Solución taller 2 de matemáticas discretas

1. EJERCICIOS PARA EL TALLER 2
a.

2. b.

3. CAMINO MAS CORTO = 1- 9 →9+8+7+3+1=74
previo opuesto
/ * 3*8 24
raiz ^ 24^3 13824
raiz ^ 13824^2 191102976
- + 191102976 + 191102982

4. 6
- +
191102976 +
4 191102986
^ raiz
191102986 ^
1/2 13824,0003
x 13824,0003

5. previo opuesto
/ * 2*10 20
raiz ^ 20^2 400
- + 400+4 404

6. a.
A’=2x
B’=2x+(1((x-1) ^2))
C’=1/(2x/1)+(1/(x-1) ^2)=2x+1=1/2x
D’=(2x/1)+(1/x)=((2x) ^2+(1/2x))=1+2x
E’=3sen^2(1+2x)*cos(1-2x)
F’=2x
G’=2x+3sen^2(1+2x)*cos(1+2x)
H’=2x
I’=2x+1
K’=2x+1/2x=((2x^2+1)/2x)=1+2x
L’=-sen(1+2x)
M’=((2x)+(3sen^2(1+2x)*(cos(1+2x))/-sen(1+2x))

7. b.
A=x^2
B= (x+1) ^1/2
C=A+B
D=A+x
E=arcsen(C)
F=arctan(D)
H=A*E
I=F+A
J=Cosen(I)
K=H/I
A’=2x
B’=(2) ^1/2
C’=A’+B’
D’=A’
E’=C’/((1-C^2) ^1/2)
F’= D’/1+ D^2
H’=A’E+AE’
I’=F’+A’
J’=-I’*sen(I)
K=(H’J-HJ’)/J^2
SOLUCION
[2x*arsen(x^2+(x+1) ^1/2)+x^1/2)+x^2((2x+2^1/2)/(( (1-(2x+2^1/2)) ^1/2 ) )) (cos(arc(x^2+x)+ x^2)+ x^2 )]-
[(x^2*arsen(x^2+(x+1) ^1/2))- (2x/1+(x^2+x))+2x sen(arctan(x^2+x)+ x^2)]

8. a.
INORDEN 2,3,4,5,6,7,8,9,10,11,12,13,14,21,22,24
POSTORDEN 2,3,5,4,7,6,9,8,13,12,24,22,21,14,11,10
PREORDEN 10,8,6,4,3,2,5,7,9,11,14,12,13,21,2,24

10. b.

11. }

12. Punto A
(1/3)*(5/8)+(1/3)*(2/3)+(1/3)*(2/3)=37/24
Punto C
(5/24)/(24/37)=185
F= 3xy +2x^2*((x+y+z)^1/2)
X=2t+ sen(2t-q)
Y=3t^2*cos(q^2+1)
Z=t*tanq
X=2.8515042
Y=-1.505783
Z=1.732050
T=1
Q= pi/3
DF/DX= 3y+4x(x+y+z^2) ^1/2 + 2x^2(1/2(x+y+z^2) ^-1/2)
DF/DX=35.253
DF/DY=3x+2x^2*1/2(x+y+z^2)
DF/DY=42.5929
DF/DZ=2x^2*1/2(x+y+z^2)
DF/DZ=34.147840
DX/DT=2t-2cos(2t-q)
DX/DT=0.84119
DX/DQ=-cos(2t-q)

13. DX/DQ=-0.5794012
DY/DT=6t^2*cos(q^2+1))
DY/DT=5.541415
DY/DQ=3t^2*(-sen(q^2+1))*2q
DY/DQ=-5.4343
DZ/DT=tanq
DZ/DT=1.7320
DZ/DQ=tsec^2(q)
DZ/DQ=4
DF/DT=DF/DX*DX/DT+ DF/DY*DX/DT+ DF/DZ*DX/DT
DF/DT=32.253(0.84119)+42.5929(5.5414)+34.1478(1.7320)
DF/DT=322.299
DF/DQ=DF/DX*DX/DQ+ DF/DY*DX/DQ+ DF/DZ*DX/DQ
DF/DQ=32.253(-0.57949)+42.5929(-5.43439)+34.1478(1.7320)
DF/DQ=-191.00599
F= (3xy/z) +2x^2y^3 -3xe^(x+y+z)
X=2t^3+ sen(2t-q)
Y=3t^2*cos(t*pi-q^2)
Z=3t*cosq
T=1
Q= pi/2

14. X=-1.5839
Y=-0.06618
Z=0
DF/DX= 4xy^3 - 3xe^(x+y+z) - 3e^(x+y+z)+3y/z
DF/DX=
DF/DY=6x^2y^2-3xe^(x+y+z) +3x/z
DF/DY=
DF/DZ=-3xe^ (x+y+z)- (3xy/z^2)
DF/DZ=
DX/DT=2*cos(2t-q)+6t^2
DX/DT=7.8168
DX/DQ=-cos(2t-q)
DX/DQ=0.9093
DY/DT=6t*cos(q^2-t*pi)+3t^2*pi*sen(q^2-tpi)
DY/DT=1.1963
DY/DQ=-6t^2*q*sen(q^2-t*pi)
DY/DQ=-5.8836
DZ/DT=3*cosq
DZ/DT=0
DZ/DQ=3t*senq
DZ/DQ=3
DF/DT=DF/DX*DX/DT+ DF/DY*DX/DT+ DF/DZ*DX/DT
DF/DT=-1.1398*-7.8186+8.4823*1.1963+1.8897*0
DF/DT=19.0590
DF/DQ=DF/DX*DX/DQ+ DF/DY*DX/DQ+ DF/DZ*DX/DQ
DF/DQ=-1.1398*0.9093+8.4823*-5.8836+1.8897*3
DF/DQ=-45.2738

15. a.

20. Validaciòn Matlab

21.  Transformada
 Antitransformada
Punto b
Validación Matlab
Transformada

22. Antitransformada
Punto C
Validaciòn Matlab
Transformada
Antitransformada
Punto D
Validaciòn Matlab
Transformada

23. Antitransformada
Punto e.
Validaciòn Matlab
Transformada
Antitransformada
Punto F
Validaciòn Matlab
Transformada

24. Antitransformada
b.

27. Diagrama de estados