examen muestra unam - ingenierias

30
 0 0  12  45  67  8 9       9!  6"#  $7"   % & ' (  ) * +  ), - '  ) . / %  ).  ; <=> @ABCD EF<GH<C IJKL=MMN=>< @ABCD EF<GH<C IJK LOPMMPM= =>NMO ;DQD @ABRG< OO

Upload: irugami-p-cruz

Post on 07-Apr-2018

242 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 1/30

  1 2   4 5  67 8 9

 

    9 !   6 " #   $ 7 "

  % & ' ( ) * +   ) , - '  ) . / %

  ) .

 33:

 ;@ A B C D E F < G H < C I J K L = M M N = > < @ A B C D E F < G H < C I J K L O P M M P M = = > N M O ; D Q D @ A B R G < O O

Page 2: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 2/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

&  2 7 2 3 3 1 3 5 5 2 6 3 3 2 1 2 7 2 3 7 2 3 2 2 7 1 3 1 2 3 7 7 9 9 6 3 1 2 7 3 6 3 7 ' 2 2 5 1 7

  ' 2 1 2 7 6 ( 2 1 2 2 6 2 3 2 5 2 7 2 6 2 9 ) * 7 9 5 2 1 3 6 3 7 7 9 9 2 2 7 + 7 2 1 ( 3 9 2 7 ,

  - 7 2 2 3 2 2 7 1 3 1 2 1 2 7 2 3 7 6 2 . 2 1 9 9 ) / 3 7 1 2 3 7 ' 2 7 2 9 6 2 3 3 1 2 2 1 2 2 6 2 3 "  2 5 2 7 2 6 2 9 )   6 9 3 6 ' 2 2 6 2 3 2 5 2 7 2 6 2 9 7 2 7 2 9 2 1 3 % # $ 1 2 3 7 1 3 9 3 5 3 7 5 2 6 3 7 9 9 2 2 1 3 ,

 4 : ; < = > ? @ < A C @ D < @ ; :

  - 7   3  E 6 % F

  G   7 9   3 % H  ! 3   2     9   3 7 # H  / 9   2   1 3    1 3 % $  2 1 3 3 % $  I 9   6   3 % $

  J   9   3 % $

  K 9 7     1 9 3 9   ( 2 1  7 3 6 % $

  K 9 7     1 9 3 5 2 !   9   % $

  L M  L 4 N O P Q - 7 3 7 1 2 3 7 7 5 2 9 R 6 9 6 2 9 2 2 3 1 9 2 7 5 2 1 2 7 2 7 3 5 2 6 3 7 3 6 2 7 7 6 3 2 7 6 3 1 1 2 3 )  - 6 3 7 7 9 9 2 2 7 9 3 7 2 1 1 9 3 7 3 S . 3 5 2 9 7 1 9 2 7 1 3 5 2 1 2 7 2 7 3 7 7 9 9 6 3 1 2 7 3 6 3 7 ' 2

  1 2 9 + 9 1 7 2 6 5 3 5 2 6 2 3 2 ) G 3 9 6 9 3 1 3 2 6 3 7 9 7 1 9 2 7 ' 2 9 2 2 3 5 3 3 5 2 2 6 6 3 7 )

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

 UZ [ \ ] T ^ _ V ` a V ] b c d e W f f g W X V Z [ \ ] T ^ _ V ` a V ] b c d e h i f f i f W W X g f h U T j T Z [ \ k ` V h X

Page 3: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 3/30

  2 3 4 5 6 7 9 6 4

 

                  !    

  " # $ % ' ( % ) * ( % + $ % $ , $ % ) ' ( - * . + $ % / ( , ( $ ( . / ( % ( , ( . % ( $ . + $ ' . ( . * . $ 8 $ / ( ' ( % ) * ( % + $ %   " # $   8 $ / ( ' ( %   ) * ( %   + $ % % ( ) '   (   % $ ( .   : *   . $ % ( , (   + '   .   $ % ; ) ' , : * ( ( % .   / %   ) ( .   % $   < , ( = > ? . / < , $ '   , $ .   $ ' ' * - $ '   , $ ; @ ? A (   '  B   $ ' : * ( , $   8 $ . ( %   + C ' + $ ; *   +   , $   / $ ) ' (   % ( .   + ( / (   D (   + % / ( ) ' ( % . E + $   , ( %     $ . $ % ; A $   , % .     ) , (   + % F < , $ .   % ? ; F G ? . $   ( ' $ '   $ % $ . + $ . ( % ( . * $ ,   : * ( ' ) $ '   + ( / ( , $   8 $

  " H ( ' B $ : * ( ( . , $ 8 $ / ( ' ( % ) * ( % + $ % ( % + C . ' ' ( + $ ( . + ( $ . + $ / % + * E % ? . < ' ( E % ? ; $ ) ( , , / % F ( ,  . I ( ' / ( ' ( - % + ' : * ( + ( $ % - . , $ J ' ( . K ( . ( ' $ , / ( L / . % + ' $ . M % , $ ' / ( , $

  N O L P

 

  Q   R           ! !      

  > M . ( , ( %   ) $   ' (   % ( '   A $   / ) $   ' $ ( , S T M L ;   ) $ ( , . I   (   ' '   $   . : * ( ( %   + ( .   (   ' ' $   / ( . ( , ' (   * $   / ' / ( , $  ) ' + $ / $ / ( , * $   / ( '   . / ( , ( $   ( . M , . I   (   ' U   ' ' ( %   ) .   / ( $ , $ % V ( .   $ % W X   %   P $ + ( + $ % F / ( , $ %

  Y . - ( . ( ' X $ % ; ( , U U $ , $ % V ( .   $ % Z   ,   -   $ % ; [ * X $ % F / ( , $ \ $   , * / ; ( , U U U $ , $ % V ( .   $ % \ $   , ( % F ( , U ] $ , $ %

  ^ *   $ . / $ / ( % F , $ % L '   + ( %

  @ M . ( , ( %   ) $   / ( %   +   . $   / $ , $ H M T   \ Y _ O ;   ) $ ( , . I   (   ' $ '   <   - : * ( $ ) $   ' (   ( ( .   (   ' ' $   / ( . ( , ' ( * $   / ' / (  , $ ) ' + $   / $ / ( , * $   / ( '   . / ( ( $   ( .   G L .   + $ ( . ( , $ .   A ( '   % , $ % ' ( %   ) * ( %   + $ % / ( , $ % ) ' (   - * .   + $ % > $ ` a F ( . % * ' (   A ( '   % ; , $ % ' ( %   ) * ( %   + $ % / ( , $ % ) ' (   - * .  b  + $ % ` c $ > @ d ; * +   ,   e $ .   / (   , *   %   A $   ( .   + ( ,   ) e / ( , . I (   ' @ @

 >

 f

 @

   ` # , (   . $ ) '   ) , (   + ) (   ' % . ' (   < $   % $ '   ; ( , A $   , : * ( % ( .   %   / (   ' (   ' ( %   ) * ( %   + $   ' ' (   + $ ; ( . ( , ' ( . - , .  ' ' ( % ) . / ( .   + ( $ $   / $ ) ' (   - * .   + $ E A ( ' ( 8 (   ) , % ( . , $   8 $ / ( ' ( %   ) * ( %   + $ % ?   a # , (   . $ ' % / ( * . A $   , ) $   ' $ ' ( %   ) .   / ( ' , $ %   $ ) ' (   - * .   + $ % ( .   %   / (   ' $   ' ) ' (   - * .   + $ . . + ( %   + $   / $

  c Z   ' ' $   ) , (   + $   ( .   + ( * $ ,   : * ( ' ' ( %   ) * ( %   + $ : * ( : * (   ' $ % $   < $ ' \ , $   8 $ , , ( - $ $ % *   D ' ' $ ,   - I . / $ g ;

  * . X $   , $ , ( $     . $   / '

  h V   ( , + (   ) ) $   ' $ ' (   % ,   A ( ' ( , ( $   ( . ( % ,     + $   / ; ( % ) ' (   D (   '   < , ( . / (   + (   . ( '   % ( / (   $   % $   / ( . , $ % ) ' (   - * .  b  + $ % : * ( ) $   ' ( e   $ . * F /   D X     , ( %   i j   / $ % , $ % ' ( %   ) * ( %   + $ %   ' ' (   + $ % + (   . ( . ( , %   A $   , ' F $ ) '   + $ . * . ) * .   + $ , $ % *   $ - ,   < $ , ; ) ' , : * ( ( %  ) ' + $ .   + ( .   + ( %   + $ ' ( , $   F ' . I   (   ' / ( ) ' (   - * .   + $ % / ( +   / $ % , $ % $ % -   . $   + *   ' $ % : * ( % ( ( A $ , I $ . ( . ( , ( $   ( .

  M # M k L   P M O O l \ M   T S H S   # Y   J l \ Y O # L W Y T   P L J M # L \   m Y   T L O  j M

 ns t u v w x y o z { o v | } ~ p � � � p q o s t u v w x y o z { o v | } ~ � � � � � � p p q � � � n w � w s t u � z o � �

Page 4: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 4/30

Page 5: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 5/30

  2 3 4 5 6 7 9 6 4

  ! " # # ! " $ % " &

Page 6: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 6/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ( ) * + ,  

   / ' 4 4 :   ; 4 < = > ? @ 4 4 A 4 B   > C = 4 D     E F G H I J I K H L M N I H O K P H N J L Q P Q R S T U I   V L I O P W  X F Y P Z R O I K P O N K P R T Q Z N [ I P Z P V L I H \ P W

 ] F Y P V L I H \ P I M L Q R L T P P Z H I T H R ^ Z I W

  _ F Y P H ` L Z L T U K R T P H a R K M P T I Z V I K ` P M R T L

  U I Z Q R I Z L W

 

   b c = 4 A 4 A ? @ 4 < ? < :   > ? @ 4 < 4 D 4 = > d ? ? A e    g h i j k l m n k h i j k h o h o l j h i p n q h i j q r o h i   s l h p n t k r p r s q n i n k r u p n j l n p k r v r q l w r x   y z v { q r p n j r j r | j r j n q k n v l v q r p h x j n k h   i n y { n j n k y n v v l h u r u p h q r l p n r } r i o r

  ~ { n i n q h t k { u r m n w v q r p n r q m l p u

  p n j r j r x r t { r | { u j h q � m n k h h k t � u l v h �

 

  E F E K ` N M I T O P Q R S T W

  X F � P K K P Q R S T W

  ] F _ I M L H O K P Q R S T W   _ F _ I H Q K R V Q R S T W     ) > ? = 4 ? : < A 4 ? @ < 4 @ > 4   = ; = < 4 D 4 = � = < = < > ? D = < �   �  

  Y P a R Z L H L a \ P I H Z P U R H Q R V Z R T P � N I V L K I � Q I Z I T Q R P

 H I L Q N V P U I Z V I T H P M R I T O L W Y L H a R Z S H L a L H H R ` N I T

  H R I T U L I H L H � I T P M L K P U L H U I Z P H P ^ R U N K \ P �

  Q N [ P Z P ^ L K Q L T H R H O I I T V K I ` N T O P K H I Q L H P H

  P Q I K Q P U I Z P J R U P [ I Z M N T U L W Y L H Q R I T O \ a R Q L H �   V L K I Z Q L T O K P K R L � H L T J R H O L H Q L M L V I K H L T P � I H   � N I H I L Q N V P T U I N T P Z P ^ L K M � H V K � Q O R Q P �   K I P Z R � P K I � V I K R M I T O L H V P K P V L T I K P V K N I ^ P H N H   � R V S O I H R H H L ^ K I Q S M L a N T Q R L T P Z P T P O N K P Z I � P W   ] N P T U L N T Q R I T O \ a R Q L H I I T a K I T O P P N T P   V K I ` N T O P � N I T L V N I U I Q L T O I H O P K � I H a K I Q N I T O I  � N I K I H V L T U P � I H L I H M N [ a R Z L H S a R Q L � � U P T U L P   I T O I T U I K � N I T L H I U I ^ I K \ P V I K U I K I Z O R I M V L

  Q L T I H I O R V L U I O I M P H W � R T I M ^ P K ` L � Z P

 K I Z P Q R S T I T O K I Q R I T Q R P [ a R Z L H L a \ P I H M N [ P T O R ` N P

  [ I H O K I Q � P W _ I � I Q � L � Z P H U R a I K I T O I H Q R I T Q R P H

  H N K ` R I K L T � R H O S K R Q P M I T O I Q L M L V P K O I U I Z P

  a R Z L H L a \ P � [ Z N I ` L a N I K L T R T U I V I T U R � � T U L H I   Q L T a L K M I U I � P K L T U I H I K U R H Q R V Z R T P H ^ P H P U P H   V K R M L K U R P Z M I T O I I T Z P K I a Z I � R S T V P K P   Q L T J I K O R K H I I T P Q O R J R U P U I H Q I T O K P U P H I T Z P   I � V I K R M I T O P Q R S T W   G � R H O I N T P K P M P U I Z P a R Z L H L a \ P � N I   P ^ L K U P I � Q Z N H R J P M I T O I Z L H V K L ^ Z I M P H U I Z P   Q R I T Q R P W E Z ` N T L H H L T Z L H H R ` N R I T O I H � � � N � O P T   ^ R I T a N T Q R L T P T Z P H O I L K \ P H Q R I T O \ a R Q P H Q L M L

  K I V K I H I T O P Q R L T I H U I Z P K I P Z R U P U � � � N �

  U R H O R T ` N I P Z P Q R I T Q R P U I L O K P H a L K M P H U I

  Q L T L Q R M R I T O L � � ] S M L U I Q R U I T Z L H Q R I T O \ a R Q L H

  P ^ P T U L T P K N T P O I L K \ P V P K P P U L V O P K L O K P � � �

  a R T P Z M I T O I � Z P V K I ` N T O P U I Z L H � � M R Z V I H L H �   � V L K � N � a N T Q R L T P Z P Q R I T Q R P � � L K � N I � P V I H P K   U I Z L � N I V N U R I K P V I T H P K H I � T L I H V P K P T P U P   L ^ J R L � N I Z P Q R I T Q R P T L H V K L V L K Q R L T I   Q L T L Q R M R I T O L L ^ � I O R J L U I Z P T P O N K P Z I � P � H S Z L   T L H ^ K R T U P M L U I Z L H I R T O I K V K I O P Q R L T I H � N I  V N I U I T H I K M � H L M I T L H Q L K K I Q O P H L   I T ` P � L H P H W _ I � I Q � L � T L V N I U I U I M L H O K P K H I   � N I Z P Q R I T Q R P H I P R T O K \ T H I Q P M I T O I H N V I K R L K P

  L O K P H a L K M P H U I Q L T L Q R M R I T O L W � � H R T I M ^ P K ` L �

  Z L H K I H N Z O P U L H V K � Q O R Q L H � N I L a K I Q I H L T

  R T Q L M V P K P ^ Z I M I T O I M � H I a I Q O R J L H � N I Z L H U I

  Q N P Z � N R I K L O K P a L K M P U I P ^ L K U P K Z P K I P Z R U P U W

  � T Q Z N H L � P Z ` N T L H a R Z S H L a L H � P T U I H P K K L Z Z P U L   K I Q R I T O I M I T O I N T P � I V R H O I M L Z L ` \ P   I J L Z N Q R L T R H O P � � N I H N ` R I K I � N I Z P Q R I T Q R P I H   N T P P U P V O P Q R S T U I T N I H O K P I H V I Q R I Q N [ P   a N T Q R S T I H P N M I T O P K T N I H O K P H V L H R ^ R Z R U P U I H U I   H N V I K J R J I T Q R P � Z P Q R I T Q R P Q L M L V K L U N Q O L U I Z P   I J L Z N Q R S T W   � L U L Q R I T O \ a R Q L U I ^ I K \ P Q L T L Q I K P Z ` L U I   a R Z L H L a \ P U I Z P Q R I T Q R P W _ I H ` K P Q R P U P M I T O I � P [

  M N Q � L H � N I T L H S Z L T L Z P Q L T L Q I T � H R T L � N I Z P

 U I H V K I Q R P T L R T Q Z N H L Z P J I T Q L M L P Z ` L

  P M I T P � P T O I W � I H N T P Z � H O R M P � V L K � N I T L H I

  V N I U I O K P ^ P � P K ^ R I T I T P Z ` L H R T L H I H P ^ I

  Q S M L a N T Q R L T P W         

 

 �¡ ¢ £ ¤ ¥ ¦ § � ¨ © � ¤ ª « ¬ � ® ® ¯ � � � ¡ ¢ £ ¤ ¥ ¦ § � ¨ © � ¤ ª « ¬ ° ± ® ® ± ® � � � ¯ ® ° � ¥ ² ¥ ¡ ¢ £ ³ ¨ � � �

Page 7: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 7/30

  2 3 4 5 6 7 9 6 4

 

  ! " ! " ! " # "

    % & ' ( ) * + , - . . / ( ) , * * + + ,   ) * - ( ) + . + ( . - / ( 8   & : * ( ) . / ( , ) , ) +   , * * + + , ) . + ( . - / ( 8   ; & : * ( ) . / ( , ) * < * ( . /   + = * ) * - ( ) +   . + ( . - / ( 8

  > & ' ( ) * + , - . . / ( ) * < * ( . /

  + = * ) , ) + . + ( . - / ( 8

 

 

  ? @ A B "   " " C D ! !   " # " E     % & F + . / ( ) G < / . + , = ( . + H * ( , * I -   / ( < / + + < G ( + J K . / ( . / L K +   < / + < + M I - . / ( . /   . + ( . - / + ( K * - ) , + H * N . ) / . +   - K < . ) / O + 8

  & > , + I - , / < * ( ) . / ( . /

  - * / * + ( J / ) * / . ( ) . + + H * )

  , < / + + < G M , = J = * - (

  . + H ( ) * / , , ( ) * . / ( . / K   < / + + < G 8   ; & % - ( I - , * - ) , + N H * N . ) / . +   I - + ) * < + * , . + ( + . / / ( ) + M   . / ( . / ( + , = . + ( / , * * P ( / .   < + * , Q H / . * * / , , 8   > & F + . / ( ) G < / . + , = ( . + ( + . *   * < Q / ( I - + < * . < / + + < G + = *

  I - J . * . / ( ) G < / . + L , ) + , +

  H + , * N ( * / R * S + * - ) * = S + 8

 

 

  T @ A B " " U V   W ! " # " E     % & X + * / ( , . / ( . / 8   & F + + = S ) / O + , . / ( . / K ,   < / + + < G 8   ; & X + * / ( , < / + + < G 8   > & F * < Q / ( < / + < / . ,

  . + ( + . / / ( ) + 8

 

  Y A # ! Z [ ] ^ _

  ` a b c [ d ` a e c f " g h i

    % & % , / ) I - . / ( . / ( + H - ,   Q H / . * + ) + , + 8   & j < S - < + * , ( ) ( , *   < / + + < G 8  ; & k ( / < / ) - , . + ( + . / / ( ) + ,   < / + + < G 8   > & % . H ) I - < / + + < G ) / ( - H * + H / +

  . H + , ) - , / + 8

 

 

  l " m

  " ! # ! " f   h ! ! " n "   h i     % & X Q H / . * * / , , 8   & ; / < / . * * / , , 8   ; & o = * O * * / , , 8   > & k , / * * / , , 8  

 

  p q B ! ! "

  ! ! m ! " m

 

 % & r - / R N ( - ( ) H + H / H / +   . - ) / O + * ( - K S O ( K   . H = ( H * / , / . ( ) 8   & F + H * J / H N ( / . + - ) / / R = ( +   H - , - S + + ) M H * + ( + . + G (   - . * ( 8   ; & F + H * J / H N ( / . + I - * G ( I - +   - S + + ) M - ( O R - * ) + M

  H * H * * ( ( + . * / , * + 8

  > & F ) * , / . / ( , . * / ( R , - S + + )

  , + s ) / . + < - , H R ( , + J . /

  ( + * ) 8   

 ty z { | } ~ u � � u | � � � � v � � � v w u y z { | } ~ u � � u | � � � � � � � � � � v v w � � � t } � } y z { � � u w �

Page 8: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 8/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ) * + , - , * - . / * * - . 4 / 4 * *

  * / 4 ,

  : ; = > ? @ A B C D E D = > D E F C ; G E H > @ F I > B C B I D   = ; @ A D = J C D @ J E A = K = > G E > D = > L E > I J @ M    N O P Q R S P T U T S V W X Q Y V W Z U V Q   [ O \ X W P ] Q Y T U V ^ V W P V ^ R U X _ ^   ` O W P _ ^ P V W P a ^ P S Z Q   b O P Q R S P T U T S V V W P V ^ R U X _ ^  

 

  c d ' e * - . 4 / 4 * * * / 4 , 4 * 4 f 4 , - ,

  f / 4 g * - , h . i j , - , k l , h . i *

  m , n o . / - , h . i n . * - * 4 , - , j 4 g

  l l * , ' p . 4 * l , * - * q '     r @ s = t E A @ u @ F v A = w x C E x @ G @ A s E y A = > E s   > @ y C E s D = > E s z = { = s | } ~ � } u � ~ M     N O � Y W V U Z Q V ^ �   [ O � � � W T ^ V U Y W Z T ^ �   ` O � � � W T ^ U X V U Y W Z T ^ �   b O � � � W T ^ Z U Y Z S X � T Q X Z U Q P �

 

 

  c c ' � * 4 f 4 , * - * * m j - * * - / , - � , n /

 * l l l . 4 � 4 � / * j l � , 4 . 4 , .

  4 * l j l * , 4 * . '     N O ` ^ X Q � ^ R � Y ^ � � S Q X � U ^ Z � R ^ � Q Y T � X   W X _ Q � Q � Q Q � S � S W _ Y Q �   [ O \ P V W � W X � Q Y W Z P Q R � S X Q � Q P T Q Q P � Y � U T Y ^   � S W X S X Z Q W � U � T U � �   ` O � X V � Q � S W � Q P U � Q V Q Y S X Q � S W P T Q   W X Z ^ X T Y � Q � S Z � ^ � W Y �

  b O \ X W P � � X W � U � � W � W Z � R ^ b U ^ � Z Y W �

  Q P � ^ R � Y W V W � Q Y Y ^ �

 

 

  c � ' ) * - * 4 , - , j 4 g � / * m j - * * * -   . 4 / 4 * * * / 4 , � * m , * l , � / *   / * l * * - / . f l m , - * - ,   - * / , '     L C = ; = @ { C J C K ; � � � � � � � � > @ s J C = ; J C @ s M     N O ] ^ Y   [ O ] Q Y Q

  ` O Q

  b O � ^ � Y W

  c ' ¡ * * / 4 , n * * l m 4 , - ,

  l * - , 4 g � / * * k * / , l , l - .

  * / 4 , . * - . . 4 / 4 * * .   f l , m * . ' ) * - * 4 , * - l / j *   * l * . � / * j * l m 4 * l * , - 4 ¢ , l 4 � ,   l * - , 4 g '     £ : > ¤ @ ; J E D = ¥ ¦ § C J E ¨ @ = s @ I B K ; E F E   � � � � � � � � D = y = s = G I C A s C ¦ ; D E > E M : >   © E ; G A = s E D = y = ? A = E J I ? @ A s = ? E A   = s B @ y > = J = A > @ A = > @ J C K ; z I A v D C J @ ¨

  ? E > v B C J @ J E ; = s @ C ; s B C B I J C K ; H � � � � � � � �

  s I E ? = A @ J C K ; ; E = s B ¦ D C s E J C @ D @ D = > E s

  F = J @ ; C s F E s D = A = ? A = s = ; B @ J C K ;

  � � � � � � � � s E ; C ; ª = A = ; B = s @ > @ { I ; J C K ;

  ? « y > C J @ M £     N O ] ^ Y P ^ � S W ¬ Q � � ¬ � S W   [ O ¬ V Q V ^ � S W ¬ P ^ � Z S Q P W �   ` O Q � � � S W ¬ ] Q Y Q � S W ¬ ] S W �   b O ¬ V W R ^ V ^ � S W ¬ � S W     c ® ' ¯ * , / * l - , l * - , 4 g *

  ° ± ° ¡ ² ³ ´ ° � / * * * - . 4 / 4 * *

  * / 4 , . * * . , k - * * * l * - , .

  j , - , k l , . * - * l , . m , n o . / - , . � . * + , - ,

  - , j 4 g � / * j l * . * , / , l * - , 4 g

  . * m * , * '    L I D C s J I A s E y @ A A E J E ¨ J E ; D C G A = s C E ; = s   ? A E x E J K ~ ¤ | u u � ¥ � : } L � = ; = >   @ I D C B E A C E ¨ H = ; J E ; s = J I = ; J C @ H I ;   G = ; = A @ > C w @ D E ¤ � L : µ � M     N O ¶ Y Q ¬ Q _ Y W � U � X �   [ O b U � W Y � U � X ¬ � ^ X Y U � Q �

  ` O b U � T Y Q Z Z U � X ¬ W Y Y ^ Y �

  b O ¶ R ] Q Z U W X Z U Q ¬ Y W � W P U � X �

 

 

         

 

 ·¼ ½ ¾ ¿ À Á Â ¸ Ã Ä ¸ ¿ Å Æ Ç È ¹ É É Ê ¹ º ¸ ¼ ½ ¾ ¿ À Á Â ¸ Ã Ä ¸ ¿ Å Æ Ç È Ë Ì É É Ì É ¹ ¹ º Ê É Ë · À Í À ¼ ½ ¾ Î Ã ¸ º È

Page 9: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 9/30

  2 3 4 5 6 7 9 6 4

 

  ! " # " ! $ %

  & ' ( ( ) *     - . / . 8 : 8 ; <   = . > ? @ 8 ? A 8 B C D / / >   > 8 ? E F G H I J - K H L . /   / > 8 / @ 8 = . . : B /   8 / 8 E / > / : > M . : . 8 N     O P Q R S T R U V W X Y Z

  [ P Q R \ Y R S T Z

  ] P O W ^ S _ V X Z

  ` P [ V a T Z

 

   b c & d ( e f g   ) & ( ( )       h = . > > 8 B i i B j 8 8 B @ >   8 . L i i B / > ? / i i 8 E : 8 >   @ 8 B / 8 / : / M . 8 : ? 8 8 N   k L @ / l B / B ;

  B / = . / m / i i / B l B 8

  G ? B / l 8 : B 8 / . / M . 8 B N

 

  O P S n S n o n S

  [ P p n p n o n p   ] P S n p n S n S   ` P S n p n S n p     q c & d g & (   ( ( e f ! " r % s s c r t u     O P v w ^ _ ^ \ ^ x T y V z { p T R | R W ^ X X Y \ Y } ~ _ Y U T

  x ^ Y a T Z

  [ P O S � S Y Y S \ | x ^ Y w { R S ^ R U Y p ^ w y V X V W w V

  X V w z T w V \ T Z

  ] P ` ^ a T V U ^ { S \ T p � R U T S Y Y X V X V U Y X   S T _ W w Y w T p T R S | _ V R T Z   ` P � ^ Y w T R � | Y � | z Y R ^ V S Y � | Y y T w X V   x Y w Y U V _ | \ Y _ y w V R T Z      

 

 

  � c g ( ( e f

  r % s s c r t u

    O P � � � Y S � V X X � V � | Y w V Y S \ � X X T x ^ Y R U T Z  � � T S ^ Y R \ Y S Y X z T X y Y V w U Y X V X X | x ^ V � �   � Z � | X � T Z     [ P � � Y S � V X X � V � | Y w V Y S \ � X X T x ^ Y R U T Z   � � T S ^ Y R \ Y S Y X z T X y Y V w U Y X V X X | x ^ V �   � � Z � | X � T � Z  

  ] P � � Y S � O X X � V � | Y w V Y S \ � X X T x ^ Y R U T Z

  � � T S ^ Y R \ Y S Y X z T X y Y V w U Y X V X X | x ^ V �

  � � Z � | X � T P Z

 

 ` P � � � Y S � O X X � V � | Y w V Y S \ � X X T x ^ Y R U T Z  � � T S ^ Y R \ Y S Y X z T X y Y V w U Y X V X X | x ^ V � �   � � Z � | X � T P Z    

  $ u t c $ � t ! r u

  

  � ) & e � & ( d

 �

 �

 �

 �

  � ' �

  '

 �

 �

 

 

 � �  � �

 �

 �

 �

 �

 � �

 V W O P V W  [ P � V W P  ] P V W

  ` P � V W P

 �

 � � � �

 �

 

 

 

 �¤ ¥ ¦ § ¨ © ª « ¬ § ® ¯ ° ¡ ± ± ² ¡ ¢ ¤ ¥ ¦ § ¨ © ª « ¬ § ® ¯ ° ³ ´ ± ± ´ ± ¡ ¡ ¢ ² ± ³ � ¨ µ ¨ ¤ ¥ ¦ ¶ « ¢ ·

Page 10: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 10/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ( * + , - . / ,

 

 

 4

 +

 +

 

 

  :

  , / , ; < = , +

 

 ? 

 ? 

 @ A @

 @ A @

  ? @ A @

 ? @ A @

 B C D D  E C D  F C D

 G C D D

 H

 H

 H

 H

 

 

   & I ( J K ; , + / / L K K + / M -

 &

  N O P Q

 O

  , L R S , ,     B C T

 U

  V W T

 X

  Y Z ? [ T

 \

 Y

 ? 

  V ? [ Y

 ]

   E C T

 U

  Z W T

 \

  Y V ? [ T

 ? 

 Y

 ? 

  Z ? [ Y

 ]

   F C T

 U

  V W T

 \

  Y Z ? [ T

 ? 

 Y

 ? 

  V ? [ Y

 ]

   G C T

 U

  V W T

 ]

 Y

 ? 

  Z ? [ T

 ? 

 Y

 ]

  V ? [ Y

 ]

 

 

 

  & & ( ^ 4 . K _ = + ; L

 &

  - ` - a

  & + - a +

 H b

 H

  , L R S , ,

 

 ? 

  c T ? C c T ] C B C  ? D  c T ] C E C  ? D c T ? C

  c T ? C

 F C

 ? D

  c T ? C G C ? D

 H H H H

 H

 H

 

      

 

 

  & O ( * + / + d = , ; , K + , = < + =  

 e -

 &

  f I a - f I ` g ' L  

 

 h ? 

 h ? 

 h ? 

 h ? 

 ] X B C T i T ? ?  X  E C T ] i T  \ ] X

 F C T i T

 ? ? 

 ]

 G C T i T X

 \

 j H j H j j H

 j j

 j H j

 

    & e ( * + L K < = ; , K + ; , k < + K ; + ;   O - l ` m - f a ,     h h  B C T ? 

 h

  E C T

 ? 

 ?   F C T h h ?   G C T  h h

 n

 n

 n n H

 

  

 ot u v w x y z p { | p w } ~ � q � � � q r p t u v w x y z p { | p w } ~ � � � � � � � q q r � � � o x � x t u v � { p r �

Page 11: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 11/30

  2 3 4 5 6 7 9 6 4

 

 

  ! " # $ %    & ! ' # $ ( ) * + *

      - . /   . /

 

  . /

 

  . /

 * ) * )

 * )

 *

 

    8 : ; < = : > ? @ = ;   = A B C > : > D  

 

 

  - . E

  . E E

  . E E E   . E F        

 

 

  & ! G " H > >

 

  - .    .    .

 

 

  .

 

 I I I

 I

 

    ( J < > = K > > >   G A > <

 L

  >   = M     - . N O / . P Q R S O / T  L .   . N O / . P Q R S O / U  L .

  . N O / . P Q R S O L  / .

  . N O / . P  L  Q R S O / .

 

   % J > = > G >    V W ? X # Y W " ? Z $ X     - .   . [

  .

  . [

 

  

 \a b c d e f g ] h i ] d j k l m ^ n n o ^ _ ] a b c d e f g ] h i ] d j k l m p q n n q n ^ ^ _ o n p \ e r e a b c s h ] _ p

Page 12: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 12/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ $

  % & ' ) * + , - . / / * 4 - . / , , -

  * / 4 + , - . / 4 : ; < = > ; < 4

    @ A B C D E A   F A B G D E G A   H A B E G D G A   I A B J G D E G A     % ; ' K L M , L M N - / O - L O L * L L . O P

  * 4 , - . . O Q - , * / . O L P L L 4

  * * L / R S 4 

 

 

 

  @ A T U V W X Y Z   F A T U V W X Y [   H A T U V E X Y \   I A T U V E X Y Z     % ' K L M , L M N - * L M O M , - ] O - M L ,

  . - M - . O / - * / O - = O L /  ̂D  4 . Q

  L L + / O

 

  @ A X

 E

  Y T

 E

  Y _

 E

  U C

  F A X

 E

  Y T

 E

  ` _

 E

  U C   H A X

 E

  Y T

 E

  ` _ U C   I A X

 E

  Y T

 E

  Y _ U C     

 

 

 % % ' K L M , L M N - * L + L O Q a / * L M / - b c O . M

  - * / O - d ] / M L * + L O L * * / L * d e

  = , + L 4 L + / O * + , - . / f g h < 4     @ A X

 E

  U ` i T   F A T

 E

  U i T   H A X

 E

  U i T   I A T

 E

  U ` i X  

 

 % g ' K L M , L M N - * L + L O Q a / * L M / - b c O . M

  j % g < + L O Q . O / k , L * L l = d

  ] / M L * + L O L * * / L * d e 4

    @ A X

 E

  ` Z X ` E C T Y i n U C   F A T

 E

  ` Z X ` E C T Y i n U C   H A X

 E

  ` E C X ` Z T Y i n U C   I A T

 E

  ` Z X Y E C T Y i n U C   

  % l ' o p , c M , L M N - M / O O 4 + / - L * L

  4 , - . O Q ] M L q

 

 

 

  @ A X

 E

  ` T U r

  F A T

 E

  Y X

 E

  U r   H A X

 E

  ` T

 E

  U r   I A X

 E

  ` T

 E

  U ` r   

 sx y z { | } ~ t � t { � � � � u � � � u v t x y z { | } ~ t � t { � � � � � � � � � � u u v � � � s | � | x y z � t v v

Page 13: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 13/30

  2 3 4 5 6 7 9 6 4

 

 

  ! "

  # $ # % &

    ( ) * + , - . / +   ) *   ) * 8 , . / +   ) , : ; +     < = > ? $ @ & @ A # % % B &  

  > C D C E ? $ @ # F

  C > % $ # > ? H $ # D A I J

  % # D @ @ K ? & L % D

  M M M M M M M M

    ( ) N O .   ) N P .   ) N Q .   ) N R .   

 

 

 C

  I J

 C

 S S  % B @

 

  ( ) T N U V N   ) T N

 W

  U V   ) T N

 W

   ) T N

 W

  U V N U X     Y C # Z C C ! I

 

  J

 [

  % 

 

  ( ) \ ] P X W N

 W

 

  ) \ ] P ^ N

 W

  _ W N

 T

  U ` )

 T

 

  ) \ ] P V N

 W

  _ W N

 T

  U ` )

 W

   ) \ ] P W a N

 W

  _ W N

 T

  U ` )

 T

       

 

 

  [ " b @ ? > Z ? & > C $ # & K @ % & c

  # B C > $ > # @ $ # %

  A I & J ! d &

 

  & d D C $ C C @   & ? $ >  e  ? C C > % B C > %   f = c @ % @ Z @ > C C C @ $ # & K @   & ! % g     ( ) N ] _ ; ) P h ^ i j   ) N ] _ ; ) P ^ i j   ) N ] _ ; ) P X k W i j

  ) N ] _ ; ) P h k i j

 

 

  [ d $ # % A I & J ! > % I & J %   A C $ > % C ? > Z ? & >   # ? > l @ $ # % $ # @   @ # %     ( ) + _ ; ) P m a : / _ W ; U T )   ) + _ ; ) P m : / _ W ; U T )   ) + _ ; ) P : / _ W ; U T )

  ) + _ ; ) P m a : / _ W ; m T )

 

 

  [ b @ $ & > ? c ? > C ! % I J   I n

 o

 l

 o

  J %     ( ) X T  ) W

 X

  )

 W

  ) k

 

  

 pu v w x y z { q | } q x ~ � � r � � � r s q u v w x y z { q | } q x ~ � � � � � � � � r r s � � � p y � y u v w � | q s �

Page 14: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 14/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ( * + , - + . / + - 4 / - + -

 

 

 

 

 : 

  ; < - + -     > ? @  A ? B C D ?

 E

  F ? C

 

 

   & & ( G - 4 / - +   H ; ' I . ; J  K

 :

  ;     > ? B L M N O P Q R L O P D   A ? Q R L O P L M N O P D   D ? B Q R L O P E L M N O P D

  F ? S B Q R L O P E L M N O P D

 

 

 

  T U V W X Y

    & Z ( [ - / - < - , + . I - I . ; 4 - 4 \ + -   / - ] ^ ;     > ? _ M N R ` a b M c d _ d e N f g b h h M c d   i M c R Q f h d h j

  A ? _ d k R ` a b M c d _ d e N f g b h h M c d

  i M c R Q f h d h j

  D ? f e b d c a b M c d _ d e N f g b h h M c i M Q g R ` h M c d

  i M c R Q f h d h j   F ? e ` d h b d c _ M N g M Q ` M Q f M N g M j        

 

 

  & l ( m - < 4 . - / / - I - - I + / - .

  I . ; 4 - 4 n 4 o p n q ;

 

  r + - , + . I -

  + - < 4 . . ; ; < . ; ; ] < s ;   I - / ; < n . , n 4 . ;     > ? t _ u L   A ? v C _ u L   D ? E B _ u L   F ? E w _ u L  

 

  & x ( m - n < y / Z z ; 4 { 4 / . <

  + , - . / I < - . ; / . n ] + - I < / -

  - I / . | I - ( } < / - 4 + - I - ~ - \ I < { +

  ; + - < / ^ - � � 4 . ; � < + ] ; .   + + , - . / y / I ; . � / + . ; ] ;   + - n < y / �     X . ; / - � o n q ;

 

     > ? � � @ @ @   A ? � @

  D ? �

  F ? @

 

   & p ( V . � / < . � y 4 . o � ; - ] + I -   . ; < / ^ - ; H < - � |   . 4 / - ' � J I . + - n ; n - / I I �   ] / . ; 4 . I . 4 / - / . \ I < { + ; + -  n - 4 < + - - I + / - I � + . � y 4 . �     > ? @ j v _ u L

 B

   A ? @ j B _ u L

 B

 

  D ? @ j E _ u L

 B

 

  F ? @ j � _ u L

 B

 

 

 

 �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ¡ � � � ¢

Page 15: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 15/30

  2 3 4 5 6 7 9 6 4

 

  ! " " # $ $ $ ! $

  % & ' (   " $  # $ ) ) ) ) ) ) ) ) (   " * $ " " ( &     , - . /   8 - . /   : - ; < = /   > - ? @ A B

 

 

  C D E F F $ $ F G %

  " H " $ $ $ ' %

  % $ " $ H $ I J   $ H % $ $ $ " $   "  

 

 

 , - K B L M N O N P Q <   8 - K B L L M N O   N P Q <   : - K B L L L L M N O   N P Q R A B L L <   > - K B N M N O ? @ A B   N P Q <

 

 

  C S E T $ G D U $ " J "

  " ' T $ " V

  " W % X $ ' " $ Y   V " J $ S W % X $ Z [ J $ % $   " \ ] ^ $ H _     , - . < ; ` @   8 - = < ; ` @   : - a < = ` @   > - ; < b ` @

 

  C W # $ ! F $ % $ $

  V $ % H $

  ! % $    , - c ? d N c N A <   8 - N c N A @ e ? N <   : - @ e ? f N ? B A B @ e   c N ? B <   > - @ e c N ? B c ? d <

 

 

  C G # & ( [ * " $ g $ $

  " % "

  " $ $ " ( $ $ $ $   % ! % " " Z [ J $ $   " % " \     , - h i ; ; j :   8 - ; j k   : - ; j l   > - ; j :

 

 

 C m $ " $

  " ( $ " $ $

    & $   I # "   I I & $ ! $   I I I n " % * "    [ " ( $ " $

  o $ " %

  " $ % " $

  F # $ " ( $ ! F J

  "   # $ " ( $ ! F % "       , - L p q L L p P q L L L p   8 - L p P q L L p q L L L p   : - L p P q L L p q L L L p   > - L p q L L p P q L L L p  

 

 rw x y z { | } s ~ s z � � � � t � � � t u s w x y z { | } s ~ s z � � � � � � � � � � t t u � � � r { � { w x y � ~ s u �

Page 16: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 16/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & & ' ) * + , - . / * + 4 + / , + , 4 ,

  + / 4 , * : - , ; 4 - 4

  = > ? @ A = B ? C =

 C ?

 D

 E

 F ? D

 

    & G ' H , + / 4 I + 4 + * , . / * 4 /   4 + 4 ,  J K

   

    L > ? M N M L

 B ?

 N

 L

 C ? O N O L F ? N

 

   

 

  & P ' Q 4 * R * S / - , ; 4 + / + 4 , ; 4 T

  U + , - V 4 , / + / * 4 - . / W

  / +     > ? X Y Z [ Z \ A ] Y ^ Z _ Z D Z \ ^ ` D ` a Y ^ Y b c d c   b Y X c \ e   B ? f [ b Y d a c Z X g b h \ ` b c ^ Z _ Z Z i ` D h ` \ Z [ Z X   X ] d ` h Z ^ Z X h ` Z d a c e   C ? f [ Y b c \ \ ` Z [ h Z ^ Z _ Z j X f ` \ Z [ j f [ b ` k [ ^ Z   X Y l Y \ ` Y b ` k [ ^ Z X h ` Z d a c e

  F ? f [ Y   m n o   ^ Z _ Z Z i ` D h ` \ Z [ j f [ b ` k [ ^ Z X Y

  l Y \ ` Y b ` k [ ^ Z X h ` Z d a c e

 

 

  & q ' H , . 4 T , - / R 4 + , 4 - 4 :   * ) + / - . , , , + / * , * 4 *   * - , . / I * ,     > ? ^ Z [ D ` ^ Y ^ ^ Z X Y ` \ Z b Y d _ ` Y e  B ? Y X h f \ Y ^ Z X Y b Y a Y ^ Z Y ` \ Z D c a c \ h Y ^ Y Z D   d Z [ c \ e   C ? a \ Z D ` k [ r ` ^ \ c D h s h ` b Y ^ Z X d Y \ ` [ j X f t Z e

  F ? ^ Z [ D ` ^ Y ^ ^ Z X Y ` \ Z D c a c \ h Y ^ Y Z D d Y t c \ e

 

 

  & u ' v + , * - + / + 4 V , * , * w + /   + / - . / , - 4 / , * W /   R 4 , I * + / 4 , + / - /     > ? a Y \ h ] b f X Y t c [ ^ Y e   B ? Z [ Z \ A ] Y t d c l ` d ` Z [ h c e   C ? b Y X c \ t ^ ` j \ Y b b ` k [ e   F ? \ Z j X Z i ` k [ t \ Z j \ Y b b ` k [ e  

 

  G x ' y ) I U , + 4 V 4 T z , , - { 4

  * . - 4 / | / V * }

 

  > ? ~ ] D ` b Y t B ` c X c A ] Y e   B ? Z ^ ` b ` [ Y t � f ] d ` b Y e   C ? � f ] d ` b Y t B ` c X c A ] Y e   F ? ~ ] D ` b Y t � f ] d ` b Y e     

 �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

Page 17: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 17/30

  2 3 4 5 6 7 9 6 4

   

   ! " # $ $ % & % " ' " $ ( ) % ( " $   * # + , # ' " - % # " $ . ( - , # ! ( $ / % # , " ' "   ) ( - " " , " ' ( $     8

 :

  ;

 <

  =   > ?

 :

  @ A 8 ?   8 B

 C

 

 :

  B ?

 :

 

  D 8 ? = B C

  =

 

 

  E # % - " " $ " F " , ) ( ! "

    G H I J K L   > G A M J L   8 J H G N K A = O H L   D A A G A P O H L     Q R ( $ ( - ! " # , % " ' ( $ * ( - % S ( ' # " $ " #

  T # U # V " - % W ! % # $ " # , #

 

  X K N H = L

  > Y G Z Z = L

  8 P Z [ A A = L

  D N A X Z H \ H = L     ] - " # % W - " ) - " $ " ' # #   . ( - , # % W ! " # $ #     B ?

 :

  ^ @

 :

  ? _ @

 :

 B ?

 `

   > 8

 :

  ^ @

 :

  ? _ @ 8

  8  :

 ? a

  ^ @ :

  ? _ : @ ? `

 

  D @ 8 ^ b ? @ _ b 8 ^ @ :

 ?

 

 

  c ! " # $ $ % & % " ' " $ $ $ ' # % # $ " $   % ! (      @ 8   > ? @   8 8   D 8

 :

   

  ! " ( $ $ % & % " ' " $ d # ( - " $ ! " ) e

  ( - - " $ ) ( ! " # # , # + ( - ( " ' - # % W

  ! " % ( " $ f e g     :   > h   8 C   D i `     j # $ % & % " ' " - " # % W  

  k l f E

  _  W k % ! ( % ! ( m n " $ 

 

  = H \ Z H L

  > P Z O X o A P H L

  8 G P A = Z H L   D J J Z H L     p # S / # - ( , / q $ # # - ( $ # r " $   # % , " ' ( ( $ ' % ' % ! ( ) ( -     = o H s N Z \ H = L   > = o H J X t H u Z \ X O H = L

  8 N X H O A s P = v J X t H u Z \ X O H = L

  D s N Z \ H = v J X t H u Z \ X O H = L

 

 

  w # ) - ( ' " x # " $ ' . ( - , # ! # ) ( -     K P = A X Z A \ A A P M Z G = L   > K P J \ A P \ A G Z P H y J Z \ H = L   8 K P N H s G A X H \ A J X t H u Z \ X O H = L  D K P J H P z K P O H \ A O X Z Z J I X Z \ H = L     j { ( - " $ ) " ' ( # ( $ % ' " - # , U % ( $ ! "

  " " - & x # " # - " # % W | x , % # m

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

  d " - ! # ! " - (

 

  } P K P X A J J Z o P A P \ H O I X G Z J = A   \ A = N X A P \ A A P A X s L  > } P K P X A J J Z o P ~ K s G Z J = A X H G N A P v   Y H X G P A P J A = L   8 } P K P X A J J Z o P A H O I X G Z J = A   t = H X t A A P A X s L   D } P K P X A J J Z o P \ A J H G t K = O Z o P = A   t = H X t A J H X L

 

 �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

Page 18: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 18/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ( ) ( * + ,  

   / ( 4 : 4 : ; 4 < = = < 4   > : = ? @ 4 @ A B @ = @ C < B A 4 @     D E D F G H G I J K L M J N O P Q   R E S P I J T J U K H P G Q   V E W P X J X J Y G Q   Z E [ P \ J X J Y G Q  

 

  / ] ^ : @ B 4 = 4 _ : = B ` = 4 @

  B 4 @ 4 = @ a B = 4 @ C 4

  a : 4

    D E D S b   R E c D Z   V E d D Z   Z E D e b     / f g h : i : i @ C 4 @ @ = : = B @   4 4 B A @ B = 4 @ @ ` B 4 j 4 @

  k = ? = 4 @ C 4 < C : = ? @ l : 4 m

 

  ' n o = B 4 < C : = ? C

  C @ C = B @ = C a B = @ 4

  < = B   ' ' n < = = 4 4 ` 4 = 4 k = = C 4 C a B = 4 <   = B 4 o k = a B = C : 4 B 4   o = @ = @ ; 4 > : C 4 = ?   ' ' ' p 4 B = 4 C = = ? C = < = C C 4   @ < = < 4 : = ? C 4 o B @ C   C = > B < = B  

  D E q q q

  R E q r q q

  V E q s q q r q q q

  Z E q q r q q q

  

  / t u 4 : C 4 o 4 B : 4 C

  p C @ 4 4 B @ @ = ` @ @ B i

  < @ B 4 C @ B 4 @     D E Y P U v X T w N G X x \ E Q   R E Y G r v X T w N G X r Y P U v X T w N G X x R \ E Q   V E Y P U v X T w N G X r Y G r v X T w N G X x \ R E Q   Z E Y P U v X T w N G X s Y G r v X T w N G X r Y P U v X T w N G X   x \ R \ E Q  

 

  / y ) 4 @ o : B 4 = @ @ = o < B 4 B @

  < _ :  

 

  D E L N P Y P U G U J H O G U P X Y J X K z \ P N L X r   L U { L H Y P | J X Q  R E F H J K w T L U N G } G H P G \ P N P K G K X J \ H L N G ~ w L   J F L H G N G X L N L T T P U U G I w H G N Q   V E J H P O P U G U } G H P G \ P N P K G K U J � L H L K G \ N L Q   Z E X L F H J K w T L U L U N J X P U K P } P K w J X Y L U J X   G F I J X Q

 

 

  / � , j : B C B a = 4 @ _ : � 4

  < @ = k 4 = @ 4 o = B � @ B : C = �

  o C = > = 4 = ? ; B 4 @ > = 4 C @   C : 4 = @ o 4 B @ 4 o 4     D E P U O L U P L H � G O L U z I P T G Q   R E H L T J Y \ P U G T P U O L U z I P T G Q   V E F H J r L T I J O L U J Y G Q   Z E I L H G F P G O z U P T G Q   

  / / � 4 @ : C 4 o = B 4 C C @ = � � � 4

  � A 4 � : = o = @ = B a B = 4 > o : 4 C 4 <

  ( < 4 = ; � 4 C 4 < o = B = ?

 

 D E L N K L X T w \ H P Y P L U I J K L N G L X I H w T I w H G   I H P K P Y L U X P J U G N K L N J X � T P K J X U w T N L P T J X Q   R E N G G F L H I w H G K L w U U w L } J T G Y F J K L   T J U J T P Y P L U I J s N G \ P J N J O � G T L N w N G H Q  V E K L Y J X I H G H K L Y G U L H G L � F L H P Y L U I G N   ~ w L N G Y G I L H P G J H O � U P T G L } J N w T P J U G   F G H I P H K L Y J N z T w N G X X P Y F N L X Q   Z E K L Y J X I H G H N G L } J N w T P U \ P J N O P T G K L

  N G X T z N w N G X L w T G H P J U I L X Q

 

 �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ¡ � � ¡ � � � � � � � � ¢ � � � � £ � � ¤ �

Page 19: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 19/30

  2 3 4 5 6 7 9 6 4

 

  ! " # $

  % ! &     ( ) * + , - . + / / - .   ) + + , .   8 ) - . + / / - .   : ) . + , .     ; < = ! & > !

  ? @ $

  & !

 

  ( ) A . * , B C . - / A

  ) A - , / D .   8 ) A B / , D .   : ) A . + . E .     F G H I !   &     ( ) J + , K - , +

  ) 8 , A D / K , +

  8 ) : - , D * , A K , +

  : ) : * + K . K , +

 

  

  L M N O P Q M R S T M U < Q N R

    V < ! & W X Y Z [ \ ] ^ ` X ] [ X a "   & b   c  

  ( ) . * , d , K e . K , f A / K , K ( D g + / - .

  . C . A . - / , A C . / A , . D + / - . A . * . + .

  , + D . + h , B / + A , + * B C / - . A ,

  ) i . C . D / A , K j A / A h A . A . - / A   + , * . K B / A + k A / + A C ,   . A , K C - , A / A A . D + / - . A ,   8 ) / A + g A , + . D + / - . A , * , + - , A + , C . +   , K . C . + . A . - - / , A - , D + - / . C   A ( D g + / - .   : ) . - + K , K A + . . K , K * . E d C l D /   - , A , K , C , * B C , K , D / A . K , * , +

  C m D * + / , * . i , C

 

  n c # H > ! H

  % & o &

  H = & # % & p ^ [ Z ^ q a r   s t a u r X v     ( ) w K / D ,   ) x , - / . C / D ,   8 ) 8 . + / D ,   : ) w / B + . C / D ,   

  y ! & & & z M z #

  { &

  | = & M

  & I } } } } } } } } ~ %

  } } } } } } } } $ Q ! } } } } } } } }    ( ) J . � / � A � � . + + - , � ( A h , C .   ) � + . A h � x . � . C l A � � A   8 ) 8 . A . K � � � . d . A . � � � / A h � � . ,   : ) m A K / . � 8 , A h , � � + � � A     � S ! & �

  � ! c ! & !

 

  ( ) - + . - / A K C . � + h . A / E . - / A K C .

  � . - / , A f A / K .

  ) , + D . - / A K K , B C , j � - . * / . C / .   d , - / . C / .   8 ) K / A h + . - / A K C m D * + / ,   . + , � A h . + ,  : ) / A h + . - / A K C B C , j , k / g / - ,   

  � & @

  I R > !

 

  ( ) , D A C + k . A - / D , . C D � A

  - , A + . C , k A - K , +

  ) . * , d - , A D / - . D A . C . - C .   + . B . � . K , + .   8 ) C / D / C . / A + k A - / A D / C / . + A C   h , B / + A ,   : ) . B C - / A h , B / + A , K D , - + � / - ,   

 �� � � � � � � � � � � � ¡ ¢ £ � ¤ ¤ ¥ � � � � � � � � � � � � � � � ¡ ¢ £ ¦ § ¤ ¤ § ¤ � � � ¥ ¤ ¦ � � ¨ � � � � © � � ª «

Page 20: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 20/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ( * + , - . / - - , + 4 - + . ,

  4 + + + - , / - 4 / : ; + ,

  4 + 4 + + - (     < + 4 - +   = ( > / 4 / (   = = ( ? ; , / / (   = = = ( > / , + 4 (    * + + +

  - ( A - B / (

  C ( ? / , / - 4 / (

  . ( D - . / (     E F G H I J G G H K J G G G H L   M F G H L J G G H K J G G G H I   N F G H I J G G H L J G G G H K   O F G H K J G G H L J G G G H I     & P ( Q - . - 4 - . + 4 / . - R + , - S ; + 4 4 - D 4 - +

 

 E F T U V I W W X Y Y I W Z [ L X [ \ Y ] L ^ X U [ ^ W U T X V

  _ I ` V U V a V ] [ W U _ U W L Z V ] X [ U V U [ X ^ W I V

  W U b ] X [ U V T U Y c Z [ T X d

  M F _ W X _ ] L ] I W Y I L I W W U W I I W c I c U [ ^ ] V ^ I   U [ ^ W U Y X V e V ^ I T X V f [ ] T X V T U E c g W ] L I   h Y I f [ ] i [ T U j U _ k K Y ] L I V l X L ] I Y ] V ^ I V   l X m ] g ^ ] L I V d   N F \ X c U [ ^ I W Z [ I U L X [ X c ` I b Y X K I Y d   O F ] [ V ^ I Z W I W U Y Z V X T U I W c I V [ Z L Y U I W U V   U [ b Z U W W I V _ X V ^ U W ] X W U V I n o p q d  

 

  & & ( r , R . ; + : ; + s / 4 - 4 t u - +

  , - / - + 4 / . - . 4 + / v R +

  - s - C 4 / . - 4 w 4 + . / C / 4 w - , - . + - 4 /

  4 C - 4 - 4 - ; . , + - 4 + x y , z - . + 4   ; R + , - + + 4 - - y / . - . s / +   - . s / . + , + . . + . + , C 4 +   R +     E F { W I ^ I T X T U { Y I ^ U Y X Y L X d   M F { W I ^ I T X T U | ] X ^ X   N F } I L ^ X T U ~ I W V X m ] I d   O F { W I ^ I T X T U Y E ^ Y [ ^ ] L X � X W ^ U d

 

 

  & � ( > + . z : ; + + . / R + 4 y . + ,

  / / . / R + , . - C / , / . -

  s / - , + R + , / , � � + , - � ; 4 - R + ,   + + (     E F } I � I W c I T I d   M F � Z U W W I � W ` I d   N F O U V I _ I W ] L ] i [ T U Y c Z W X T U M U W Y ` [ d   O F � Z U W W I T U Y X V M I Y L I [ U V d   

  � � ( � + R + . / - - , - . + + + ,

  . 4 - / + R + , - R / / -

  + . - - . / - , + x - C / + 4 - .

  + 4 . - R , / C 4 + R + R - 4 + + . / -

  + - - , (     E F � Y X K I Y ] � I L ] i [ d   M F e Z W X L U [ ^ W ] V c X d   N F N X c Z [ ] V c X d   O F G c _ U W ] I Y ] V c X d    

  > = � � � * = r � � ? � � = � �

 

 

  � t ( r R + � R + , - � / 4 - . / y R +

  � ; + 4 v - 4 w - , ; - . - ; - R + , -   = R + + R + . / - R + ? v � / .     E F Y I ] [ m I V ] i [ [ I _ X Y U i [ ] L I I e V _ I � I h Y I   I K X Y ] L ] i [ T U Y I U V L Y I m ] ^ Z T d   M F Y I V j U \ X W c I V M X W K i [ ] L I V h Y I   I K X Y ] L ] i [ T U Y I U V L Y I m ] ^ Z T d   N F Y I ] [ m I V ] i [ [ I _ X Y U i [ ] L I I e V _ I � I h

  Y I V j U \ X W c I V M X W K i [ ] L I V d

  O F Y I V � Z [ ^ I V T U Y I } W X \ U V I h Y I I K X Y ] L ] i [

  T U Y I U V L Y I m ] ^ Z T d

       

 �� � � � � � � � � � � ¡ ¢ £ ¤ � ¥ ¥ ¦ � � � � � � � � � � � � � � ¡ ¢ £ ¤ § ¨ ¥ ¥ ¨ ¥ � � � ¦ ¥ § � � © � � � � ª � � « ¬

Page 21: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 21/30

  2 3 4 5 6 7 9 6 4

 

  ! " ! # $

  %    &   ( &   ( ( ) !    ) ! " !   * % + ! $ ,

  ! $ % ! ,

  - ! % !

  . ! ! -

  % ! ! $   !   ) ! $ !   % ! !   ) ! $ ! $   ) ! ! $ / % " ! ! !     8

  : ; 8

  < ; 8

  = 8 ;

 

   > ) $ - $ /   ? @ $ !     < A B C D 8 E F G B H I E I I J   : K G L M F C N 8 D O I B C K C I B P 8 F J  < < L I Q L C D 8 D O I B C R G L B 8 E L R L C A E D 8 L   8 L I Q B G S L G J

  = T D G M B C P G E L B U L I ; C M L I E B J

 

 

 

         

 

  V * ) ! ! $ / W X Y Z [

 

  ( \ !   ] ^ @ %   ( ( ! " $   _ !   ( ( ( . ! " $ ` ! !   ( a \ b " ( %   "  

 a . ! " $ ` % $

 

 

  c   : c d d   < c d   = c d     Y e % " ! !   % \ f " ^  

  g B Q R B E L C R G D I 8 D R D L B I L G B B C B 8 8 D O I

  C R 8 D h D 8 8 D O I B C R A Q J

 : H F R G B Q D O I B C Q C D B G E B Q R i C D 8 Q

  C G B R G B Q D O I J

  < K L C A E D 8 B 8 L I 8 D C D 8 D O I B C   h L G E C B 8 D M D B I E L B C M D C D 8 D J   = = D S D Q D O I B C E B G G D E L G D L B I j L I Q   M D C D E G B Q C 8 B I E G C D j 8 D O I   M D I D Q E G E D S J     k . ) " $ * ^ %

  ) ? W l W ! $ -

 

 

  h F I G F I M L S D M D B I E L B L R L Q D 8 D O I

  C D 8 E F G B = A j J   : D M R F C Q G C G B B C B 8 8 D O I B C N B I B G C   = A j J   < C D M D E G C R G E D 8 D R 8 D O I B C L Q L G B G L Q   B I C R L C A E D 8 J   = 8 L I Q E G F D G F I M L S D M D B I E L h S L G C B C   8 I D E F G B U B G L J

 

 

 mr s t u v w x n y z n u { | } ~ o � o p n r s t u v w x n y z n u { | } ~ � � � o o p � � m v � v r s t � y n � �

Page 22: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 22/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

 & ' ( * + , - . / 4 /

  : 4 - / 4 4 - ;

  < = > ? @ = A B C     E F G H I J K L M N K O P Q R S   T F U H V W J K X L Y H Z J [ \ J H H O [ S   \ F ] ^ _ J K L \ ^ K ` O R J [ S   a F E N O H J K ` L b L ` K Z P V O _ S     & c ( d ; 4 ; e ; f g 4 ; ; 4 ; 4

  h e 4 h ; i g j ; k g 4 ;

  l - ;

 

  E F X K O J X m Q R ` O H O n m ` L X L H O X W m I L S

  T F o m K p J ` O H q K J W J ` L ` O ] m N K O \ L p O K X m L S   \ F X K O J X m Q R ` O H T J R X L ` O r s t m X L S   a F L K P J R m _ J X m Q R ` O H J X L p m [ m Q R ` O   X J K K O W O K J [ S     & & ( d f u f 4   4 f g 4 v w ; - ; x / f 4 y x

  ; - u 4 l ; - - ; x

  l - z z , - { & | } y { & ' ~

  f

 

  E F U H J R O t O R J H S   T F a O [ J K K L H H L X L p � J K W m ` L S   \ F r m H J P K L p O t m X J R L S   a F � R m ` J ` R J X m L R J H S     { ~ ~ ( � h e u f e ;   h e 4  

  E F ] V m [ Y X � O I O K K Z J G H I J K O _ � � L [ s ] Q � O _

  U L K W m H H L S

  T F r m P V O H ` O H J r J ` K m ` � V K W J ` L � � L [ s

  ] Q � O _ U L K W m H H L S   \ F r m P V O H ` O H J r J ` K m ` � V K W J ` L � \ J K H L [   J H m R J [ ` O � L K W J K m S   a F \ J K H L [ J H m R J [ ` O � L K W J K m � ] V m [   Y X � O I O K K Z J G H I J K O _ S    

 

  i � � � � + � d � +  

   { ~ { ( � ; ; 4 ; , - ; ; - : (    E F \ H Z p J t S   T F q O p J S   \ F a O [ J K K L H H L S   a F E R s X ` L W J S   

  { ~ } ( � : , - ; e ; / ; ;

  / ; 4 x . ; / ; l - j ;

  , - ; l y - �

  l ; f 4 ; (

    E F � L I O H J S   T F � J K [ J S   \ F a K J p J S   a F \ V O R W L S     { ~ � ( � : 4 ; f g , -   / ; � / / ; / 4 ;

  / ; j ; y h - ; 4 - ;

  ; y - 4 ; g x / e ; 4 ; , -

  ; x ; - ; - / e f ; (

 

  E F q K J P O ` m J S   T F a K J p J S   \ F q K J P m X L p O ` m J S   a F Y R W K O p s [ S   

 �� � � � � � � � � � � � � ¡ ¢ � £ £ ¤ � � � � � � � � � � � � � � � � ¡ ¢ ¥ ¦ £ £ ¦ £ � � � ¤ £ ¥ � � § � � � � ¨ � � © �

Page 23: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 23/30

  1 2 3 4 5 6 8 9 5 3

 

  ! " ! # # $ ! #

  % & ' (     * + , - . / . , - . / . , . - - . .   7 . / /   : ; < = / , . > = / . ? @ > < > . <   . 7 . / / A   B . , C . , . D E . , 7 7 ,   B . , < / < , . . , / F . G   B . , = 7 > C . . . H 7 , . / , I J

  : ; < = / , . > = / . ? @ > < > . <

  . 7 . / / A

 

  L ! # M

   N O P Q R S T Q U V W Q W W X P Q Y V W Q Z   [ O P \ ] Q ^ X _ V Q P W X P Q Y V W Q Z   ` O P \ a S b X _ R P S \ W X P Q Y V W Q Z   c O P \ X a b V _ V ^ S Q P W X P Q Y V W Q Z     d M e  

  f / / < . 7 < g 7 . / . F . h / . i E F ,

  = / < . H , , < = / < , < / < , . C . > = 7 < ,

  . - 7 < / F E < / . , ? 7 7 7 . I / 7 j . ,

  . 7 7 > > < , k . . E < , l , 7 E . 7 . g / m

  E < < < . 7 j , < = / < = < . 7 / . 7 . H   / . . < , E < / . . n / . 7 .   . 7 = ? , . o 7 . , J J J    L ! $ #   p      N O q b V U \ Z   [ O P r _ V U \ Z

  ` O W V W s U ^ V U \ Z

  c O U \ ] X W V Q Z

 

 

  t u v ! w   # ! # # x y x " !   # v # !   M ! ( # ! w &   z ! !    N O { X \ U P Q a V U V a ] \ Z   [ O | Q } T S Q _ W V a ] \ Z   ` O ~ X Q P V a ] \ Z

  c O S _ _ X Q P V a ] \ Z

 

  �

  ! ( w p p

  $    + 7 I / I C ,   + 7 j < / , . / < 7 7 . I m , 7 . < 7   . , E m . , . / J B I / - 7 C .   . , < E < E / 7 . D g ?   j I < . . � / . > < J B . . C I m . 7   / < , / < E < = i . 7 < F E < 7 > <

  . - , . / > / m 7 < , / . 7 . , . , .

  = . / ? . . 7 D < / H < . J � . , 7 . < F

  = . , - < E < , 7 m , / . 7 < C @ 7 D < /

  C , . . . 7 / . . g ? . = / / J

  � � < , l f / / . < 7     N O � } ^ _ X ] q a Z   [ O ` S X } ^ \ Z   ` O � } a Q � \ Z   c O � s � S P Q Z     � L $ w

  � # �

 

  y v v !

  # #

  y y L M v #   y y y � # $   $ $ �   y � � � # $   $ ! " # (   #   � � # # ' $ $

  #

 

  N O � � � � � � � �

  [ O � � � � � � � |

  ` O � � � � � � � |   c O � � � � | � |   

 �� � � � � � � � � � � � ¡ ¢ £ � ¤ ¤ ¥ � � � � � � � � � � � � � � � ¡ ¢ £ ¦ § ¤ ¤ § ¤ � � � ¥ ¤ ¦ � � ¨ � � � � © � � ª ª

Page 24: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 24/30

  0 1 2 3 5 2 6 3 7 8 9 2 9 3 7 7 9 3 2 9 3 7 5 2 6 3 7 2 9 2 1 3 7

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ( ) + , - . / - , - / . / . 4 - , - /

  , / - , : . ,

    < = > ? @ @ ? A B C D E F @ D G ? H I G A @ J K A J @ ? K D L F M I N ? O  P = > ? @ @ ? A B C D E C I @ G D H I G A @ J K A J @ ? B > A I > G ? O   Q = R @ ? L S A B K D E F @ D G ? H A I > G B T > K D > G A ? > A I O   U = M V @ B K D E F @ D G ? H I G A @ J K A J @ ? > ? @ @ ? A B C ? O     & & ' ) + / - W - W / X Y / Z  

  [ . \ ] ^ , . , _ ` : - / . ) a b : . /

  + / / - W . / W . / ) ^ : c , _ d ,

  e W , f , . - _ & ( g h _ i ) j k )

 

  < = P B l M B D m @ S n B K ? O   P = U I @ I G J L I > O   Q = o I L I @ D m @ S n B K ? O   U = U I Q B A ? O    

  p f q p r a [ s a

 

 

  & & & ) f - i / ] / b , , - , -

  - c i / , b , , - W / / -

  , . . - , t  

    < = L ? > A D O   P = > u K M I D O   Q = n D > R D D K I S > B K D O   U = ? m J ? O     & & j ) + / d . . / ^ / . d W . / . / - / / -   / -

 

  < = Q v B ? F ? G H w I @ ? K @ J x O

  P = w I @ ? K @ J x H y M ? z K ? M ? O

  Q = y M ? z K ? M ? H { ? z ? K ? O

  U = { ? z ? K ? H | J I @ @ I @ D O    & & } ) f b W , / - b / ~ , . - . - . / -   . : , - - , / ] /     < = D @ A I ? L � @ B K ? O   P = � J @ ? L � @ B K ? O

  Q = � J @ I G A I R I < G B ? O

  U = � I R B D { @ B I > A I O

 

  & & � ) + / - b / ~ , . - . - . / - / W / W

  W - . , i / / / - . i . - /

    < = M D G @ V D G O   P = M D G m M ? K B ? @ I G O   Q = M ? G ? m J ? G G J F I @ n B K B ? M I G O   U = M ? G ? m J ? G G J l A I @ @ S > I ? G O     & & k ) + / . t / W . / . - W / , b /   � � W � / / / ` W / ` , , -

  /

 

  < = A ? B m ? O

  P = I G A I F ? O

  Q = F @ ? R I @ ? O   U = G I M C ? O     & & h ) f / W b , � t c , / . � , ,   / / b t - X . / � W , . / X ,   . / . , - � /     < = M ? K D L l J G A B T > R I M F I A @ T M I D O

  P = I M J G D R I ? I @ D G D M I G O

  Q = M ? R I G A @ J K K B T > R I M ? K ? F ? R I D x D > D O

  U = M ? F @ I G I > K B ? R I M M J C B ? S K B R ? O

 

   & & g ) + / - , - \ . / - b / ~ , .   , . / t / i , � / t   b W , - , Z    � ) a - / q . / )   � � ) f W . , i / q / )   � � � ) a - / q / )

  � e ) a - / ^ . , / )

  e ) f W . , i / ^ . , / )

 

  < = � H � �   P = � � H � � �   Q = � � � H � w   U = � w H w      

 

 �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ¡ � � ¢ £

Page 25: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 25/30

  2 3 4 5 6 7 9 6 4

  ! "

  " " ! # " $ # "

  % & ' ( ) ! ) * + !     - . / 8 : ; < = < > ?   @ . A = < B C D E = F G : H < 8 I ?   F . B J < @ = 8 : - = E < ?   K . L M < N 8 < : O 8 ?     P Q ! * " R S T

  Q ( " ! T U V

  W R * ! * " "

  " & & !

 

  - . C 8 < ?   @ . X I = ?   F . E X < ?   K . X < ?     Y Z [ ! " " ( !   & ! # V  

  - . A \ B ?

  @ . F > > ] > 8 ?

  F . F > > A J ^ ?

  K . / < > > F J C G ?

        

 

 

 

 

         

 

 

 

 

     

 _d e f g h i j ` k l ` g m n o p a q q r a b ` d e f g h i j ` k l ` g m n o p s t q q t q a a b r q s _ h u h d e f v k ` w x

Page 26: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 26/30

 0 1 2 3 4 5 6 7 0 9   1 2 3 4 5 6 7 9 0   1 2 3 4 5 6 7 9   1 2 3 4 5 6 7 9   1 2 3 4 5 6 7 9   1 2 3 4 5 6 7 9

  1 2 3 4 5 6 7 9

  1 2 3 4 5 6 7 9 0   1 2 3 4 5 6 7 9  0 1 2 3 4 5 6 7 9  0 0 1 2 3 4 5 6 7 9  0 1 2 3 4 5 6 7 9  0 1 2 3 4 5 6 7 9  0 1 2 3 4 5 6 7 9 0

 0 1 2 3 4 5 6 7 9

 0 1 2 3 4 5 6 7 9 0  0 1 2 3 4 5 6 7 9  0 1 2 3 4 5 6 7 9  0 4 4 2 0 9 0 9   4 4 2 0 9 9   0 4 4 2 9 0   4 4 2 9

  4 4 2 9

  4 4 2 9 0   4 4 2 9 0 9 0   4 4 2 9   4 4 2 9 0 9 0   4 4 2 9 9 9   4 4 2 9 0   4 4 2 9

  4 7 4 2 ! " 4 2 # $ 2 6 % 4 4 2 & 7 4 2 ' " ( " $ 4 2

 + , $ 4 3 4 4 3 3 4 4 7 - 4 " 2 7 . " 3 4 4 " ( 2 4 4 7 4 7 " 4 , 4 / 0 0

   

 

 

 

 

 

     

 

 

 

 

 

     

 

 

 

 

 

     

 

 

 

 

  8 : 8 ; 8 < = > 8 < ? < : 8 8 @ A 8 B A > 8 < ? ;

 = C D E F G H I J K E G I H F C I ? D L I ; D J M F D J H I N O C C D N H I ? F C D J M F D J H I

 PU V W X Y Z Q [ \ Q X ] ^ _ ` R a a b R S Q U V W X Y Z Q [ \ Q X ] ^ _ ` c d a a d a R R S b a c P e U V W f [ Q g R

Page 27: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 27/30

  2 3 4 5 6 7 9 6 4

      !   " #   $   % " !   $ !

  & %

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

 " % ' ( #

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

 $ " ' ( $ #

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

 + , - . / . / , - 8 - / - ; < , , - ; / , - / -

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

 >C D E F = G H ? I J ? F K L M N @ O O P @ A ? C D E F = G H ? I J ? F K L M N Q R O O R O @ @ A P O Q > = S = C D E T I ? U O

Page 28: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 28/30

 0 1 3 4 5 6 7 8 9 1  0 3 4 5 6 7 8 9  0 3 4 5 6 7 8 9  0 3 4 5 6 7 8 9 1  0 0 3 4 5 6 7 8 9 1 1  0 3 4 5 6 7 8 9  0 3 4 5 6 7 8 9

 0 3 4 5 6 7 8 9

  3 4 5 6 7 8 9   7 5 9 1 1   1 7 5 9 1 1   7 5 9 1   7 5 9   7 5 9 1   0 7 5 9

  7 5 9

  7 5 9 1   7 5 9 0   7 5 9 0 1   7 7 9 7 ! 9 1 1   1 7 7 9 7 ! 9 1   7 7 9 7 ! 9 1   7 7 9 7 ! 9 1

  7 7 9 7 ! 9 0 1

  0 7 7 9 7 ! 9   7 7 9 7 ! 9 1   7 7 9 7 ! 9 1   7 7 9 7 ! 9   7 7 9 7 ! 9 1   7 7 9 " ! # $ % 7 8 1   1 7 7 9 " ! # $ % 7 8

 & ' ( ) * + , - . / ) + - , * ' - ( 2 - ( / * ( / , - ' ' ( , - * ' ( / * ( / , -

     

 

 

 

 

 

     

 

 

 

 

 

     

 

 

 

 

 

     

 

 

 

 

  ! 9 " ! 9 : 7 ! 8 7 9 ; 5 7 8 < 9 ! 6 = 7 8 9 > " ! 9 ? ! 7 ! 5 9

  B 4 5 9 C 9 9 C ! C 9 9 ! ! % 9 6 ! " ! ! ! 8 8 7 D C 9 9 7 ! 9 9 9 7 8 ! 8 7 9 4 9 E F # G 1

 HM N O P Q R I S T I P U V W X J Y Y Z J K I M N O P Q R I S T I P U V W X [ \ Y Y \ Y J J K Z Y [ H ] M N O ^ S I _ X

Page 29: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 29/30

  2 3 4 5 6 7 9 6 4

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

  ) ) ' *

  ) + , #   ) " + , *   ) + , !   ) + , $ " !   ) $ + , " !   ) % + , " " *   ) & + , " #

  ) ' + , " #

  ) + , " " !   ) + , !   - . / !   " - . / " (   - . / (   - . / " " #   $ - . / " (

  % - . / " " !

  & - . / " !   ' - . / " $ (   - . / " % *   " ) - . / " % " (

  8 : ; 8 8 < = 8 > : ? : 8 A B A 8 < : ? : 8

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

 DI J K L C M N E O P E L Q R S T F U U V F G E I J K L C M N E O P E L Q R S T W X U U X U F F G V U W D C Y C I J K Z O E [ \

Page 30: Examen Muestra Unam - Ingenierias

8/6/2019 Examen Muestra Unam - Ingenierias.

http://slidepdf.com/reader/full/examen-muestra-unam-ingenierias 30/30

  3 3 1 3 1 2 3 1 3 1 2 6 2 3 2 5 2 7 2 6 2 9 3 1 3 9 1 2 7 3 1 3 6 3 6 9 2 9 3 1 3 ! " # $ % %

  & ' ( ) * ) + & + ,

  . / 4 : /

  ; 2 7 5 2 2 6 2 3 2 2 7 1 3 1 3 3 5 5 2 7 9 6 3 1 6 3 7 5 9 9 2 7 < 2 7 2 1 2 7 2 3 1 2 6 5 3 5 2 6 2 3 2  5 2 7 2 6 2 9 = 2 9 2 5 7 6 6 9 2 7 5 2 6 # #

 %

 >

 #

  = 3 5 2 ? 1 1 3 1 = 7 3 3 3 7 = @ A 3 5 2 1 2 7 2 7 3 7 2 6  2 3 2 B  ! 9 5 2 2 6 9 2 < 2 3 1 5 2 7 2 2 7 3 1 6 C 2 5 1 7 9 5 2 D @ 1 3 7 2 6 5 3 5 2 6 2 3 2 E B

  F 3   5 @ 3   3 7   6 9   5 = 3   6 9  G   3 7 1 2 7   2 7   3 7 B

  F   6 2   3 6 3 7 9   9 2   2 3   ? 6 3 < 2 2 2 1   9   9   1 3 3   6 9   H 3 1 5 2   7 2   2   I 3   1 1 2   9   7 9 B  J K L M   O P Q L R S T   U T   V P W X X X X X X X X @ 1 7 B X X X X X X X X 9 B

 Y 7 3 I 6 % Z

 [ 7 9 3 % \

 ! 3 2 9 3 7 # \

 ] 9 2 1 3 1 3 % $  2 1 3 ^ 3 % $ _ 9 6 3 % $ ` 9 3 % $

 a 9 7 1 9 3 9 b 2 1 7 3 6 % $

 a 9 7 1 9 3 5 2 ! c 9 % $

 d e d f g h i j

 k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k

 k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k

 k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k

 k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k

 k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k

 k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k

 k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k

 lq r s t k u v m w x m t y z { | n } } ~ n o m q r s t k u v m w x m t y z { | � } } � } n n o ~ } l k � k q r s � w m � �