Apuntes de clase. 13.

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′
 =
 + −  
→
 
 + −  
 
!
#
→
 + −  
!
→
" !
′
 =
" !
'(
→
" !
 + −  
→
$  =
=
 + −  
=!
%
 + %−
!
%
!
=!
&
=
→
% +
=
%
!% ≃ ) *
=%
′
 =%
!
=% −
*
%
$
%
$
$%
′
,
 
 
"
′
 
+
 =
′
 =
′
 =
′
 =
′
 =
′
 =
 =
 =
′
 =
−
′
  =!
 =
′
 =
 =
′
!
 =
 =
′
 =
 =−
 =
+ !%
 =
+
 =
%
−
%
  =  +  
′
 =
 =    
  =   
′
  + ′ 
 =
′
′
 =
′
′
 =
′
′
 
 
 =
    +   ′ 
  −  
% 
′

   ′  
.
$
  = % =    %
′
  = % ⋅    ⋅    ′ = % 
= %  ⋅
 ⋅ = )
&
′
 <
′
⋅

⋅
 >
′=
!
′
,
"
′
 =
0
"
/
!
′
+
/
′
+
′
 =
′′
 =
′′
&
 
 <
!
′′
 ≤
"
1!
′
 >
 =
− %− + ,
=
=− ,
′′
 =*>
=
′′
−  = −* <
=−
"
  = %−% −
′′
  = ) −%
′
$
!
!
!
& .
!"
!"
20
′′
34
′
+
 >
&
!
′′
,
3
 =
$
′′
 =%
′′
′
+
%
 + %
⇒
=
"
.
 
=
→−∞
=
=
4
=−
0 &
4
 
→
 =
=
+
 −
→∞
4
!
′′
 
 =∞
 =
+ /
→∞
+ &
=
′
!
4
 =
. '(
=
 =
4
→∞
2
−
. '40
%
%
 + %
=
%−
4
&4
/
 =−
!
2 ′′   <
→+∞
/
 <
 
2
&
+
!"
 =
−∞ % ∪ % +∞
.
'-   =
$
4
&4
.
40


=%
6 +
#
=
=
%
−%
%
+
%  −%−
 −% %
 *
4
′′
 =
→∞
&
= →∞
 −  =
→∞
&
,
4
′
 =
%
/
 
→∞
=
%
5
%
−%
=
→∞
%
−%
−
% −%
=
= →∞
"
% −*
 −% %
=
=∞
% − % +%
=
=
−%
+%
=∞
→∞
%
−%
=%
−∞  ∪ * +∞
 −*
 −% %
% +∞
7
 −%
−%
+
→∞
%
−%
→%
−∞ %
8
$
$8
8
$8
$
.
$
 = −%
4
9 −  1
&4
2 4
40
:
=−
 
'&
=
=
→∞
0
&
=−
%
− %+ *
′
4  =
= % − − %+ +
% %
− + 
−∞ −
∪
′′
4   = −%
+∞
+ %
− + % 

 
=
→∞
%
−
%
= −
=
−
%
−∞ −  ∪ 

→∞ 
  − −   =
−
 ∪  +∞
*
%
$*
$%
%
$%
$*
−
*
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