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2partetransformda
1. 1. Resolución
2. Resolver
1
( ) ( )
( ) 1 2 3
3 2 ' 2
( ) ( )
' '
( 3) ( 1) (2)
( 3) ( 1) (2)
1
19 37
2 1 3
19 37 ; 2 1 3
0 3; 1; 2
2 5 6 3 4 5
10; 6; 15
20; 18; 75
19 37
2 1 3
s s
s
s s
s
L
s s s
Solucion
P s Q s s s
Como Q entonces
Q s s s Q s s
Q Q Q
P P P
s
L
s s s
( 3) ( 1) (2)1
' ' '
( 3) ( 1) (2)
1 3 2
3 1 2
19 37
2 3 5
2 1 3
t t t
P P P
L
Q s Q s Q s
s
L e e e
s s s
1
3 3
3 3 2 2 2 2
2 2
3 3 2 2
2 2 2
2 2
2
2
2
1
1 1
( 1)( )
1
1
1
0; 0 ; 1
1
3
1
3
2
3
1
L
s a
Solucion
A Bs C
s a s s as a s a s as a
A s as a Bs C s a
s a s a s as a
A s as a B S as C s a
A B s s aA aB C a A aC
A B aA aB C a A aC
A
a
B
a
C
a
s
3 3 2 2 2 2
1 2
2 2 2 2 2 2 2 2 2
1 1 2
3 3
1 1 2 1 1 3 3 3
cos sin
3 3 3 3 3 3 3
a
t
at
s a
a a s a a s as a
s a a
L e e t
a s a a s as a a a a a a
2. 3. Resolver
4. Resolver
2
1
2
2
2 2
22 2
2
1 1
2 2
1
2 3
1 1
Re
2 3
1 11 1 1
2 3 2 1 1 1
1; 2 2; 2
5
4
1
4
1
2
2 3 5 1 1
4 1 4 11 1 2 1
s s
L
s s
solucion
s s A B C
s ss s s
s s A s s B s C s
A B A C A B C
A
B
C
s s
L L
s ss s s
s
L
2
2
2 3 5 1 1
4 4 21 1
t t ts
e e e
s s
1
2
1 1 1
2
2 2
1 1 1
2
2 2
1 2 3
4 1
1
1 2 3 1 2 32
1 14 1 4 4
4 4
1
1 2 3 1 3 1 32 sin cos
1 14 1 2 2 2 2 2 2
4 4
s
L
s
Solucion
s s
L L L
s s s
s s t t
L L L
s s s
3. 5. Resolver
6. Resolución
'
' '
0
2 2 2 2
2 2
2
22
sin( ) cos( ) cos( )
( ) ; ( ) ; ( )
1
sin( ) ; cos ;
sin( ) cos( )
1 1
1 1 1
1 1
1
1 1
1 1
11 1 1
t
at
t
x x t t t e
Solucion
L x sL x x L x sL C L x L
a s
L at L at L e
s a s a s a
L x L x L t L t L e
s
sL C L
s s s
s
s L c
s s
s C
L
ss s s
x L
1 1 1
22
1 1 1
22 2
1 1 1
1 11
1 1 1
; sin( );
sin( )
at t
L CL
s ss
L e L at L te
s a s a s a
x t
2
5
0
2
1 2
1 1
5 5
0 0 0 1
2 2
2
2 23
2 2
2
2
1;0 1
( )
1;1 2
( )
( )
1
( 1)
( )
1 1
1
1 1
( )
1 1 1 1
1 1 5 1
tanh
21
t
s
s st
t t
s s
s s s
s
s s s s
s
s
t
f t
t
e f t
L f t dt
e
e e
e dt e dt s s
L f t
e e
e e s
e es s s sL f t
e s e s e s
e e
ss e
1
x
y
e
4. 7. Resolver
8. Resolver
'
(0)0
'
0
2
2
2 2
( ) 2 2
1 1
2 2
(
1; 1
1 1
ln(1) ; 1
1 1 1 1
1; 1
3 3
1 1 1 5
1 1
1 3
1 1
1
sin( ) cos( )
1 1
Re
t
t
x
x xdt x
Solucion
L x L xdt sL L
s s
s
s L L
s s
s
L s
s s s s
L
s s
Donde
s
x L L t t
s s
mplazo
L
) ( ) 0
0
( ) (0)
1 1
2 2 2 2
1
1 1
5 3
1
;
3
5
sin( ); cos ( )
x x
t
x
x
sL x sL
L xdt L L
L L L
a
L t L a t
s c s c
'' '
(0) (0)
2
2
2 2 2 2 22
( ) 2 2 2
1 ; 2 ; 1
1
2 1
1
1 2 1
1 2 1 1 2 1
1 1 1 1 11
1 2 1
1 1 1
1 cos sin
x
x x x x
Solucion
s L s L
s
s L s
s
s s s
L
s s s s s ss s
s s
L
s s s s
x t t
5. 9. Resolución
10. Resolución
'
0 0
''
''
''
2 '
( ) 0 0 ( )
2
( ) ( )
2
( )
1 2
1 2
1 2
400 ; 2 ; 50
0; 10
4 0
4002 200
50 200 0
4 0
5 4 0
10 4 0
4 10
10 4
5 2 4
5 2 4
5 sin(2 )
s s
s s
s
k
w s m M kg
m
x x
L x L x
k ws
x x
x x
s x x x x
s x x
x s
L s
L s
L s
x t
1
2
1 1
2 2
1 1
2 2
1
2
3 5
7
3 5
7 7
5 1
3 5
7 7
7 1
3cos(7 ) 5
77
5
3cos 7 sin 7
7
s
L
s
Solucion
s
L L
s s
L L
s s
t L
s
t t
6. 11. Resolución
12. Resolución
2
1
4 2
2
4 2 2 2
2 2 2
2
2 2 2 2
2 8
4
2 8
4 4
2 8 1 4
4
2 8 4 4
1 1
0; 2; 1; ;
2 2
1 1 1
2 cos(2 ) sin(2 )
2 2 2
s s
L
s s
Solucion
s s A B Cs D
s s s s s
A B Cs D
s s s
s s s
s s s s A s s Cs D
s B D C A
t t t
1
2
1 1 1
1 1
2 2
1
2 2
0
0
3 5
7
( ) ( ) ( ) ( )
1 1
1 1
sin( )
( ) ( ) ( ) cos( ) sin( )
sin( ) sin( )
1
sin sin cos cos
2
t
t
s
L
s
Solucion
L f s g s L f s L g s
L L
s s
a
L at
s a
f t g t f x g t x dx v dv v
x t x dx
A B A B A B
1
0 0
0 0
0 0
1 1
cos 2 cos( )
2 2
1 1
cos 2 2 cos( )
4 2
1 1
sin(2 ) cos( )
4 4
1 1 1 1 1
sin( ) sin( ) cos( ) cos( ) cos( )
4 3 2 2 2
t
t t
y t
x t dx t dy
x y dx t dx
x y t
t t t t t t t
7. 13. Resolución
14. Resolución
2
1
2 3 2 ' 2
( ) ( ) ( )
' ' '
( 1) (2) (3) ( 1) (2) (3)
22
( 1) (2)1
' '
( 1) (2)
2 4
2 1 3
4; 4 6 1,2,3; 3 8 1
2; 4; 14; 12; 3; 4
2 4
2 1 3
s s s
t t
s
L
s s s
Solucion
P s Q s s s raiz Q s s
Evaluar
P P P Q Q Q
P e P es
L
s s s Q Q
3
(3)
'
(3)
2 3 2 32 4 14 1 4 7
12 3 4 6 3 2
t
t t t t t t
P e
Q
e e e e e e
2
2
2
2
2
1
( )
( ) 3 2
3
3
3
3
1
( ) 2 1
1
10 ( ) 2 1
0,5
10 2 ( ) 2
2 2
( ) ( )
( )
( ) 1
2 1
1 2
5 1 2
s
s
s
s
ir i t dt t
C
i t dt t
i t dt t t
donde i t dt f t
Si i t dy t t
Si L i t dt t
i
Si
s s s
t
i s
s s
s t
i
s s
8. 15. Resolución
16. Resolución
1
1
1
1 1
3
3
1 3
3
( )
1 3
3
1 3 1 3
3 1
3 3 1 ; ;
2 2
1 3 1
( )
2 1 2 3
1 1 3 1
( )
2 1 2 3
1 3
( )
2 2
t t
s
L
s s
Solucion
s
f t L
s s
s A B
s s s s
s A s B s B A
f t L
s s
f t L L
s s
f t e e
1
( ) ( )
( ) 1 2
2 '
( ) ( )
2 3
( 2) (3)1
'
( 2) (3)
1 2 3
2 11
2 3
2 11; 2 3
0 5 6 0; 2; 3
6; 2 1
2 11
2 3
2 11 15 5
3
2 3 5 5
s s
s
s s
t t
t t
s
L
s s
Solucion
P s Q s s
Donde Q s
Q s s Q s
P e P es
L
s s Q Q
s
L e e
s s
2 3t t
e e
9. 17. Resolución
18. Resolución
19. Resolución
1
3
3 4
0 0
4 3 3
0
1
3 1
1 1
( ) ; ( )
3 1
( ) ; ( )
( )
( )
4 4 4 4
t t
t t
t t n t
t
t u t t t t
L
s s
Solucion
f s g s
s s
f t e g s e
f t e e dv e dv
e e e e e
f t
1
1
1( )
0
1 2
1 2
ln
1
1 1
ln 2 ln( 1)
( )
( ) 1 1 1 1
2 1
s
t t
s
L
s s
Solucion
L s s
s s
f
L f u du
s
f t
L e e
t t s s t
10
( )
( )
2
( )
( )
( ) (0) ( )
2
( )
( )
( ) 5 1
im
t
di t
L R E
dt
di t R E
im
dt L
di t R E
L i t L
dt L L
R E
SL i t i L i t
Ls
R E
s L i t
L Ls
E E A B
L i t
RR L s sLs s
LL
i t e
10. 20. Resolución
21. Resolución
1
32
3 2 322
3 3 2 2
1 1 1 1 1
3 22
1
2
1
22 2 2
1 2 2 2
1 1 1 1
0; 2; ; ; ; ; 0
8 8 16 4
1 1 1 1 1 1 1 1
16 8 8 2 42
s
L
s s
Solucion
s A B C D E
s s ss s s s
s As s B s Cs s Es
s s B C A E D
s
L L L L L
s s ss s
3
1 2 2 2
32
1
2
1 1 1 1 1
16 8 8 82
t t
s
s
L t e t e
s s
1
1 1
1 1 1
3
1 1
3
1
1
: ( ) ( )
3 1 3 1
ln ln ln( 3) ln( 1)
1 1
3 1 1 1
ln
1 3 1
t t
s
L
s
Solucion
d
formula L f s L f s
t ds
s d s d
L L L s s
s t ds s t ds
s e e
L L
s t s s t
11. 22. Resolución
23. Resolución
3 2
2 2
3 2
2 22 2
3 2 2 2 2
3 2
1 1 1 1
2 22 2
5 2 5
( )
4
5 2 5
44
5 2 5 4 4
5 2 43 14
0; ; ; ;
4 9 9 9
43 14
5 2 5 2 1 5 1 9 9
9 4 44
s s s
y s
s s
Solucion
s s s A B Cs D
s s ss s
s s s As s B s s Cs D
s B A C D
s
s s s
L L L L
s s ss s
3 2
1 1 1
2 22 2
3 2
1
2 2
5 2 5 2 5 43 14 2
9 4 9 4 9 2 44
5 2 5 2 5 43 7
cos(2 ) sin(2 )
9 4 9 94
s s s s
L t L L
s ss s
s s s
L t t t
s s
2
1 3 4
1 2 3
2
1
3
2
2
4
2
3
1
3 7
( ) ; ( )
3 4 1
3 7 9 9 7 7
lim 3 ( )
4 1 3 4 3 1 4
3 7 16 12 7 3
lim 4 ( )
4 1 4 3 4 1 5
3 7 1 3 7 3
lim 1 ( )
4 1 1 3 1 4
t t t
s
s
s
s s
y s L f s C e C e C e
s s s
Solucion
s s
C s f s
s s
s s
C s f s
s s
s s
C s f s
s s
1 3 4
20
7 3 3
( ) ( )
4 5 20
t t t
L f s F t e e e