ejercicios resueltos

c

  




   |

{
     |

{  

¦

   
 
 
     

             
 
   
        
      
 
   
 
 
    ¦
        
  
           
     
    

       
 
 


{ 

        

  ¦!"#$#%#&$ '


 
 
 


 

      (    
 
(

        
     (
  
        
 
(
  


 
)"   **+

 "  **",   
 {  ¦    
  



  - +{ !#  



   .
      

 

    
   


 
 / 
 


  
 
   
 





'






 
  
   
       
 
 
 
 
 
'
 ( 

   
       

     
 

 )" *0 + 
 
   (
  
 

 / 
 


 "  *0  ( 



  

|
| |

c

  




   |





"  *0  ( 



 |

|||||||

|

"  *0  ( 



   12 3% | + {  - '
 
     

  
  
  
  
  



    
 /       
 -
      ( 

   
 
     
  

 
     
   
   
    
      
         

 
  
    ,      
   
 
  
    '

    

  

     
 
)
 
+ 
    
 ( 

           
 
    
  !  
 ( 


 
 ( 

          ( , )" *4+'

 
 


 
 



 
-  "#!  
  
   

        

  
   
  
 
  
   
 
 
  $ !¦         
  
    
  /  
 
  
   


 
    
 .
 

  
 
 
  $ ! 
  
 
 
 


 
   
 

   
             /    
   
 
    
 


 
  " %!      
 

   
 
 
 
       

.    

 

 ,
 

)" *4*5*5+ {{  {     !!  

 ( 
 6  
 
  
        " %! 
 6    

  
   
  
 |
| |

c

  




   |

{


  |
 
|
||

 " *4%
  





  ( 



 8

 

  7   

     

 À
 

 { 

8



 

8



 





   9





" *5  
    
 


 


 " *5       
 


    '
  (           
 (  

                
  
   
  6 
 
 
   
 
 
    
         
             
   
 
 
   
 


 
    
  
  6 
 !.
 
 
  

   
 
          

   (     
  { $"     '

    

  
 
 

 
   
- |
| |

c

  




   |

 %    :'          (
  /
           

  
      

  


 
)


+  ÿ| % 
   :' 
   

 
 
     
   
 

     

; 
      
   
          ÿ| %     :' 
  
: 
  

 
 
    
 

     
  
   
 
 
 
 ,
  & $&'    å| '
  
   

 

 
   
 (        
    
               
 (   

  , !

  

   

  /        ,     
· -

       
 ( 

   )" ?+
 .
  0 <  

 ,  · -
                    ,      
  
 ) 
" ?+ .
    |
| |

c

  




   |

Y     Y· -
            

 ,  Y


   



  
    
 ,   À · -
   
       .
        
· -
                   
          À · 






 .
  À

'      î · -
  
     
  
          
  

     
 .
   A

· -
          
  
 (  

            
 .
  4B
 C       · -
       .
   B


    "   ,  (  -! !
  

      ,   /   

     


 ࡭ξࡰ ට  ࡭ ࢀ

 *


 
 
   
   
  
  
  



.  × 

Y      

0-*

DEFG

2 
 

5-*D-* ?FE*0G

Y 
   



*-*

5E

%   

*-*(*0-*

5E4FE5G



  
 
    

*-*

44E

2   
  

 
 0-*

0?E

 0C
       
 2  u ·  
   
  ( " 

.  -&

 &

,/&

Y ) 
  

+

4

5



   )
  +

0

4

5





*D

0

0

2 
 


0

4

44

   

*4

*D

0

<     )    =


¹

® 



 =

 ® 


 

   
  -

)***+|

 ¦  -
       0              
% Ó  
 
    ×    
         



   



¼   


   


 
  ¼        

 ,  - 

 ¼
 



 ¼
 

   Y     =

$

!

ea # pe "e

 

 













)**0+













)**4+

   5!%%#&$%#Y%I' Y     

 %             
     )   /+ 
 (  

 
  ),   +    ' !  
 
      
   , 
 &

ξ3

ହH ,

>

బ i ξబ jX

 

ʹሺ ͳሻሺͳ ͷሻ൯   ͹ͳʹ: Q

 ͳͳ/ Ͳ͸ͷ

  #ξÙä  ͳͳ/ Ͳ͸ͷ ͲͲͲͷ ሺͲ ͹ͷሻ  ʹ ʹ/͸: Q!Q   ܳ  ¹   ͷሺʹ ʹ/͸ሻ   ܳ  / Ͳ͹L: Q " !Q ‫ܤ‬k
  < WI!Y-#  

 

0 &00 బ బ0$ బ బ0X >YY Y ξబ jX

YY Y>

‫   ׵‬L ͹Ͳ ͹ͷሺͲ ͲͲͲͷሻ  ͳ /Ͳ/: Q!Q  ܳ  ሺͳ /Ͳ/ሻሺ ͷሻ





‫  ܳ  ׵‬͸ /ͷ

< 2 $$#$A-#  



 L ͹

0

 YZ,ሺ
Hହሻl

: Q "    Q 

 L ʹL

 L LͲ ͹ͷሺͲ ͲͲͲͷሻ  ͳ /ʹL: Q!Q  ܳ   ሺ ͷሻሺͳ /ʹLሻ  ‫׵‬ : Q " ܳ  ͸ ͸ ‫ 


ܯ‬ Q 

ହ

|
 | |

c

  




   |

*40 ¦
  
 (           
 (       

        /        
   
 
   
  

 
        
     
  0 4B
     
  
 0 ¦
- M=0 4B
 =0 =*D



=*-*=*  .=* B






 =5 B
 % -

ܳ
 ä 

 ¹ !" 

ሺʹ ͷሻሺͲ Ͳͳ͹ሻ  ¹ !"  ሺͲ ͲͲͲʹሻ! Ͳ Ͳʹͷ  ¹ !"  Ͳ Ͳͳͳ 

 Ͳ  ¹ " 


      -¹  E ൅ ݉   E ൅        
 *

!  

 ,  -9  E ൅ ʹξͳ ൅ ݉   E ൅ ʹͳ ൅ ሺͳሻ  E ൅ ʹ / 

     (  .     
-Ù  ǡ

 
Ù  ¹!9   - ® 

E ൅      ʹ E ൅ ʹ /

ʹE ൅ ʹ   E ൅ ʹ /  

ʹE @ E ൅ ʹ  @ ʹ /   Ͳ

E @ Ͳ /   Ͳm
‫  
݋‬ E @ Ͳ /  Ͳ E  Ͳ / 


   
     -

¹  E ൅     ሺͲ / ሻ ൅     Ͳ /  ൅    ͳ /  

V 


 -Ù  !ʹ

 Ͳ  ¹ !" 

® !"

 Ͳ   ሺͳ /  ሻ S  U

 Ͳ  

 Z"®&!$ !$





 Ͳ  ͳ ͳͷ Z!"  |


 | |

c

  




  

"
"!Z

¦
 ,    -  S ହU

|

 ሺʹ ͸Ͳ/ሻ
"Hହ  ͳ ʹ݉ 

E  Ͳ /ሺͳ ʹሻ  ͳ ͳ/L݉

% 



  
       

  
     ¹  E ൅ ݉   ͳ ͳ/Lሺͳ ʹሻ ൅  ሺͳሻሺͳ ʹሻ  ͳ ͹Ͳʹ ൅ ʹ Ͳͷ   ͹ͷ݉  9  E ൅ ʹ ͳ ൅ ݉   E ൅ ʹ /  ͳ ͳ/L ൅ ʹ /ሺͳ ʹሻ  ͷ ʹ݉ Ù







¹  ͹ͷ   Ͳ ͹ͳͷ݉ 9 ͷ ʹ

ܳ ʹ ͷͲ ݉   Ͳ ͸͸͸  ¹  ͹ͷ Q 

*44   
  
    
    4 4B
      
 (      
     

)=0+  0-*       =F¦   -4 !      
        
 = 5  %4 !                
          )+        
     
 C = *0 B
 !M=4 4B
  =F =0 =5 C=*0 B
  =0-*   (- ¹  E ൅ ݉   Ͳ ൅ ʹ ͷ  

9  E ൅ ʹ ݉  ൅ ͳ  Ͳ ൅ ʹͳ ൅ ሺͳ ͷሻ  Ͳ ൅ ͷ L 

ܶ  E ൅ ʹ݉  Ͳ ൅ ʹሺʹ ͷሻ  Ͳ ൅ ͷ  ܳ
 ä



 ¹ " 

ሺͲͲሻሺͲ ͲʹͲሻ 

ሺͲ ͲͲͲͲ/ሻ



 ¹ " 

 ͸  ¹ "  Ͳ ͲͲ/L 

͸͹ͳ ͳ͹  ¹ " 



Ͳ ൅ ʹ ͷ  " d  ͸͹ͳ ͳ  ሺͲ ൅ ʹ ͷ  ሻ c Ͳ ൅ ͷ L

Y
  
  (  -