17* +-
?∴≤7*&1+5H1 ) 7*%+3
∩+ 0 ⇒+≤≤≤&1
#+ 1 ∴+≤≤≤<1
∪+ %1
∩→⇒⋅≤≥∴∆⋅
CD'#;0' B'!
7(7⇒ 7(7
E071
F#&#⇒
(7⇒7
CD'#;0' B'!
7(7⇒771F#&#!
(7⇒7
∩→⇒∉⋅⇒∞≅∪⋅≤
D1*Q2RG+6,"-$
"()
∈≠ ∈∈≤≤∈≠ ∩∈≠ ≤∴
∈≠ ∈∈≤<∈≠ ∩∈≠ →∈
∩+
#+

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∪+
⇒+
+
∩→⇒⋅≤≥∴∆⋅
∩+∈≠∩→⇒⋅∩≤=∈ <<∈≠
#+∈≠∩→=∈ ≤≤∈≠≠∈≠
∪+ !⋅≥≥∴∞∩
+ /)"()
+ /)"()
∩→⇒∉⋅⇒∞≅∪⋅∪
DE *R\ ?+>,"#
"() " ≤∆⋅≥≤≤5≤7* +
> 7*&+≤I≤7*7*.1++3
∩+ .& ⇒+≤≤%
#+ .% ∴+≤≤≤&
∪+ D
∩→⇒⋅≤≥∴∆⋅
≅#⋅&,-7%∩#⇒⋅/'∅#0!
7
777
7
F#&#!7>77>
∩→⇒∉⋅⇒∞≅∪⋅∪

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞

"() ≤∴≅≤⇔≤⋅≠≤∉∴⊂∩⇔≤∪⋅≅
-
#-
, , ()
($ "B()B

( )
"()
∈≠ ≠∈≠ ∈ ≠=− ∩- D)
7* +)"()
$ K7* +
"()
-
$
() /
# #
"≠→()⋅≤7* +≤⋅≤∪⋅→⊂≠→∞⋅≤≤5≤∅ ≤∈≤O≤:≤ ≤≥%

"()#$
(C ()
6 "
(C
() )
%7+
y fx fx n N
n=≥∈∈≠ ∈≠ ∈
→∈≠
&7+y
fx
fx=⇒≠
]
^
_`
_`
;
() "()

6 "
(C
%7+7* +≤5≤0

≤I≤H ≤.≤'
≤5≤O
&7+7* +≤5≤
∈−∈
≤.≤H≤≥ D≤⇒≤ ≤≥≤H
≤5≤∅ ≤∈≤O≤:≤ ≤≥≤H∀
07+≤7* +≤5≤∈+∈

≤5≤O

6 $
$$

<7+≤7* +≤5≤

≠∈+
≤I≤'≤Z≤D≤⇒≤ ≤Z≤.'
≤5≤∅ ≤∈≤O≤:≤ ≤Z≤.'∀
17+≤7* +≤5≤






≤.≤1≤≥≤D≤⇒≤ ≤≥≤1
≤.≤'≤≠≤D≤⇒≤ ≤≠≤'
≤5≤∅ ≤∈≤O≤:≤ ≤≥≤1≤∴≤ ≤≠≤'∀
(
" "()
$ $
∉∴→∞∴→(∩≤7* +
# $
(C (7* +

!# () #
$ ,
-
,-)) $.
D% 6 "(C
#
∩+7* +≤5≤0

≤I≤E ≤I≤'
#+7* +≤5≤

∈≠G−
∪+7* +≤5≤∈+∈
⇒+7* +≤5≤∈≠

∈+
+7* +≤5≤

≠∩

∈+
∩→⇒⋅≤≥∴∆⋅

)≠⇒⋅∴⋅≠⇒
>≥⇒∴⋅≥⇒∈≠∈∈≥∈
'B'#0#0',B,H8'#,%#'B'
0',⋅∅∈%#,⋅#8⋅%&8∈.⋅∈⋅D',#⋅:∈,∈⋅,∈$D'0⋅→'⋅$∉→%∩'⋅⇔
'⇔ I'∅#0⋅8∅∈⋅,∈%D⋅∩#∅⋅$∉→%∩'⋅:∈,⋅∉#⋅→'∉#∅%∉∈;
→#,⇒⋅∈00%∅!

∈≠∩→⇒⋅≤≥∴∆∉∞

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
>J⇒⋅⋅∴⋅J⋅∈
K
L
xR/x–
5
7
∈>






D& *! " .O+
?∴≤fx
xx
xx
∈≠=





"() ≅⋅∴≅
⇔≤∴→∞)⋅≤3
∩+∈≠∩G≠G∈≠ →
#+∈≠ ∩∈≠∈ ∈∈≠ ≠±→⇒⋅
∪+∈≠ ∈≠∩∈≠ ∈ ∈∈<>→≠≤≥∴
⇒+∈≠ ∈≠∩∈≠∈ ∈∈> <≠∈≠
+∈≠ ∩→ ⇒xR x x∈<< > → →⇒⋅
∩→⇒⋅≤≥∴∆⋅
G∈G≠

∈⋅ ⇒ ∈≠∈∩→⇒⋅

⋅≠
∈∈


' ∈∈≠ ∩


∈≠≠' ∈∈≠±
∩→⇒∉⋅⇒∞≅!⋅≥
D0> "()
∩∈∈=++ ∈3
∩+∈≠∩ → abxRx∈≥ c
#+∈≠∩ → ⇒⋅≤ dxRx∈≠
∪+∈≠R∩
⇒+∈≠∩ → abG≠G∈> c
∩→⇒⋅≤≥∴∆⋅
∈∈ ∈⇒≥
x4 x 0 x – 4+⇒+≥⇒≥∈

∈≠∩→ ⇒⋅→≤≥∈≥
∩→⇒∉⋅⇒∞≅!⋅≤
D< *Q!.?+
"()3
fxx∈≠ ∩→

→ ∩⇒⋅

U
∩→⇒⋅≤≥∴∆⋅
→≠≠→→⇒ ⋅


E8./%:.%##0#%0',#0:#,
(x–1)0
3 2

F'∅≠,∈∉→#⋅H8'⋅H8∈.H8',⋅∉+∅',#⋅,'∈.⋅'.'B∈→#⋅∈#
H8∈→,∈→#⋅4⋅:#0%/%B#⋅#8⋅∉8.#⇒⋅0M⋅/'∅#0⋅8∅∈⋅#:93#!
G∈≠N

=
G∈

=
G∈=

" # " # $



!
"(C )
" $X R ,
$
"

A"(C )"(C


.2)7* +5O $ O"()

.5O5O 5O
.3"
()," "()
$
O
; ," 3

.2)7* +5 $

.5O5O 5O
.3"
()," "()
# $


/
.2)7* +5 I" D
.5O5O 5O

≅⋅∪⊂∅⇔∀∴∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
.≤3"
A ∈ZD
! 7* +≤5≤& .%
A ∈≤J≤D
! 7* +≤5≤.≤ I%
()," "()%7
∈≤Z≤D≤∴≤≠≅∩
≥∴∞∩≤⇒∴∪≥∴∉∪∴→∞∴≤∆∩≥∩≤JD
.≤*4 "() $
," #
"()
$ #"
7* +5D/"()%7 3
⋅⋅⋅⋅⋅⋅∈∴≤I≤≠≤5≤D≤
∈≤∈∴≤5≤.≠≤∈≤ ≤5≤.≠:∈
.≤(
∈ " ≠
"
.≤ ()
," "() ≤∴≤⋅∪⋅≥≥∴
≤5≤D⇔≤∉∴≅∆≥∴≤→⋅≤∞∴≥≅⋅
/"()%7
⇒∴≤∉∴→∞∴→(∩≤7* +≤5≤∈∴≤I≤≠B B,
" ⋅≠

?∴≅∆≥∴≤$≠∴≤≠≤≠D
,""* +#≠⇒≥⇔⇒∈.56∈/
≤∴≤⋅≤≠⇒≥⇔⇒∈.7865/∀
,,"
"()
.≤#9)
() "
()%7 ()
$
)

)," ≤≥∴∆≥∴∉∴→∞∩≥,
,
$ )
#
()
⇒∴≤≠≅∩≤"≠→()⋅≤⇒⋅≤%7
" ≥∴∞∩⇔≤$≠∴≤∆⋅⇒∴≤∉∴≥
* + *
+ "()

≅⋅∪⊂∅⇔∀∴"≥∴∉# " # $!

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
! "()7* +≤5≤∈∴≤I≤≠≤∪⋅≅≤∈≤≠≤D⇔
∴≅≤$≠∴≤

"()"* +

"()%77* +≤5≤∈∴≤I≤≠⇔≤∪⋅≅≤∈≤≠ D⇔
, ≤$≠∩→⇒⋅≤⋅
⇔≤⋅≤∞∴≥≅⋅≤≠⇔
" "()%7
#
,-)) $.
D%*R\ ?+"()⋅7 "
∆⋅≥⋅"* +≤5≤∈∴≤I≤≠?# $ "*.%+50
"*%+≤5≤%⇔≤⋅≤ "*0+3
∩+ D ⇒+≤≤.0
#+ & ≤∴+≤≤.%
∪+ .1
∩→⇒⋅≤≥∴∆⋅
∈≠∩ → ⇒ ≠∩ ⋅ →
∈∩ ∩ ⇒ ∩ ⋅ ∩
⇒≠∩≤⋅≥
∈∴ ≠∴ ≥∈≠ ∈≠
∈≠
∈≠=⇒⋅ +=
=⇒⋅+= ∩


⋅⇒
⇒= =
∴=+
≤00%∅⇒≤7>
∩→⇒∉⋅⇒∞≅∪⋅2
D& *Q2RG+? ∈⋅J≤D≤∴≤≠⋅ZD-
()," "()"* +
5≤∩ ≤I≤≠3
∩→⇒⋅≤≥∴∆⋅
##P7893#'B'0',','0'/'1
##J'B'%/',':/,#'% #:,/'
:#0%/%B%#'% # 1
∩→⇒∉⋅⇒∞≅∪⊂≤
D0*Q2L+"() ,
""* +≤5≤*0≤.≤&∈+ I&
$≠∩→⇒⋅3
∩+∈≤Z≤D ∪+ a=


#+a<


⇒+a>


∩→⇒⋅≤≥∴∆⋅
A,7 0',,'0'/''B'#0/',J
F#&#!J(
≠∈≠ ∈


<⇒<
∩→⇒∉⋅⇒∞≅!⋅≥

≅⋅∪⊂∅⇔∀∴∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
D<A#(,"
"
$ "≠→(C∴∉3
∩+ "* +≤5≤& ≤.≤%
#+ "* +≤5≤&≤.≤
∪+ "* +≤5≤&
∩→⇒⋅≤≥∴∆⋅
7 487893##Q&,8'/3#
'
##J7893#4,'0'/'1
7
7 487893##Q&,8'/3#
'1
##P7893#4','0'/'1
7
7 487893##0//''/3#
'
D1*Q"!A+? 7"() "
∆⋅≥≤∩∈

∈≠∈≠∩

⇔≤∆∩≥∩≤∞⋅⇒⋅≤ V.0M%W
? 3
∩+ O
#+−

≠∩

⇒⋅]

]∩
⇒+ −

≠∩

⇒⋅]




∪+−

≠∩

⇒⋅]

]


+
]



∩∈
≠∩

⇒⋅
∩→⇒⋅≤≥∴∆⋅
##7 4#Q&,8#&,-7%#0',%8,'/1
I#→∈B%∈⇒⋅∩#∅#⋅#⋅→#∅$∉%#⋅4⋅8∅⋅%∉/',B∈.#⋅,'∈.⋅'⋅∉3#⋅∞⇒
#⋅&,-7%∩#⋅0',-⋅8∅⋅0'&∅'∉/#⋅→'⋅,'/∈1
∈≠∩→⇒⋅ ≤→


∈≠∩∆→∆∉ ≤→









F#&#⇒⋅#⋅∩#∉R8∉/#⋅%∅∈&'∅⋅0',-⋅→'7%∉%→#⋅→'⋅


⋅∈/4⋅


1
≤00%∅!
∈≠


S
T

=

≠∩

⇒⋅
U,-7%∩#
∩→⇒∉⋅⇒∞≅∪⊂2

≅⋅∪⊂∅⇔∀∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞


"
#$
6 "()$,"
()
"() "()
O O$
S# S5

I#I
∉∴→⇒⋅≤∩≤∈≤Oe⇔≤#≤∈≤O≤∴≤∪≤∈OM,
S, M# ) "
"()
"≤3≤O≤→≤O
S5"*+5

I#I
∩≤∈≤Oe⇔≤#≤∈ O≤∴≤∪≤∈ O
?∴≤#≤≠≤D≤∴≤∪≤≠D"()
M, ,

+ "*+50

I&.1"()&7

#+ "*+5
∩∪
.EI<"()&7

+ "*+5.&

I&I%"()&7

+ "*+5.

I1"()&7
*#5D+
+ "*+5<
∩∪
I0"()&7
*5D+
"+ "*+5.

"()&7
*#5D 5D+
+ "*+5&

.0

I&.1)"()
&7
+ "*+50.1)"()&7
+ "*+5.0IE)"()&7
).
/ ,""()
&7#
,#/"(C &7
,#
*ZD+#*JD+
3

$0
"()$,
"*+5

I#I)
$ "*+5D (C $
()


I#I5D
() $()&7
" f"@
9\g



∩→⇒⋅ ∈ ≠ ≤∈
≠∩
∈≠→→


h
i

># $ 3
?∴≤∆ZD $() ,
$ )3



→≥



⇒⇒
=
−+
=
−−∆∆
?∴≤∆5D $() ,
$ )3
≥≥




==

≅⋅∪⊂∅⇔∀∴∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
?∴≤∆≤J≤D⇔≤∉∩#∴→⇒⋅≤$≠∴≤→∴∉∉∴≤∪∩∉⋅≤⇔≤∆∉≠∩
$ $())

1+) +'2) 0
L
$ "()$,)
# ,#

A→∞)⋅3
32) "&4
,#$ "
"()&7
$ ,
"$ :
#
*

+" $ ,"
()
*

I\+ *

≤.≤\+≤∩∆≥∴∉∴→∞∩≅≤∩≤≅∴∉≅∩
"*

I\+5"*

.\+?
"*+5

I#I 3
"*

I\+5*

≤I≤\+

I#*

≤I≤\+≤I≤∪≤5≤S

"*

.\+5*

≤.≤\+

I#*

≤.≤\+≤I≤∪≤5≤S

! $ S

≤5≤S

⇔≤∞∴≥∴≅⋅∉3




=


$ # *

+

*S

+" $
K,# $


S

⇔≤⋅≠≤∉∴⊂∩⇔≤S

5"*

+

S

5*

+

I#*

+≤I≤∪≤→≤S

≤5≤
−∆
∈∈

$ *S

+
S

≤5≤
−∆
≠∈
) )' ,- 5$
*DS+ ()
"()"*+5

I#I S#
" 5D
"*D+≤5≤∩≤j≤D

≤I≤#≤j≤D≤I≤∪≤→"*D+5
F,# S
*D+
6 ,4 &)
*$) +
() S)"
( #(,"
"()&7

" # " # $


7 8 '+'
> "()&7 ,
K *S

+

≅⋅∪⊂∅⇔∀∴∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
,-)) $.
D% A#(,"
"(C #
+"*+5

.EI'
#+"*+5.

I&I0
+"*+5
]



II%
∩→⇒⋅≤≥∴∆⋅
7

) >
#B%'!J
→⋅:∈,∈⋅∩%∅∈
,$D'0
∆ "

'


<4,/%∩'⋅!⋅⋅




=

=

⇒;
∈≠ ∩→∈


==− =

=

=−∈<⋅≤





/',0'93###'% #!
∞'0:#0/∈!
&'!
∈⋅∞V⋅∆⋅≥
20≠#9#
#+"*+5.

I&I0
! 35.%JD#M 3
∆5%EM

5.%

≤5≤0
; 3

≤5≤
−∈
≠∩
≤≤5≤%≤≤≤M≤≤S

≤5≤
−∆
≠≠
≤5≤<
L () S350
∩→⇒∉⋅⇒∞≅!
∈ ∞⋅V⋅∆⋅≤
20≠#9#
∪+≤∈≠ ≠ ≠∈<=++




! 35
]

∈>M 3
∆≤5≤.%≤→≤∈
; 3

≤5≤.#:&∩≤5≤.%≤≤M≤S

≤5≤

=



∩→
L () S35%
∩→⇒∉⋅⇒∞≅

∈⋅⊂∞⋅V⋅∆⋅≥ ⋅
]


20≠#9#
y
x–1
1
2
1
eixo de simetria

≅⋅∪⊂∅⇔∀∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
D&*; + > ," "()
$, "S5

.I*.%+
⋅→⇒∴≤- -
#A)
S$ "()5&3
∩+ .& ⇒+≤%
#+ .% ∴+≤&
∪+ D
∩→⇒⋅≤≥∴∆⋅
∪#∅#⋅∈⋅78∉93#⋅/'∅⋅8∅⋅+∉%∩#⋅:#∉/#⋅'∅⋅∩#∅8∅
∩#∅⋅#⋅'%∴#⋅5⇒⋅#⋅B∈.#,⋅→'⋅
∆⋅4⋅D',#1⋅≤00%∅!
∆→
≤→
((→
F#&#

>1A#,//#:,
/'#0!

(>
∩→⇒∉⋅⇒∞≅∪⊂
D0*Q2O/+? "*+5

.% )
3
∩+≤VD⇔≤∞V ⇒+≤W. ∞⇔≤%W
#+≤V.%⇔≤%W ∴+≤W. ∞⇔≤DW
∪+≤V.%⇔≤∞V
∩→⇒⋅≤≥∴∆⋅
7


20≠#9∈∉→#⋅#⋅&,-7%∩#⋅→∈⋅78∉93#⇒⋅/'∅#0!
F#&#⇒⋅∈⋅78∉93#⋅4⋅∩,'0∩'∉/'⋅:∈,∈⋅/#→#⋅∴⋅≥1
∩→⇒∉⋅⇒∞≅∪⊂≤
D< *Q2L+Q",#*+5

≤I≤&∞
@
,? ",# ("
K') %D %%
)3
+ H
#+ '
+ %1
+ &0
∩→⇒⋅≤≥∴∆⋅
A,/W#,0/'#0!
:

>(⇒::,'0'0:/#
A,/W#,0/'#0!
:

>(:,'0'0:/#
F#&# '/,'' W#,0 0',3# :,#8D%#0
:,'0'0:/#1
∩→⇒∉⋅⇒∞≅∪⊂≤
%"&
!'
>,""()&7
"*+5

I#I≠D,#A
,#
$ZD
#$JD
32) "&4
,#$ "
"()&7
$
,"
)3




=


≤≤≤≤∴≤≤≤∈


=
−∆

3 ,-'
>≤S

"
()? ,#
#S

,,
"()M
S
≠∪
,"()

≅⋅∪⊂∅⇔∀∴∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
,-)) $.
D%*! O[+>
kS5

I#I,"
"3
∩+ .% ⇒+≤ −


#+ .& ∴+≤ −


∪+−


∩→⇒⋅≤≥∴∆⋅
*&,-7%#7893#

⋅>⋅≠∴⋅>⋅∩⋅:∈00∈⋅:'.#0
:#/#0'1F#&#!



→>>→
F#&#!7


*⋅B∈.#,⋅∅$∉%∅#⋅0',-⋅




≠∈

≠ ((
F#&#!⋅

=


=
−∆


≠∩

≠→
D& *Q!?+> "()
S5

.'I%13
+ ,;5*<%+
#+ ;5*<.%+
+ ,;5*.<.%+
+ ;5*.<.%+
+ ,;5*<.%+
∩→⇒⋅≤≥∴∆⋅
@7893#

>#B.#,'4"
.#&#⇒⋅∈⋅78∉93#⋅/'∅⋅:#∉/#⋅→'⋅∅$∉%∅#!
G









≠≠≠∩





∈≠



X
X
X
X
Y

A#,/∈∉/#⇒⋅#⋅B∈.#,⋅'∴/,'∅#⋅→∈⋅78∉93#⋅4⋅:#∉/#⋅→'
$%# 1
∩→⇒∉⋅⇒∞≅∪⊂≥
D0 *2!!?+Q ,KY
E 0 #
$ # # ?
$() @# ()
"
S5

I*%.<+,
#3
∩+ 1 ⇒+≤0⇔1
#+ <⇔1 ∴+≤0
∪+ <
∩→⇒⋅≤≥∴∆⋅
*:#/#):',/''#&,-7%#.#&#!
)

> ()
)>)

∈=
−≠

?80/%/8%#
⋅∈

⋅∉∈⋅78∉93#!
∩ ∈∈∈




≅⋅∪⊂∅⇔∀∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∪∈.∩8.∈∉→#⋅∈⋅∈./8,∈⋅∅-∴%∅∈!
∈≠

→⇒⋅≤≥∴

∈∈









∩→⇒∉⋅⇒∞≅∪⊂∪
D< *2!R?!?+!
Y 'D, ,$
Y3
∩+ &DD≤≅

⇒+≤EDD≤≅

#+ &1D≤≅

∴+≤'DD≤≅

∪+ <DD≤≅

∩→⇒⋅≤≥∴∆⋅
>→ > →
(
F#&#!
(




> "
≅∪⊂








∈≠


≠∩
→⇒
∩⋅
∩⇒
?' →


F#&#!

≅∪⊂
(


∩→⇒∉⋅⇒∞≅∪⊂∪

"
#$
R)" k
"()&7
# "$#
," )
,
() "()
(C
#
,-)) $.
D% *Q?+6

X
"()3*+5!*O

≤.≤≥

+≤∴≅≤∪≅:∉⇔
! O
? $
!≤5≤%⇔'≤j≤%D

≤∴≤O≤5≤%D

3
+
X M
#+

∩→⇒⋅≤≥∴∆⋅
A,,/'#0!
∈≠ ∩→ ≠
∈≠ ∩→
∈≠ ⇒⋅≤⇒≥ ⇒≥
∈≠ ⇒⋅≤⇒≥ ⇒≥
∈≠ ⇒⋅≤∴∆∉∞




∈∈∈≠∩→
∈≠
∈≠ ∩→
∈≠
∈≠=−⇒
=
=⋅ ⋅
=⋅ ⋅
=


≠⇔ A∈,∈⋅∈


=



∩∈





∩∈









⇒⋅≤ ⇒≥


⇒≥



⇒⋅∴∆ ∉∞ ≅ ∪









=−












⇒∈



=−










=












=⋅ ⋅⋅




=






∩→⇒∉⋅⇒∞≅!V0"V0
D& *2 ?+Q# (
* +
$ # *+5&D.1


@(

6 3
+ ,#
,U
#+ ,U
+ # ,
@
,U

≅⋅∪⊂∅⇔∀∴∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∩→⇒⋅≤≥∴∆⋅
∈⇔⋅*⋅/'∅:#⋅∉#⋅H8∈.⋅#⋅#≠R'/#⋅∈/%∉&%,-⋅∈⋅∈./8,∈
∅-∴%∅∈⋅4⋅#⋅∴

1∈ ≠ ∩≠ →⇒≠ ⋅

→≥
→⇒
→∩


∈≠
∈≠=− + =

=

⋅−
=
∩→⇒∉⋅⇒∞≅∪⊂/0
≠⇔∈ ∈
≠∩
≠→→
⇒→
⇒→ ⋅

==

=


=

∩→⇒∉⋅⇒∞≅∪⊂W
≅∪⊂

@#0#.#W⇒/

>/
/#8/
∩→⇒∉⋅⇒∞≅∪⊂ ⋅0
D0 *2G;?+>
F*+5.

I0D.1
$
+ , U
#+ A $ $
%=1U
∩→⇒⋅≤≥∴∆⋅
F8,#- %#





=


=

≤≠
∩∩N

→NN
A,H8'#.8,#0'R'B'#0/',!


> ⇒

>
#8
≤∉∈.%0∈∉→#⋅#⋅&,-7%∩#⇒⋅#≠0',B∈∅#0⋅H8' ≤⋅∴⋅≤

∩→⇒∉⋅⇒∞≅∪⊂≤⋅∴⋅≤

D< *QO[+/#@
,
()
$ "()
"@3
≅*∞+≤5≤.0

≤.≤0

≤I≤%D'
, $
C
$ 3
+ " %1
#+ %1 " 0D

+ 0D " ED

+ ED " =D

+ =D " %&D

∩→⇒⋅≤≥∴∆⋅
/
≤∀


>
≤∀


(

>
/



(

>
Z8∈∉→#⋅#⋅∅∈/',%∈.⋅'0/%B',⋅/#→#⋅B#.∈/%.%D∈→#⋅/',';
∅#0⋅H8'⋅∈⋅∅∈00∈⋅→#⋅∅∈/',%∈.⇒⋅∉#⋅'0/∈→#⋅0M.%→#⋅#8
.$H8%→#⇒⋅0',-⋅%&8∈.⋅∈⋅D',#1⋅≤00%∅⇒




(

>7D'#




( >⇒ #8 11



#8



⋅⇒ /
/W#,0%8/#0
∩→⇒∉⋅⇒∞≅∪⋅2
D1 *2?+?$ 1
# %==1? ( R
A ?) "$
?)
,K%< $
"*+
"() fg
∆⋅≥≤ "*∞+≤ 5≤ .∞

≤ I≤ #∞≤ .≤ %1E⇔≤ $≠∩→⇒⋅
'JJ&D
># #
∩+ %< ∴+≤≤<&
#+ &% ⇒+≤≤01
∪+ &'

≅⋅∪⊂∅⇔∀∴"≥∴∉# " # $!

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∩→⇒⋅≤≥∴∆⋅
*⋅W#,-,%#⋅→∈⋅/'∅:',∈/8,∈⋅∅-∴%∅∈⋅∩#,,'0:#∉→'⋅[
∈≠0∩%00∈⋅→#⋅B4,/%∩'1⋅≤00%∅⇒
G

∩∩
⇒⋅

∩⇒
∈∩≤

=

⇒=

⋅−
⇒− =−
∈≠

*≤∞≠⇒∞⇔∩)∈!
DE *2?+!#
"$≠∴≤∩≤∞∴≅∆∴≥∩∞≠≥∩
,1 #
%==1"3
∩+ <D
#+ 01
∪+ 0D
⇒+ &1
+ &D
∩→⇒⋅≤≥∴∆⋅
/':',/8,- %##,,'8[0 W#,0.#&#
/
≅∪⊂
7

>( ) 1
∩→⇒∉⋅⇒∞≅∪⊂≤
DH *LP?+>
# K (C
#Y$
% $
$
,# $
()* +@&1 3
=./ (./
% 0⇔DD
& 1⇔DD
0 %⇔DD
∩+ 0⇔ED ⇒+≤ 0⇔H1
#+ 0⇔E1 ∴+≤ 0⇔'D
∪+ 0⇔HD
∩→⇒⋅≤≥∴∆⋅
∪#∅#⋅∈⋅\.%∉W∈]⋅4⋅8∅∈⋅:∈,-≠#.∈⇒⋅∈⋅78∉93#⋅H8'
,'.∈∩%#∉∈⋅∈⋅∩#∉∩'∉/,∈93#⋅∩#∅⋅#⋅/'∅:#⋅4⋅8∅∈⋅78∉93#
#QU,8!
7

> >1?'#0%H8'7"
7'7100%
∈≠∩ →
⇒∈⋅≠ ∩ ≤
≥∈→≠ ∩ ∴
++=
++=
++=∈


→∩
∞'0#.B'∉→#⋅#⋅0%0/'∅∈⇒⋅'∉∩#∉/,∈∅#0!
"'
A#,//#7

> 1A,
/'∅#0!
7(

>((
∩→⇒∉⋅⇒∞≅∪⊂
D' l #kKF
R " $
"
),$ Y
F #@#Y
/
# " $
# , -(
$ "
∞⋅≤∴≅≤$≠∴≤∩≤"⋅≥(∩≤⇒∴≤∩∞≥∩()⋅≤⇒∩≤P∴≥≥∩≤∴≤⇒∩≤F≠∩
) $ Q
@(,
()F "(
() 9$ ()
$
6 / T"(
()
$

$ Y $
∈≠
∩→

=
⋅∈



? R
P m (
Y " "(
$ P
( ,






∈→∩⇒
== =



"($ F
" ,G:*.+


F Y$
P ()
" # $
F P ># $

≅⋅∪⊂∅⇔∀∴∴"≥∴∉# " # $

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∈≠

→≠
⇒∩

=

∈≠




→→∩∩
=
−+



()R:
$ '%1


∈∈≠≠



→⇒ ⋅
−+
=≤
6
'D1
∩∪
.%E0DI'%1

≤5≤D
A$() $ "



5D=M

≤5≤%⇔%&⇒
K) $ #
∩≤≥∴∞∩≤$≠∴≤≠→∴≤⋅∉≤∪∴→∞≥⋅∉≤⇒∩≤F≠∩≤∴≤⇒∩≤P∴≥≥∩⇔
() #
# "
3D= Y$

P M%%& Y
>Y P
F
0'<DDD\M
≥∩⇒⋅∉≤∉∴≤∴→∪⋅→∞≥∩≤∩≤0<E≤DDD≤\≅≤⇒∩≤P∴≥≥∩⇔≤∴
<0DDDD\
N $
$ " K
# Y$

Y $
? " "
$
P F"
, " "
K #
>Y " ,
%⇔%&≤⇒≤.≤D⇔=⇒≤5≤D⇔&&⇒≤
≅≤'<≤DDD≤\≅
/ $ "
" ,"(
# " $
"( ()F
P
2%
># "
$ P# )
(%&
" ,
L"
"

$()$ "(
()P $ F
)@"
, U, #
"
) " "
#
∈≠∩→⇒⋅→∩≤≥ ∩≤≥ ∴∆∉∞≤≥∈≠∩→⇒⋅≤≥ ∴∆∉→∞∩≤≥ ≅∩∪⇒⊂≤⇒⋅∅≥≅∪

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞





&$
(
$(C
$



+ #
#
$
∩≤Z≤#≤⇒≤∩≤I≤∪≤Z≤#≤I≤∪
⋅≠
∩≤Z≤#≤⇒≤∩≤.≤∪≤Z≤#≤.≤∪
⋅≠
∩≤J≤#≤⇒≤∩≤I≤∪≤J≤#≤I≤∪
⋅≠
∩≤J≤#≤⇒≤∩≤.≤∪≤J≤#≤.≤∪
! $X 3#
I#Z
# #
∞∩→∞∴≤.#⇔≤∞∴≥∴≅⋅∉3
∩≤I≤#≤.≤#≤Z≤∪≤.≤#≤⇒≤∩≤Z≤∪≤.≤#
2 f()g,
$
fg-
##
-


+6 ∩∈0∈∉⇔≤∆⋅⇒∴≅⋅∉
, #
# )
3
∩≤j≤∀≤Z≤#∈j∈∀≤≤∉∴≤∩≤∪⋅→∉∞∩→∞∴≤
⋅≠
∩≤j≤∀≤J≤#≤j≤∀∈≤∉∴≤∩≤∪⋅→∉∞∩→∞∴≤
$

) "
$
$

! $X 3
j#Z
6 # #
∞∩→∞∴≤#⇔≤∞∴≥∴≅⋅∉3
∈≠





→⇒≠

>⇒ >∈≠

⋅≠
∈≠






→⇒≠

<⇒< <∈≠





($ $()
%7 "
)I#
I# , 3
≥≤ > <∈∈≠≠ ∩∈→⇒∈
> () $()
%7
() $()%7


#
O $()0I%&ZD
. fg%&&7 # 3
0Z.%&
. 6 0
3Z.<
. !()3?5∈O:Z.<
$
O $().1I%1JD
. fg%1&7 # 3
.1J.%1
. 6 .1
3Z0
. !()3?5∈O:Z0

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞



! $(C &7GK
∞∴→(∩∉3


I#IZD

I#I≥D

I#IJD


I#I≤D #)-
≠D @
2 *+5S5

I#I
$()" $
3
S≤Z≤D⇔≤S≤≥≤D⇔≤S≤J≤D⇔≤S ≤D
L "
"()"*+5S5

I#I
() "
()&7G "
(C () ,"3)
,$ ()
#$ M
) # ()
,""() S
$ )
# )
() SA
# () "
()&7# ()
,#
# $
$
! "()"*+5
∩∪
I#I
∪⋅≅≤∩≤≠D

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
2 ()
$() C $
K
#
O $()

.EI'≥D
.2 S5

.EI'
.A() "
()S
.P() $()
$SZD3
?5∈O:J&Z<

(C )
" " $
O
,-)) $.
D% O LO $(C
+0*.%+.&*%.+≥ D
#+
≠≠

+


>−




∩≠⇒


> ≥

≥ ⇒ ≥⇒⋅⋅∴⋅≥
? ∈⋅∞V⋅∴⋅≥
≠⇔
G∈

G∈

∩G


+


>−
J
J)⇒⋅∴⋅P⋅

≠≠
? ∈ ∞⋅V⋅∴⋅P⋅

≠≠

D& O LO $(C
+

.E.H≤≤D
#+

.<I<≥≤D
+

.<I<≤≤D
+ .&

I1.&ZD
∩→⇒⋅≤≥∴∆⋅
D0 *2 ?+? "3O⇒O"()
""*+5*.%+

II%∈LO>
$ "
" (3
∩+


∈<<∩ ⇒+≤∞ ≠≤&≤∴≤∞≤≠≤%
#+ .≤<≤J≤∞≤J≤< ∴+≤∞≤≠ D≤∴≤∞≤≠≤%
∪+ D ≤≤∞≤J≤'
∩→⇒⋅≤≥∴∆⋅
A,H8'70'R87893##Q&,8!/≠

⇒⋅/⋅≠1
A∈,∈⋅H8'⋅7⋅/'∉W∈⋅→8∈0⋅,∈$D'0⋅,'∈%0⋅'⋅→%0/%∉/∈0⋅→';
B'∅#0⋅/',⋅
∆ J1


((J1
/

(/(J1
/

/> J1

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
⋅/⋅≠∈'/≠
∩→⇒∉⋅⇒∞≅∪⊂
D<*Q!?O?+ > "()
∈≠ ≠∈≠=− +

∩3
∩+ V.&M≤&W ⇒+≤ −∈∈≠
#+−∈∈≠∈≠ ∴+≤−∈∈≠∈≠
∪+−∞ − ∪ +∞∈∈≠≠∈≠
∩→⇒⋅≤≥∴∆⋅
∈≠ ≠ ∩
∈≠=− +
#%93#!

>≥
∈≠∩→∈ → →⇒→∈− ≤≤ =−∈≠
∩→⇒∉⋅⇒∞≅∪⊂
)* &
! $()
$() ()
C *.%+j*I&+j*0.+ZD/
)
() ()
$ # $()07
" ()
()
$()$ ,
. 2 $
C *" +
"()3
S

5.%S

5I& S

50.
. A()
≠≅∩≤⇒∩∉≤"≠→(C∴∉≤⇒∴≤∩∪⋅≥⇒⋅≤∪⋅≅≤⋅∉≤∉∴≠∉
,"
y
1
1
x
y
2
–2
x
y
3
3
x
. O (C
$,
–2 3
y
1
y
2
P
y
3
1
. # ()-"$
$
() #
() $()3
?≤5≤
∈≠∈ ∩ →∈∈<− <<⇒⋅≤ ≥∈≠
)* +
! $ - )
$
$ $
$(C ")
C
() $(C
A
O $()


+





. 2 $
C
"()
3
S

5I% S

5.&

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
. A()
≠≅∩≤⇒∩∉≤"≠→(C∴∉≤⇒∴≤∩∪⋅≥⇒⋅≤∪⋅≅≤⋅∉≤∉∴≠∉
,"
y
1
–1
x
y
2
2
x
. O (C $

–1 2
y
1
y
2
Q ∈/
. # ()-"$
#
() $()3
∈≠ ∩ ≠=∈−≤<→⇒ ⋅∈≠
)
/ $()$ #
$ $ )$
"
)) "
'() )* +
/ $(C $(C
$
*.0+

*<.1+

*

.1IE+


$(C #
# #
3
%+P #
#
∩≤Z≤D≤≤ ⇒≤≤≤∩

≤Z≤D
∩≤5≤D≤≤≤⇒ ≤∩

≤5≤D
∩≤J≤D≤≤≤⇒≤≤∩

≤J≤D
&+P #
- )
∩ ∈≤O≤⇒≤∩
∩⊂
≤≥≤D≤≤*→≤∈≤/+

O $()3
*&.E+

j*I&+

≤≥≤D
2 S

5*&.E+

≤∴≤S

5*I&+

F #$
# # )
*&.E+

&.E
y
1
3
#
- ) A)*I&+


5.& ≠ .&
y
2
0
–2
2 $ 3
–2 3
y
1
y
2
P
?≤5≤∈≠∈ ∩ →∈∈=− ≥∈ →⇒∈≠
,-)) $.
D% O O $(C 3
+ *

.<I0+*.&+JD
#+
∈∈


≠∩


−+


+ *I%+*.&+*.&IE+≥ D
⇒+
∈≠







∩→⇒⋅≤≥∴∆⋅
∈⇔⋅C∈D'∉→#⋅∆



>'

/','#0!

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∈≠ ∩→≠⇒⋅≤≥≠ =∈ < <<∈≠
≠⇔ C∈D'∉→#⋅∆



>'


/','∅#0!
∈≠ ∩→⇒≠∩→⇒≠ =∈ ≤< >∈≠
∩⇔ C∈D'∉→#⋅∆

>
≤→
'

>)
/','∅#0!
∈≠ ∩→≠⇒⋅≤≥≠ =∈ ≤− ≤≤∈≠
→⇔
∩∈∩
∈→

∩∈∩
∈→
⇒⋅
∩∈∩∈→
∈→

∈∩
∈→



≥⇒


−≥ ⇒
−− −

≥⇒



∈≠
C∈D'∉→#⋅∆

'

/','#0!
∈≠ ∩→≠⋅⋅≤≠∈=∈ ≤ >∈≠
D& *2G;?+? ()
$()*

.1+*

.'I%&+JD
3
∩+ .%≤∈
#+



+ ∈ O:DJJ0⊂
⇒+ D≤∈
∴+ 1⇔1≤∈
∩→⇒⋅≤≥∴∆⋅
C∈D'∉→#;0'⋅#⋅H8∈→,#⋅:,#→8/#⇒⋅B'∅!

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
F#&#⇒⋅∈⋅∈./',∉∈/%B∈⋅∩#,,'/∈⋅4⋅∈⋅→1*80'R ∈⋅≤1
D0 *Q?+6 $()3*&.1+j
*<

.&1+j*

II%+JD()3
∩+
≠∈≠∈<









#+≠∈≠∈<−









∪+≠∈ ≠∈− <<+











⇒+≠∈≠∈>








→ +∅
∩→⇒⋅≤≥∴∆⋅
F#&#⇒⋅7∈D'∉→#⋅#⋅H8∈→,#⋅:,#→8/#⇒⋅/'∅#0!
∈≠∩∈


∈<







D< *R\ ?+ $()*

≤.≤<+
∞⋅∪
j
*.&+

ZD ()
$ 3
+ ≤≤&
#+ Z&
+ Z.&
+ J.&
+ J&
∩→⇒⋅≤≥∴∆⋅




(

J
















^
C∈D'∉→#⋅#⋅H8∈→,#⋅:,#→8/#⇒⋅/'∅#0!
∈≠ ∩→≠⇒=∈ >∈≠
D1 *Q!O?+ > "()
⇒∩⇒∩≤∆⋅≥≤∈≠

≠∈≠=
+



3
∩+∈≠∈ ∩∈∈>− <→⇒ ⋅∈≠
#+∈≠∈ ∩→∈∈<− ≥⇒ ⋅ ≤∈≠
∪+∈≠∈ ∩∈∈≥− ≤→⇒ ⋅∈≠
⇒+∈≠∈ ∩→∈∈≤− >⇒ ⋅ ≤∈≠
+∈≠∈ ∩∈∈≥− <→⇒ ⋅∈≠

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∩→⇒⋅≤≥∴∆⋅
∈∈
∈≠
N
+




>


>

Z8∈→,#⋅H8#∩%'∉/'!
≠≠∩≠ → ⇒⋅ ≠ ≤∈≤− >∈≠
DE *! O[+>
- J % $ "
$()






<⇒
∩+∈∈≠
#+∈









∪+∈≠ ∈∈−<<∈∩∩∈≠
⇒+≤≥≤∈<∈∈∈≠
+≠∩≠∈<∈∈∈≠
∩→⇒⋅≤≥∴∆⋅

∈∩


<

∈∩
∩N

−<
∈≠∩
≠∩

−−

<∈≠
∩∈∩
∈∩
N
∈⇒
∈∩
N
−+

<⇒
−+

<
20/8→∈∉→#⋅#⋅0%∉∈.⋅→#⋅∉8∅',∈→#,⋅'⋅→#⋅→'∉#∅%∉∈;
→#,⇒⋅/'∅#0!


>


>

C∈D'∉→#;0'⋅#⋅H8∈→,#⋅H8#∩%'∉/'⇒⋅B'∅!
## P/'#0!
≠≠∩≠ → ≠ ∈≠∩→⇒∈< >∈≠∩→ 1
DH*2G;?+ > ()
$()
≠≠
≠≠

+−



∩∩

3
∩+∈≠∈ ∩→∈⇒∈∈<− ≥ >∈ ⋅ ≤ ≥∈≠
#+∈≠∈ ∩→∈∈<− >∈ ∩ ⋅∈≠
∪+≠∩ ≠∈−<<∈∈≠∈≠
⇒+∩→ ∩∈−<≤∈∈ →∈≠
+∈≠ ∈ ∩ →∈∈−<≤ ≥∈→⇒ ≤∈≠
∩→⇒⋅≤≥∴∆⋅
GG
G≠G≠
N



+−




≤≤≤≤≤




>

%∪⇔&⋅≠⊂∅⇔∀∴"≥∴∉

"

$!

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
C∈D'∉→#;0'⋅#⋅H8∈→,#⋅H8#∩%'∉/'⇒⋅B'∅!
∈≠∩→∈⇒∈−<≤∈≠
∩→⇒∉⋅⇒∞≅∪⊂

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∈≠∩→⇒⋅≤≥∴∆!∞∴"
,$
! "(C *65O
!65O+ " ("*+5&IH
*+5

.%
; (
"*+ .&
"*.&+5&j*.&+IH50
(*+
*0+50

.%5'
3*0+5V"*.&+W5'
2≠→()⋅≤∪⋅≅∆⋅∉∞∩≤⇒∴≤∴≤ (

.& '
?@ "(C ≤∪⋅≅
"
"≠→()⋅≤
∉∞∉∞∴∴9≥⇒≠⊂∅≥
()()
"()*+"()"*+"*+.
f#", gf"
, g. ()
""
*"+*+> # $ 3
"*+5V*"*+W
' '
" ()"
()"(C ,
∩∆≥∴∉∴→∞∩⇒∩∉3
"*+5&IH *+5

≤.≤%
3
"*+5V"*+W5"*+

.%5*&IH+

.%5<

≤I
I&'I<=.%5"*+5<

I&'I<'
"(C

() ($ ()
"(C ("*+
3
"*+5"V*+W5&*+IH5&*

≤.≤%+≤I≤H≤5
5&

.&IH5"*+5&

≤I≤1
N#
() "(C $
())
≠≠≠≠≠
,-)) $.
D% *R/O[+? "*+50I% *+5&


)"V*.%+W.V"*.%+W3
∩+ .% ⇒+≤D
#+ % +
∪+ %1
∩→⇒⋅≤≥∴∆⋅
∪-.∩8.#0⋅∈8∴%.%∈,'0!
&


7>
7_&`7(>
&_7`&_`


F#&#!
7_&`&_7`
∩→⇒∉⋅⇒∞≅∪⊂≤
D& *AA?!?+? "*+5

*+5

⇔≤∴→∞)⋅
"V*&+W3
∩+ %E ⇒+≤E<
#+ %&' ∴+≤0&
∪+ %&

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∩→⇒⋅≤≥∴∆⋅
7_&`7

7

)
∩→⇒∉⋅⇒∞≅∪⊂
D0*2G;?+ ! "(C
"*+5&I% *+5

.%A)
$()"V*+W5D)3
+
#+
+ )
+
+
∩→⇒⋅≤≥∴∆⋅
7_& `
⇒⋅7⋅_∴

`


>⇒

>

≤→
1 ⇒⋅∴




⋅⇒ ^


⋅⇒ ^


F#&#⇒⋅∈0⋅,∈$D'0⋅03#⋅#:#0/∈01
∩→⇒∉⋅⇒∞≅∪⊂2
D< ! $ "*+5I& "V*+W5
&.0 )*+3
+ 1. +

#+ <.& +&.<
+ &.1
∩→⇒⋅≤≥∴∆⋅
7_& `& >
& >
⇒&
∩→⇒∉⋅⇒∞≅∪⊂∪
D1 ? *+5.H "V*+W50.%
"()"*+
∩→⇒⋅≤≥∴∆⋅
& ⇒ & >
7_& ` ⇒7_& `_& >`
7_& `& > ⇒7 >
,
8
Q"() $

#



≤≠

≤⇒"*

+≤≠ "*

+
O " "()
$ $
$ $ ,""()
-
"*+
*+)
* ," +

, "


148
Q"()# $
"


L5!6
O " "()
# $$$ $
$
#
4,""()
"*+#
*) ,"+
*+)#
*) ,"+
%8
Q"()# $

' '


)


Q"()# $
()#3
,-

''
6 #$ "(C $
)) #
A) # "() M
)
#

, " ∆

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
,-)) $.
D% > ," # "
(C O O
; "$ ))#
# ["$
∩→⇒⋅≤≥∴∆⋅
7
7
7
@3#40#,'R'/#,:#%07≠7
@3#⋅4⋅%∉R'/#,∈⇒⋅:#%0⋅/#→#0⋅#0⋅'.'∅'∉/#0⋅→#
#$%#/=##%&'#'.''/#1
∪#∅#⋅∉3#⋅4⋅%∉R'/#,∈⋅∉'∅⋅0#≠,'R'/#,∈⇒⋅∉3#⋅4
≠%R'/#,∈1
7
7
7
a0#,'R'/#,:#%0771
a⋅%∉R'/#,∈⇒⋅:#%0⋅/#→#0⋅#0⋅'.'∅'∉/#0⋅→%0/%∉/#0⋅∴
→#⋅→#∅$∉%#⋅/=∅⋅%∅∈&'∉0⋅&⋅→%0/%∉/∈0⋅→#
∩#∉/,∈→#∅$∉%#1
F#&#⇒⋅4⋅≠%R'/#,∈1
7
7
∩≠∩∩


∈≥−






7
@3#40#,'R'/#,:#%07≠ 71
@3#4%R'/#,:#%0' %0/''.''/#0'7
H8'⋅03#⋅%∅∈&'∅⋅→'⋅→#%0⋅B∈.#,'0⋅→%0/%∉/#0⋅→'⋅∴1
F#&#⇒⋅∉3#⋅4⋅≠%R'/#,∈1
D& 6 9 $
("*+5

""()
# 5∈≤O≤:≤.0≤≤≤< 9
6 (C #
∩→⇒⋅≤≥∴∆⋅
_∈ V ≤⋅∆⋅≤)`
@3#⋅4⋅≠%R'/#,∈⇒⋅:#%0⋅∉3#⋅4⋅%∉R'/#,∈1
)-
)
; "()"
9$

S5"*+
9
"()$ S
"()

, " ∉

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
$ *S+5A"()$ "
"()"
∞∩≤⇒∴≤"≤∴≤≥∴∪∴#∴≤∩≤→⋅∞∩()⋅≤"


,-:)
6 $
,$
"()"

- 6 "$
@ "()" "()
"≤"⋅≥≤'
6∴∉∉∩≤"⋅≥≅∩⇔≤→⋅∞∩≅⋅∉≤$≠∴≤⋅≤&≤⇒∩
"≠→()⋅≤
∩∈
≤∴≤$≠∴≤⋅
" "


3
6*"+≤5≤!6*"≤

+≤5≤L≅*"≤

+
!6≤*"+≤5≤6*"≤

+≤5≤L≅*"+
' .
() ($
"()"
"() A$"
()"
(" S
"() "

≤∞∴≅≤∪⋅≅⋅≤∞∩≥∴"∩≤∞⋅≅∩≥≤∩
S ("


;

6 "() "()
"*+5&.<
%7+ ;∩≅⋅∉≤()
"*+S3S5&.<
&7+ f
g
F
∈ ∈


∩∈≠

=+⇒=
+
07+ $ ,
($ "
S
# $S
" ()
>
A→∞)⋅3≤


=
+∩

<7+O K()
"()#S
∈→
−∈≠
2 ∈→


=
+


∈≠
"


+A *#+
K≤"≠→()⋅≤"⇔≤≤⋅≤∆∩≥≤*#⇔≤∩+≤∆∴≥∞∴→∪∴≥,≤≤K≤"≠→()⋅≤"≤


,
*#+ *#+
()K S5*# $
+L"
"(C $
," "() )
()K S5*"()
+

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞


+! $ "()
K
"()


3 ""
⇒∞
*+5"
⇒∞
"*+5
$ 3


+≤
∈→ ∈→


=

∈≠∩→∈≠


+≤∈∈≠ ≠ ∈∩∈≠

−−
=


,-)) $.
D% 6 "(C 3
∩+∈≠ ≠∈≠=−∩→
#+∩


∈≠∩ →=
+


⇒⋅


∩→⇒⋅≤≥∴∆⋅
∈⇔⋅∈≠≠∈≠=−∩→
∩∈∈≠=−⇒=+⇒∈≠∈ ≠




=
+
⇒=
+∈



≥→


=
+


∈≠
≠⇔⋅∩
≠∩→
∩→
=
+

∈≠∈≠−=+∈≠∩
≠∈∈≠−=+∈≠∩
⋅≤ ≤⋅−= +∈≠ ∩∈≠
∈≠
∩→ ⇒ ⋅
→≤≥

∩∈ ⋅
∈≥
⇒=
+

∩∈
∩∈→
∈→
⋅≤≥∈→

=
+

≠∈≠
∩→⇒∉⋅⇒∞≅
∈⇔⋅⋅∩∈
∈∩


=
+∈≠
≠⇔⋅∩∈
∩∈→
∈→
⋅≤≥∈→

=
+

≠∈≠
D&*! ?+
?∴⊂∩≤"3≤O≤⇒O"() ,"

$
,""() "3
∩+

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
#+
∪+
⇒+
+
∩→⇒∉⋅⇒∞≅∪⋅∪
*⋅&,-7%∩#⋅→'⋅8∅∈⋅78∉93#⋅'⋅#⋅→∈⋅08∈⋅%∉B',0∈⋅03#
0%4/,%#0','.93#[,'/
D0*2R[.?+
? "(C " O O "
"*+5&.% *+5\I"() ,
" 3
∩+
∈≠∩=


#+∈≠−=∩
∪+ \≤5≤&∞
⇒+ \≤I≤∞≤5≤D
+∈≠==


∩→⇒⋅≤≥∴∆⋅
7
>


≠∩

=
+
⋅⇒
∈∈

+
F#&#⇒⋅∈≠
∈≠&


+
=+






E0& O >/
F#&#O
]

'/
] ∩
∩→⇒∉⋅⇒∞≅∪⊂2

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
D< *Q2.O?+
?∴⊂∩≤"3≤O≤→O# "
"*+5

I%? 3O→ O# "
*+5
∈≠

→+

A→∞)⋅⇔≤∈
∈≠
≠∈≠I∈











3
∩+
∈∈

⇒+
∩ ∈
#+
]]

+
≠≠

∪+
∈∈

∩→⇒⋅≤≥∴∆⋅
∪-.∩8.#0⋅∈8∴%.%∈,'0
b ∪-.∩8.#⋅→∈⋅%∉B',0∈!
7
∞→
>

∞→
>→
∞→
>→⋅∆
∞→


∈∈

F#&#⇒⋅∈∈
∈≠⋅≥



∈∈≠∈≠ ∩ →

−= =
















=∈ ≠∩

+= +=
∈≠














∩∩


∩∩











=




=
⋅+
=
+
==
A#,/∈∉/#⇒⋅7

>⇒∈



≠≠

∩⇒











=+ =
∩→⇒∉⋅⇒∞≅∪⋅≤
D1"()" " ⋅→−∈∈≠≤∆⋅≥
"*+5


+



>
≠∩∈−∈≠
!
∩→⇒⋅≤≥∴∆⋅
≅∈⋅/'#,%∈⋅0∈≠'∅#0⋅H8'⋅#⋅∩#∉/,∈⋅→#∅$∉%#⋅→'⋅8∅∈
78∉93#⋅4⋅%&8∈.⋅∈#⋅→#∅$∉%#⋅→'⋅08∈⋅%∉B',0∈1⋅2∉/3#!
Q:00#≅'/',∅%∉∈93#⋅→∈⋅%∉B',0∈

≠∩
≠∩
≠∈ ∩∈ ≠ ∩
∩∩∈≠∈≠
=
+

⇒−=+⇒
⇒+ = −
∈∈≠ ∩≠∩ ∈
∩≠ ∩
≠∈
+= −⇒=

+∈≠
C%∉∈.∅'∉/'⋅∈≠
∈≠=

+
→∈≠
∈∩
Q:00#∈≠ ∩ → ≠
∈−
=
∈≠ ∩

5 >≠ ⇒⋅⋅∴⋅≠
IDf:
1−
⋅∈∈≠ ∩∈≠−∈ →∈≠1⋅F#&#
7∈≠ ∩ →−− ∴ =−⇒⇒∈≠
DE6"()"3O→ 9≤∪⋅≅
"*+5

.<I0 $ C #
+ 6 9$
"()" #
#+ ! 9
(C "
"$ "()" # U
∪+ P⋅≅∩→⇒⋅≤"≤→∩∉≤(C
# "()#
($ "


∩→⇒⋅≤≥∴∆⋅
∈⇔

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
A,H8'70'R0#,'R'/#,'B'#0/',
#80'R∈∈∩→∈ ⇒∈≥−∈≠ ∈
≠⇔
∞'0:'%/∈→∈0⋅∈0⋅∩#∉→%9c'0⋅→#⋅%/'∅⋅∈⇔⇒⋅:∈,∈⋅H8'⋅7⋅0'R∈
≠%R'/#,∈⋅≠∈0/∈⋅H8'⋅/∈∅≠4∅⋅0'R∈⋅%∉R'/#,∈1⋅A∈,∈⋅%00#⋅≠∈0/∈
'0∩#.W',⋅∈⋅,'&%3#⋅∩,'0∩'∉/'⋅#8⋅∈⋅,'&%3#⋅→'∩,'0∩'∉/'⇒⋅#8⋅0'R∈
∈≠∩→ ⇒∩⋅≤=∈ ≥ ⋅⋅⋅⋅#8
5≠∈∩→≠∩∈≤∈≠
7

>


>


>

∈≠→∩

=
±+
≠∈≠∩=± +
∈∈→∩

=± +
7⋅

⋅≠∩++
#8
→∈ →∩

=− +∩∈≠
.
; "()
? -
'2)
(;
! $
-
>$
- D* +
6 $ ? -
f@g≤⋅⇒∈≠⇒≥⇔⇒$
*"+A
- 0 @
0fYg K 6
$ fYg-
.< $
$ @ .<<
()$ @-
# -
R@ nn
(; '
9<' $
()
@Y$
)
# "()@
- 3
∈∈≠∩ ∩
∈ ∈ ≠→⇒⋅≤≥→∴∆ ∉∩ ∈ ≠∩ ∈
=≥
=− ≤∈


≅∪
3
nEn5EEZD
noHn5o*oH+oHJD
N# #$ 5D
nn5nn5o
) "()
⊂≠→∞⋅≤∪⋅≅≤
∈≠∩∈≥≤→→
(;
.2≤≥⇔≤≥∪∩)"*+5nn
#
@
. 6≤5≤O⇔≤!6≤5≤O≤∴≤L≅≤5≤O


.3")(),"
"()"
⇒∴≥∩(C∴∉3
%7+≤
∈≥⇒≠"*+5$ "()
*# %7$ +M
&7+JD⇒"*+5o$ "()%7
*# &7
$ +

, " !

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
!
,""()
3
,-)) $.
D%*Q2;RG+"#,"
⇒∴≤≠≅∩≤"≠→()⋅≤"3≤O≤→ O
,"
"()*+ $ *+5In"*+n3
∩+
#+
∪+
⇒+
+
∩→⇒⋅≤≥∴∆⋅
F'∅≠,∈∉→#⋅H8'⋅ =⋅0'⋅∴⋅≥'∩∩=−⋅0'
P/','#0!
& 7 0'7 ≥:,/'#&,-7%#%#
'%∴#⋅∴⇔⋅'⋅& 7 0'7 P:,/'#&,-7%#
∈≠∈%∴#⋅→#⋅'%∴#⋅∆⇔⇒⋅%0/#⋅4⇒⋅#⋅&,-7%∩#⋅→∈⋅78∉93#⋅&⋅0',-
0%∅4/,%∩#⋅→#⋅&,-7%∩#⋅→∈⋅78∉93#⋅7⋅'∅⋅,'.∈93#⋅∈#⋅'%∴#⋅∴

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∩→⇒∉⋅⇒∞≅∪⋅≠
D&!,""() "
"*+5∈∈≠
∩→⇒∉⋅⇒∞≅
A#'#0#0/,8%,#&,-7%#'7 :#,#%0:,#'00#0

?∈≠'∅#0⋅H8'⋅

≠∈≠ ∩
∩∈≠∩
∈≠
∩→
∩∈ ⇒




→→
→→
'∉/3#⋅7⋅:#→'⋅0'⋅→'7%∉%→∈⋅∩#∅#⋅8∅∈⋅78∉93#⋅⋅∈⋅→8∈0
0'∉/'∉9∈0⇒⋅#8⋅0'R∈
≥→
→∩→→
→∩→→
⇒⋅∈
≠ ∈
≠≠∩


∩≤≤
≤≤
∩8R#⋅&,-7%∩#⋅4!

A,%∅'%,#⋅7∈,'∅#0⋅#⋅&,-7%#'& ;1A,#≠/',∅#0
#&,-7%#'7 ∈≠∩→:,#'','#0###' ',$#
*≠0!⋅2∅⋅:,#≠.'∅∈0⋅0'∅'.W∈∉/'0⋅∉#,∅∈.∅'∉/'
#/,'#0#Q:,#'00#1
D0*Q2RG+? "3O→O"()
$ "*+5∈∈

∩−>," ∆⋅5"*+3
∩+
#+
∪+
⇒+

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
+
∩→⇒⋅≤≥∴∆⋅
7


7 ∈≠

∩−⋅→
∩→⇒∉⋅⇒∞≅∪⊂∪
D<!,"
"()
"*+5∈≤I≤%
∩→⇒⋅≤≥∴∆⋅
A,%'%,#7,'#0#&,-7%#'& ∈1
A,#/',#0#&,-7%#'7 & >'0.#;
∩∈∅#0⋅∩∈→∈⋅:#∉/#⋅→#⋅&,-7%∩#⋅→∈⋅78∉93#⋅&⋅8∅∈⋅8∉%→∈;
→'⋅\:∈,∈⋅∩%∅∈]1

, "

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
D1!,"
"()
"*+5≠−−∩∈
∩→⇒⋅≤≥∴∆⋅
& ∈−≠'/3#7 & #80'R:,
#/',#0#&,-7%#'7 '0.##0#0:#/#0
78∉93#⋅&⋅→8∈0⋅8∉%→∈→'0⋅:∈,∈⋅≠∈%∴#1
7_"∞`
DE *; + > ," "()
∈≠ ≠ ≠∩→=−−

⇒⋅3
∩+
#+
∪+
⇒+
+

, " !

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
'0#.893#
7 5



7 ∈∈

≠−⋅→
∈≠∩→ ∩ ⇒∩ ⋅

=−− →
DHA#(,"
"()3"*+5
∩∪
.≤<≤
∈I0
∩→⇒⋅≤≥∴∆⋅
∞'∩#,,'∉→#⋅[⋅→'7%∉%93#⋅→'⋅∈⋅/'∅#0
∈∈∩→
∩∩⇒⋅≤∩≥
∩∴∩ ⋅≤∩≥


=
−+ ≥
++ <



→∩∈

S≤∈⋅∞⋅V⋅S≤≥
D'*R\ .?+? "()"3O→≤O
"≤5≤∩∩−−≠>,"$
3
∩+
#+≤

, " !

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
∪+
⇒+
+
∩→⇒⋅≤≥∴∆⋅
∞'∩#,,','∅#0⋅∉#B∈∅'∉/'⋅[⋅→'7%∉%93#⋅→'⋅∅M→8.#1
G∈
G∈≠∩G∈
G∈≠∩G∈
−=
−≥
−+ <


∩ ⋅1⋅2∉/3#
?'⋅∴⋅≥ ⇒ ⇒
?' P
⇒ > ⇒ >
∩→⇒∉⋅⇒∞≅∪⋅≤
!* )*
.
;
" @ - 3
. L () 3@
- f@g≤⋅⇒∈≠⇒≥⇔⇒≤$≠∴
- K

. 6 "()3

∩∈≠∩
∩∈≠∩
=




∩ →
→⇒
" ()
$(C $(C
@3


+
≠≥≤$$
≠≠=⇔ =≤≤


+≠∈≠∈∩→≠∈⇒∩⋅∈=⇒ = =− ≥ ∈ ≤


+∩∈≠∈∩→≠⇒=⇒= =−


+≠∈ ≠∈∩→≠ ∈⇒∩⋅∈>⇒ > <− ≥ ∈ ≤


+≠∈ ∈≠∈ ∈≠∩ →<⇒−<< ≥ ∈ ⇒


+∩∈≠∈⋅=⋅


+




∈≠⇒∈=≠ ⋅


+≠≠

=


+≠≠≠
∈ ∈∈
==

≅∪




≤≤∆⋅⇒∴≅≤∉∴≥
" "
() @
() $(C
$(C
34
() $(C $(C $
∩∆≥∴∉∴→∞∩≥∴≅≤≠≅≤+?
⋅⇒≤
?≤,∅∩≥⋅⇒∈∩∈∞≤≥⇔≤≥∪∩∈∩≠→≤∞≤≥⇔∩→
,?6:?6

, " !

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
"
≤#
O $()∩−=∈≠
∈∈ ∈≠∈∈−= ⇒ = −=− ⇒ =−∈≠ ∩ ∈≠ →
?≤5≤∅.1M≤=∀
$
O $()∩∩+= −≠∩→
I15&.H⇒5%&⇒5%&
I15.*&.H+⇒I15.&IH⇒ 5


?≤5≤
≠ ∈
∩≠;∈





%
O $()3≠≠

∈≠∈−−=
*
6 3
*≤∞≠⇒∞⇔∩)∈?≤5≤∅.≤%⇔≤%⇔≤0⇔≤1∀
B
O $()∈≠∈≠−<
.1J&.0J1 *I0+
.&J&J' *÷&+
.%JJ<
?5∈O:.%JJ<
C
O 3∩→ ∈≠−≥
0.1≥≤%≤⇒ ≥≤&
⋅≠
0.1≤≤.≤%≤⇒ ≤≤≤


?≤5≤≠∈≠∩→≠∈≤ ≥










D
O $()3∩∩

∈−≥
*
6 3
∩→⇒∉⋅⇒∞≅∪⊂? ∈∈≠V⋅∴⋅≤#8 ≥
/ "
() @ (
$ @ )@
),

, " !

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
E
O $()
∈≠ ∈∩

→→

−++<
∈≠∩ ∈≠∩
># # 3
?∈→∈∈∩∈→∈∈⇒∈⋅∈→∈⋅∈









F
O ∈≠3
∈∈

−+− >∈≠∈

∈≠∩∈≠∩
*
*≤∞≠⇒∞⇔∩)∈?5∈∈≠:J%Z&
G
*2 ?+? - *%I+*%.∈≤+≤≥≤D≤∉∴≤∴≤∉⋅≅∴→∞∴≤∉∴3
∩+∈≤≤ %+ ≥≤%
#+ ≤ % + ≤ .≤%
∪+∈≤≥≤%

, " !

∈≠∩→⇒⋅≤⇒≥∴∆⇒∉∞
*
#9∈∀∩∞⇒≥≤D *%+
*%I+*%.+≥≤D
%.
∩∪
≥≤D
.≤%≤≤≤≤% *&+
*%+≤∩≤*&+≤≤≤≤∞∴≅⋅∉≤D≤≤≤≤≤%≤≤≤*L+
$9∈∀∩∞⇒JD *%+
*%I+*%I+≥≤≤D≤⇒*%I+

≤≥≤D
∀∈⋅∈≠∈≠∩
6∴≤*%+≤∴≤*&+⇔≤∞∴≅⋅∉JD*LL+
*L+≤≤∪≤*LL+≤≤⇒≤≤%
*≤∞≠⇒∞⇔∩)∈9
,-)) $.
D%*LP?+?# $ (C
∴$≠∩()⋅≤≠≠

∈≠−−= ) $()


≤.≤∈∴⋅I≤≠⋅5D "$ 3
∩+∈⋅5≤%≤≤∴≤⋅≠⋅≤5≤E
#+D≤≤∴≤≤≠≤≤5≤.≤E
∪+%≤≤∴≤≤.E
⇒+D≤≤∴≤≤.=
+ /) #$
∩∪
.I#5
D $()
'0#.893#
C∈D'∉→#⋅
→∈=⋅/'∅#0!


)
#8
≤00%∅ ≠∈≠ ∩ →⇒∈⋅∈→≤≥∴==−∩→ ∈≠
2/3#
#8
?3#⋅∈0⋅,∈$D'0⋅→'⋅∴

>
A#,/∈∉/#
?#
−−
=− + = ⇒ =


∩∈→∈≠
∩→
A,#8/#


∩ ∈∈=− ⋅ = ⇒ =−≠∈
∈≠∈≠
∩→⇒∉⋅⇒∞≅∪⊂
D&*Q2QRG+>"()
, ""*+5∩−−3
+ ∈ O:≥≤&∀
#+ ∈ O≤:≤.≤%≤≤ ≤≤&∀
+ ∈ O:≤ .%≥≤&∀
⇒+∈≠ ∈∈≤≤





⋅∩


+ O

∩→⇒⋅≤≥∴∆⋅
7 ∈≠∩→−−
∪#∉→%93#!∈≠≠→
∈≠≠


−−≥
−≥
≅'B'∅#0⋅/',!

≤;#8



≥⋅
∩→⇒∉⋅⇒∞≅∪⊂∪