Ejercicios para el taller 2

EJERCICIOS PARA EL TALLER 2

a.

b.

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

6

- + 191102976 + 4 191102986

^ raiz 191102986 ^ 1/2 13824,0003

x 13824,0003

previo opuesto

/ * 2*10 20

raiz ^ 20^2 400

- + 400+4 404

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))

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)]

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

b.

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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)

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

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

a.