trabajos autonomos final

8/16/2019 Trabajos Autonomos Final

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TRABAJO AUTONOMO #1

>>% METODO DE WILLIAM HORNER

>> %ESTE METODO CONSISTE EN EVALUAR LA FUNCION POLINOMICA ASI COMO SU DERIVADA

>> %EJERCICIO N°1>> fx='9X^ !"X^# $#X^ $X $""'fx =9X^ !"X^# $#X^ $X $"">> &=9="&=$#&1=$&(=$"">> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = 9 # # / 11#>> 0(=*+)!*#2+)!*2+)!*120( = ##

>> 3453 x>> fx=9+x^ !"+x^# $#+x^ $+x $""fx =9+x^ ! "+x^# $ #+x^ $ +x $ "">> 6fx=67fffx26fx =#8+x^# ! 1"+x^ $ 8+x $ >> )=6fx=#8+)^# ! 1"+)^ $ 8+) $ 6fx = ##

>> %EJERCICIO N°>> fx='11X^ !9X^# $"X^ $X $8"'fx =11X^ !9X^# $"X^ $X $8">> &=11=9&=$"&1=$&(=$8">> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = 11 #1 " 1( 19>> 0(=*+)!*#2+)!*2+)!*120( = ##

>> 3453 x>> fx = 11+x^ !9+x^# $"+x^ $+x $8"fx = 11+x^ ! 9+x^# $ "+x^ $ +x $ 8">> 6fx=67fffx26fx =+x^# ! +x^ $ 1(+x $ >> )=6fx=+)^# ! +)^ $ 1(+) $ 6fx =


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##>> %EJERCICIO N°#>> fx='1(X^ !/X^# !X^ $#X $"'fx =1(X^ !/X^# !X^ $#X $">> &=1(=/&=&1=$#&(=$">> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = 1( / 8# 1# (1>> 0(=*+)!*#2+)!*2+)!*120( = 1>> 3453 x>> fx=1(+x^ !/+x^# !+x^ $#+x $"fx =1(+x^ ! /+x^# ! +x^ $ #+x $ ">> 6fx=67fffx26fx =

(+x^# ! +x^ ! 1+x $ #>> )=6fx=(+)^# ! +)^ ! 1+) $ #6fx = 1>> %EJERCICIO N°>> fx='"x^!9x^#$#x^$x$#"'fx ="x^!9x^#$#x^$x$#">> &="=9&=$#&1=$&(=$#">> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( =

" 19 #" 8/ 1(1>> 0(=*+)!*#2+)!*2+)!*120( = ">> 3453 x>> fx="+x^!9+x^#$#+x^$+x$#"fx ="+x^ ! 9+x^# $ #+x^ $ +x $ #">> 6fx=67fffx26fx =

(+x^# ! +x^ $ 8+x $ >> )=6fx=(+)^# ! +)^ $ 8+) $ 6fx = ">> %EJERCICIO N°">> fx='x^ $9x^# !11x^ $x $8'fx =x^ $9x^# !11x^ $x $8>> &==$9&=11&1=$&(=$8>> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.


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,( = " 1 #/ 9>> 0(=*+)!*#2+)!*2+)!*120( = 1"8>> 3453 x>> fx=+x^ $9+x^# !11+x^ $+x $8fx =+x^ $ 9+x^# ! 11+x^ $ +x $ 8>> 6fx=67fffx26fx =/+x^# $ +x^ ! +x $ >> )=6fx=/+)^# $ +)^ ! +) $ 6fx = 1"8>> %EJERCICIO N°8>> fx='1(x^ $/x^# !1#x^ $"x $/('fx =

1(x^ $/x^# !1#x^ $"x $/(>> &=1(=$/&=1#&1=$"&(=$/(>> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = 1( 1 # 89 "/>> 0(=*+)!*#2+)!*2+)!*120( = 1>> 3453 x>> fx=1(+x^ $/+x^# !1#+x^ $"+x $/(fx =

1(+x^ $ /+x^# ! 1#+x^ $ "+x $ /(>> 6fx=67fffx26fx =(+x^# $ +x^ ! 8+x $ ">> )=6fx=(+)^# $ +)^ ! 8+) $ "6fx = 1>> %EJERCICIO N°>> fx='x^ $#x^# !"x^ $/x $('fx =

x^ $#x^# !"x^ $/x $(>> &==$#&="&1=$/&(=$(>> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = " 1" $8>> 0(=*+)!*#2+)!*2+)!*120( = 1(>> 3453 x>> fx=+x^ $#+x^# !"+x^ $/+x $(


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fx =+x^ $ #+x^# ! "+x^ $ /+x $ (>> 6fx=67fffx26fx =18+x^# $ 9+x^ ! 1(+x $ />> )=6fx=18+)^# $ 9+)^ ! 1(+) $ /6fx = 1(>> %EJERCICIO N°/>> fx='"x^ $x^# !/x^ $"x $8"'fx ="x^ $x^# !/x^ $"x $8">> &="=$&=/&1=$"&(=$8">> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = " # 1 # $19>> 0(=*+)!*#2+)!*2+)!*120( =

1(#>> 3453 x>> fx="+x^ $+x^# !/+x^ $"+x $8"fx ="+x^ $ +x^# ! /+x^ $ "+x $ 8">> 6fx=67fffx26fx =(+x^# $ 1+x^ ! 18+x $ ">> )=6fx=(+)^# $ 1+)^ ! 18+) $ "6fx = 1(#

>> %EJERCICIO N°9>> fx='1(x^ $9x^# !"x^ $/x $"'fx =1(x^ $9x^# !"x^ $/x $">> &=1(=$9&="&1=$/&(=$">> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = 1( 11 8 1>> 0(=*+)!*#2+)!*2+)!*120( =

>> 3453 x>> fx=1(+x^ $9+x^# !"+x^ $/+x $"fx =1(+x^ $ 9+x^# ! "+x^ $ /+x $ ">> 6fx=67fffx26fx =(+x^# $ +x^ ! 1(+x $ />> )=6fx=(+)^# $ +)^ ! 1(+) $ /6fx =


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>> %EJERCICIO N°1(>> fx='11x^ !1(x^# !/x^ $9x $'fx =11x^ !1(x^# !/x^ $9x $>> &=11=1(&=/&1=$9&(=$>> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = 11 # 1#" 19/>> 0(=*+)!*#2+)!*2+)!*120( = 9">> 3453 x>> fx=11+x^ !1(+x^# !/+x^ $9+x $fx =11+x^ ! 1(+x^# ! /+x^ $ 9+x $ >> 6fx=67fffx26fx =

+x^# ! #(+x^ ! 18+x $ 9>> )=6fx=+)^# ! #(+)^ ! 18+) $ 96fx = 9">> %EJERCICIO N°11>> fx='"x^ $1(x^# !x^ $"x $/'fx ="x^ $1(x^# !x^ $"x $/>> &="=$1(&=&1=$"&(=$/>> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( =

" ( 9 $8>> 0(=*+)!*#2+)!*2+)!*120( = 8#>> 3453 x>> fx="+x^ $1(+x^# !+x^ $"+x $/fx ="+x^ $ 1(+x^# ! +x^ $ "+x $ />> 6fx=67fffx26fx =

(+x^# $ #(+x^ ! 1+x $ ">> )=6fx=(+)^# $ #(+)^ ! 1+) $ "6fx = 8#>> %EJERCICIO N°1>>fx ='/x^ !X^# $1(x^ !#x $'>> &=/=&=$1(&1=#&(=$>> )=*=&*#=*+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(,(=-* *# * *1 *(.,( = / # #8 " 1(/


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>> 0(=*+)!*#2+)!*2+)!*120( = #(#>> 3453 x>> fx=/+x^ !+x^# $1(+x^ !#+x $fx =/+x^ ! +x^# $ 1(+x^ ! #+x $ >> 6fx=67fffx2 6fx = #+x^# ! 1+x^ $ (+x ! # >> )=6fx=#+)^# ! 1+)^ $ (+) ! #6fx = #(#

>> % M:TODO DE ,IR;E VIETA>> %ESTE METODO CONSISTE EN UTILI> % EL AL;ORITMO DE VIETA ES

>> % )7!12=)7 $ *(?0(2= FT>> % RESOLVIENDO>> %EJERCICIO N°1>> fx='9X^ !"X^# $#X^ $X $""'fx =9X^ !"X^# $#X^ $X $"">> % H&0@ B& )&*& 6@ &@3>> x=$1x =

$ $# $ $1 ( 1 # >> fx=9+xG^ !"+xG^# $#+xG^ $+x $""

fx = 1//9 "1/ 1 $" $"" $8 11# 8 "1#

>> 76 >> %PROCESO NUMERICO ITERATIVO>> fx='9X^ !"X^# $#X^ $X $""'fx =


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>> 76 >> %PROCESO NUMERICO ITERATIVO>> fx='11X^ !9X^# $"X^ $X $8"'fx =11X^ !9X^# $"X^ $X $8"

>> &=11=9&=$"&1=$&(=$"">> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( = ( G(((( 1"9G(((( ##G(((( 1G8#/>> 7=1)=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 = 1G(((( G(((( 1"9G(((( ##G(((( 1G8#/>> 7=)=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( G(((( 1"9G(((( ##G(((( 1G8#/>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1.V =

( G(((( 1"9G(((( ##G(((( 1G8#/ 1G(((( G(((( 1"9G(((( ##G(((( 1G8#/ G(((( G(((( 1"9G(((( ##G(((( 1G8#/

>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=G(((( B@ 3@>> %0B5@ & 06707K fx=1+1(^$>> %EJERCICIO N°#>>1(x^ !/x^# !x^ $#x $">> fx='1(x^ !/x^# !x^ $#x $"'fx =


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1(x^ !/x^# !x^ $#x $">> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= 1(+xG^ !/+xG^# !+xG^ $#+x $"fx = 1 81 /" $## $" $# (1 1(#" #1>> ) xfx2

>> 76 >> %PROCESO NUMERICO ITERATIVO>> fx='1(x^ !/x^# !x^ $#x $"'fx =1(x^ !/x^# !x^ $#x $"

>> &=1(=/&=&1=$#&(=$">> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( = ( G(((( (1G(((( 1G(((( 1G">> 7=1)=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 = 1G(((( G(((( (1G(((( 1G(((( 1G">> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.

1 = 1G(((( 1G" "#G#/( #G1#/ 1G#("(>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( 1G#("( 9G/ 1"G(#9 1G#">> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# = #G(((( 1G#" (G81" 18G//"/ 1G#8


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>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( 1G#8 (G((#1 1"G8#( 1G#8>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1#.V = ( G(((( (1G(((( 1G(((( 1G" 1G(((( 1G" "#G#/( #G1#/ 1G#("( G(((( 1G#("( 9G/ 1"G(#9 1G#" #G(((( 1G#" (G81" 18G//"/ 1G#8 G(((( 1G#8 (G((#1 1"G8#( 1G#8>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=1G#8 B@ 3@

>> %0B5@ & 06707K fx=1+1(^$>> %EJERCICIO N°>>"x^!9x^#$#x^$x$#">> fx= '"x^!9x^#$#x^$x$#"'fx ="x^!9x^#$#x^$x$#">> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= "+xG^!9+xG^#$#+xG^$+x$#"

fx = 89 1(8 $#" $( $#" $8 1(1 "/( 18">> ) xfx2

>> 76 >> %PROCESO NUMERICO ITERATIVO>> fx='"x^!9x^#$#x^$x$#"'fx =


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"x^!9x^#$#x^$x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

>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( 1G#9 (G(((1 98G989# 1G#9>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1#.

V = ( G(((( 1(1G(((( "G(((( 1G8( 1G(((( 1G8( G(/( 1#9G99# 1G#(# G(((( 1G#(# #G88# 1(#G1/# 1G#9/ #G(((( 1G#9/ (G(98( 9G1"#9 1G#9 G(((( 1G#9 (G(((1 98G989# 1G#9>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=1G#9 B@ 3@>> %0B5@ & 06707 fx=1+1(^$>> %EJERCICIO N°">> x^ $9x^# !11x^ $x $8=(

>> fx= 'x^ $9x^# !11x^ $x $8=('fx =x^ $9x^# !11x^ $x $8=(>> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= +xG^ $9+xG^# !11+xG^ $+x $8fx = 9# /" 189 $#8 $8 $8 9 # 1#(9


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>> ) xfx2>> 76

>> %PROCESO NUMERICO ITERATIVO>> fx= 'x^ $9x^# !11x^ $x $8'

fx =x^ $9x^# !11x^ $x $8>> &==$9&=11&1=$&(=$8>> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( = ( G(((( 9G(((( 1"8G(((( 1G9#>> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 =

1G(((( 1G9# (G(1 1G((9 1G9#9>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( 1G9#9 (G((1( 11G#1# 1G9#9>> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# = #G(((( 1G9#9 (G(((( 11G#89 1G9#9>> C=-'CUADRO DE CALCULO'.C =

CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1.V = ( G(((( 9G(((( 1"8G(((( 1G9# 1G(((( 1G9# (G(1 1G((9 1G9#9 G(((( 1G9#9 (G((1( 11G#1# 1G9#9>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=1G9#9 B@ 3@


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>> %0B5@ & 06707 fx=1+1(^$>> %EJERCICIO N°8>>1(x^ $/x^# !1#x^ $"x $/(=(>> fx='1(x^ $/x^# !1#x^ $"x $/('fx =1(x^ $/x^# !1#x^ $"x $/(>> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= 1(+xG^ $/+xG^# !1#+xG^ $"+x $/(fx = #( 1(/ (8 $ $/( $( "/ 818 1"8>> ) xfx2>> 76

>> %PROCESO NUMERICO ITERATIVO>> fx='1(x^ $/x^# !1#x^ $"x $/('fx =1(x^ $/x^# !1#x^ $"x $/(>> &=1(=$/&=1#&1=$"&(=$/(>> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( = ( G(((( "/G(((( 1G(((( 1G/8(>> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $

*(?0(21=-7 ) *( 0( FT.1 = 1G(((( 1G/8( /G("# 19G"/ 1G(/>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( 1G(/ (G##8 1/G"9 1G#9(>> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# =


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*(?0(2(=-7 ) *( 0( FT.( = ( G(((( $8G(((( 1(G(((( G"((>> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 = 1G(((( G"(( "G8"8# 1"1G1/" G18>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( G18 (G1( 1#G#"1 G118>> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# = #G(((( G118 (G(((1 1#G189 G118>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO

>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1#.V = ( G(((( $8G(((( 1(G(((( G"(( 1G(((( G"(( "G8"8# 1"1G1/" G18 G(((( G18 (G1( 1#G#"1 G118 #G(((( G118 (G(((1 1#G189 G118>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=G118 B@ 3@>> %0B5@ & 06707 fx=1+1(^$

>> %EJERCICIO N°/>> "x^ $x^# !/x^ $"x $8"=(>> fx= '"x^ $x^# !/x^ $"x $8"'fx ="x^ $x^# !/x^ $"x $8">> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= "+xG^ $+xG^# !/+xG^ $"+x $8"

fx = 1/11 818 11# $( $8" $8 $19 (/ /">> ) xfx2>> 76


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>> %PROCESO NUMERICO ITERATIVO>> fx= '"x^ $x^# !/x^ $"x $8"'fx ="x^ $x^# !/x^ $"x $8"

>> &="=$&=/&1=$"&(=$8">> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( = ( G(((( $19G(((( 1(#G(((( G1/">> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 = 1G(((( G1/" #G1#9# 1#/G G181/>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $

*(?0(2=-7 ) *( 0( FT. = G(((( G181/ (G("#9 1##G988 G181>> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# = #G(((( G181 (G(((( 1##G1#8 G181>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.

I = 7 ) *( 0( FT>> V=-(1#.V = ( G(((( $19G(((( 1(#G(((( G1/" 1G(((( G1/" #G1#9# 1#/G G181/ G(((( G181/ (G("#9 1##G988 G181 #G(((( G181 (G(((( 1##G1#8 G181>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=G11 B@ 3@>> %0B5@ & 06707 fx=1+1(^$


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>> %EJERCICIO N°9>> 1(x^ $9x^# !"x^ $/x $"=(>> fx= '1(x^ $9x^# !"x^ $/x $"'fx =1(x^ $9x^# !"x^ $/x $">> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= 1(+xG^ $9+xG^# !"+xG^ $/+x $"fx = #1# 1( 19# $# $" $ 1 "1# 19">> ) xfx2

>> %PROCESO NUMERICO ITERATIVO

>> fx= '1(x^ $9x^# !"x^ $/x $"'fx =1(x^ $9x^# !"x^ $/x $">> &=1(=$9&="&1=$/&(=$">> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( = ( G(((( 1G(((( G(((( 1G91>> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 =

1G(((( 1G91 1G(89 198G1/# 1G91/>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( 1G91/ (G((" 19G#1/ 1G91/8>> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# = #G(((( 1G91/8 (G(((( 19G#("" 1G91/8>> C=-'CUADRO DE CALCULO'.


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C =CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1#.V = ( G(((( 1G(((( G(((( 1G91 1G(((( 1G91 1G(89 198G1/# 1G91/ G(((( 1G91/ (G((" 19G#1/ 1G91/8 #G(((( 1G91/8 (G(((( 19G#("" 1G91/8>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=1G91/8 B@ 3@>> %0B5@ & 06707 fx=1+1(^$>> %EJERCICIO N°1(>> 11x^ !1(x^# !/x^ $9x $=(>> fx= '11x^ !1(x^# !/x^ $9x $'fx =11x^ !1(x^# !/x^ $9x $

>> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= 11+xG^ !1(+xG^# !/+xG^ $9+x $fx = 8/ 8/ $" $ $" 19/ 11# #8>> ) xfx2>> 76

>> %PROCESO NUMERICO ITERATIVO>> fx= '11x^ !1(x^# !/x^ $9x $'fx =11x^ !1(x^# !/x^ $9x $>> &=11=1(&=/&1=$9&(=$>> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( =


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

V = ( G(((( 19/G(((( 9"G(((( 1G8((( 1G(((( 1G8((( G198 #G8( 1G/ G(((( 1G/ 8G/ (#G("9 1G#989 #G(((( 1G#989 (G1/ 191G/1( 1G#98( G(((( 1G#98( (G(((1 191G//8 1G#98(>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=1G#98( B@ 3@>> %0B5@ & 06707 fx=1+1(^$>> %EJERCICIO N°11>> "x^ $1(x^# !x^ $"x $/=(>> FX= '"x^ $1(x^# !x^ $"x $/'

FX ="x^ $1(x^# !x^ $"x $/>> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> FX= "+xG^ $1(+xG^# !+xG^ $"+x $/FX = 19( 81 118 $"" $/ $/" $8 1(1 8"(>> ) xFX2

>> 76


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>> %PROCESO NUMERICO ITERATIVO>> fx= '"x^ $1(x^# !x^ $"x $/'fx ="x^ $1(x^# !x^ $"x $/

>> &="=$1(&=&1=$"&(=$/>> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2(=-7 ) *( 0( FT.( = ( G(((( $8G(((( 8#G(((( #G(1"9>> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 = 1G(((( #G(1"9 1("G9(# #1G9 G8>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $

*(?0(2=-7 ) *( 0( FT. = G(((( G8 19G/(89 (1G9/8 G"9(>> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# = #G(((( G"9( 1G##1 1G8"1 G"1>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( G"1 (G((" 1G8/9 G"1

>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1#.V = ( G(((( $8G(((( 8#G(((( #G(1"9 1G(((( #G(1"9 1("G9(# #1G9 G8


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G(((( G8 19G/(89 (1G9/8 G"9( #G(((( G"9( 1G##1 1G8"1 G"1 G(((( G"1 (G((" 1G8/9 G"1>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=G"1 B@ 3@>> %0B5@ & 06707 fx=1+1(^$>> %EJERCICIO N°1>> /x^ !X^# $1(x^ !#x $=(>> fx= '/x^ !X^# $1(x^ !#x $'fx =/x^ !X^# $1(x^ !#x $>> % H&0@ B& )&*& 6@ &@3>> x=$1x = $ $# $ $1 ( 1 # >> fx= /+xG^ !+xG^# $1(+xG^ !#+x $fx = 1#/8 #1/ $18 $" $ $# 1(/ 1 #(8>> ) xfx2

>> 76

>> %PROCESO NUMERICO ITERATIVO>> fx= '/x^ !X^# $1(x^ !#x $'fx =/x^ !X^# $1(x^ !#x $>> &=/=&=$1(&1=#&(=$>> 7=()=*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $

*(?0(2(=-7 ) *( 0( FT.( = ( G(((( 1(/G(((( #(#G(((( 1G8#8>> 7=1)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(21=-7 ) *( 0( FT.1 = 1G(((( 1G8#8 "G# 18/G9/8 1G9#>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. =


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G(((( 1G9# #G/( 18G"#9 1G8>> 7=#)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2#=-7 ) *( 0( FT.# = #G(((( 1G8 (G(/"# 119G99# 1G88>> 7=)=FT*=&*#=&+)!*=*#+)!&*1=*+)!&1*(=*1+)!&(0(=*+)!*#2+)!*2+)!*12FT=) $*(?0(2=-7 ) *( 0( FT. = G(((( 1G88 (G(((1 119G/1"/ 1G88>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *( 0( FT'.I = 7 ) *( 0( FT>> V=-(1#.V = ( G(((( 1(/G(((( #(#G(((( 1G8#8

1G(((( 1G8#8 "G# 18/G9/8 1G9# G(((( 1G9# #G/( 18G"#9 1G8 #G(((( 1G8 (G(/"# 119G99# 1G88 G(((( 1G88 (G(((1 119G/1"/ 1G88>> %LA SOLUCION APROXIMADA DE LA ECUACION ES )=x+=1G88 B@ 3@>> %0B5@ & 06707K fx=1+1(^$

>> %METODO DE LIN$,AIRSTOW>> %ESTE METODO NOS PERMITE RESOLVER PRO,LEMAS DE FUNCIONES POLINOMICAS>> %APLICANDO EL AL;ORITMO DE WG HORNER NEWTON RAPHSON E INTRODUCIENDO>> %UN FACTOR DE CONVER;ENCIAG ESTO ES

>> %)7!12=)7 $ &56&+*(?*12=FT>> %SIENDO )7=V& 7707& 3@ *)7@@ &07@6 B *3B@ 6@ Qf70&2>> %&56&=F&0) 6@ 0@@07&=$f(2?)(+6fx)(222>> %*1=V& &)@@)75 6@ &3 *>> %*(=V& 6@ & fB07K 7K570&

>> %EJERCICIO N°#>> %1(x^!/x^#!x^$#x$"=(>> fx='1(+x^!/+x^#!+x^$#+x$"'fx =

1(+x^!/+x^#!+x^$#+x$">> x=$1x = $ $# $ $1 ( 1 # >> fx=1(+xG^!/+xG^#!+xG^$#+x$"fx = 1 81 /" $## $" $# (1 1(#" #1>> %EL INTERVALO ENCONTRADO ES -1 .>> x=1(G"x =


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1G(((( 1G"(( 1G"((( 1G"(( G((((>> fx=1(+xG^!/+xG^#!+xG^$#+x$"fx = $#G(((( G88 #G/"( 1(G/"18 (1G((((>> )xfx2>> 76

>> )=1G#>> f(=$">> 3453 x>> fx=1(+xG^!/+xG^#!+xG^$#+x$"fx = 1(+x^ ! /+x^# ! +x^ $ #+x $ ">> 6fx=67fffx26fx =(+x^# ! +x^ ! 1+x $ #>> x=1G#6fx=(+x^# ! +x^ ! 1+x $ #

6fx = 1G98#>> &56&=$f(?)+6fx22&56& = (G9/>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> fx=1(+xG^!/+xG^#!+xG^$#+x$">> )=1G#&=1(=/&=&1=$#&(=$">> %C&0B 6@ &3 *>> %P0@3 B5@70 7)@&)7

>> 7=()=1G#*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12(=-7 ) *1 *( FT.( = ( 1G#(( #8G#19 $(G#1 1G#8>> 7=1)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*121=-7 ) *1 *( FT.1 = 1G(((( 1G#8 #8G"1( (G((# 1G#8>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT. = G(((( 1G#8 #8G"(/8 $(G(((( 1G#8>> C=-'CUADRO DE CALCULO'.


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C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1.V = ( 1G#(( #8G#19 $(G#1 1G#8 1G(((( 1G#8 #8G"1( (G((# 1G#8 G(((( 1G#8 #8G"(/8 $(G(((( 1G#8

>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=1G#8>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$>> %EJERCICIO N°>> %G$ "x^!9x^#$#x^$x$#">> fx='"x^!9x^#$#x^$x$#"'fx ="x^!9x^#$#x^$x$#"

>> x=$1x = $ $# $ $1 ( 1 # >> fx = "+xG^ ! 9+xG^# $ #+xG^ $ +x $ #"fx = 89 1(8 $#" $( $#" $8 1(1 "/( 18">> %EL INTERVALO ENCONTRADO ES -1 .>> x=1(G"x = 1G(((( 1G"(( 1G"((( 1G"(( G((((>> fx = "+xG^ ! 9+xG^# $ #+xG^ $ +x $ #"

fx = $8G(((( $1G(# 1(G9#" G1 1(1G((((>> )xfx2>> 76

>> fx='"x^!9x^#$#x^$x$#"'fx ="x^!9x^#$#x^$x$#"


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>> )=1G#/>> f(=$#">> 3453 x>> fx = "+x^ ! 9+x^# $ #+x^ $ +x $ #"fx ="+x^ ! 9+x^# $ #+x^ $ +x $ #">> 6fx=67fffx26fx =(+x^# ! +x^ $ 8+x $ >> x=1G#/6fx=(+x^# ! +x^ ! 8+x $ 6fx = 11(G8(>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> &56&=$f(?)+6fx22&56& = (G#((>> fx = "+xG^ ! 9+xG^# $ #+xG^ $ +x $ #"

>> )=1G#/&="=9&=#&1=$&(=$#">> %C&0B 6@ &3 *>> %P0@3 B5@70 7)@&)7>> 7=()=1G#/*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12(=-7 ) *1 *( FT.( = ( 1G#/(( #G(( 9G#9" 1G#1(9>> 7=1)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*121=-7 ) *1 *( FT.1 = 1G(((( 1G#1(9 /G88# G"## 1G9(>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT. =

G(((( 1G9( G"99 (G8(18 1G/">> 7=#)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12#=-7 ) *1 *( FT.# = #G(((( 1G/" G##89 (G1# 1G/1>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT. = G(((( 1G/1 G9 (G(9" 1G/#9

>> 7=")=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12"=-7 ) *1 *( FT." =

"G(((( 1G/#9 G88/ (G((8" 1G/#/>> 7=8)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*128=-7 ) *1 *( FT.>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1#".V =


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( 1G#/(( #G(( 9G#9" 1G#1(9 1G(((( 1G#1(9 /G88# G"## 1G9( G(((( 1G9( G"99 (G8(18 1G/" #G(((( 1G/" G##89 (G1# 1G/1 G(((( 1G/1 G9 (G(9" 1G/#9 "G(((( 1G/#9 G88/ (G((8" 1G/#/>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=1G#8>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$>> %EJERCICIO N°">> %"G$ x^ $9x^# !11x^ $x $8=(>> fx='+x^ $9+x^# !11+x^ $+x $8'fx =+x^ $9+x^# !11+x^ $+x $8>> x=$1x = $ $# $ $1 ( 1 # >> fx=+xG^ $9+xG^# !11+xG^ $+x $8fx =

9# /" 189 $#8 $8 $8 9 # 1#(9>> %EL INTERVALO ENCONTRADO ES -1 .>> x=1(G"x = 1G(((( 1G"(( 1G"((( 1G"(( G((((

>> fx=+xG^ $9+xG^# !11+xG^ $+x $8fx = $8G(((( $""G#((/ $#G1/" $G/9" 9G((((>> ) xfx2>> 76

>> )=1G9#>> f(=$8>> 3453 x>> fx=+xG^ $9+xG^# !11+xG^ $+x $8fx =+x^ $ 9+x^# ! 11+x^ $ +x $ 8


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>> 6fx=67fffx26fx =/+x^# $ +x^ ! +x $ >> x=1G9#6fx=/+x^# $ +x^ ! +x $ 6fx = 1#9G1/1#>> &56&= $f(?)+6fx22&56& = (G9>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> fx=+xG^ $9+xG^# !11+xG^ $+x $8>> )=1G9#&==$9&=11&1=$&(=$8>> %C&0B&6 &3 *>> %P0@3 B5@70 7)@&)7>> 7=()=1G9#*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12(=-7 ) *1 *( FT.( = ( 1G9#(( #G(9# $1G##" 1G9#9>> 7=1)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*121=-7 ) *1 *( FT.

1 = 1G(((( 1G9#9 #G"8(/ (G(#8 1G9#9>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT. = G(((( 1G9#9 #G""/ $(G(((/ 1G9#9>> 7=#)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12#=-7 ) *1 *( FT.# = #G(((( 1G9#9 #G"8 (G(((( 1G9#9>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO

>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1#.V = ( 1G9#(( #G(9# $1G##" 1G9#9 1G(((( 1G9#9 #G"8(/ (G(#8 1G9#9 G(((( 1G9#9 #G""/ $(G(((/ 1G9#9 #G(((( 1G9#9 #G"8 (G(((( 1G9#9>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=1G9#9

>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$>> %EJERCICIO N°8>> %8G$ 1(x^ $/x^# !1#x^ $"x $/(=(>> fx='1(+x^ $/+x^# !1#+x^ $"+x $/('fx =1(+x^ $/+x^# !1#+x^ $"+x $/(>> x=$1x = $ $# $ $1 ( 1 #


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>> fx=1(+xG^ $/+xG^# !1#+xG^ $"+x $/(fx = #( 1(/ (8 $ $/( $( "/ 818 1"8>> %EL INTERVALO ENCONTRADO ES -1 .>> x=1(G"x = 1G(((( 1G"(( 1G"((( 1G"(( G((((>> fx=1(+xG^ $/+xG^# !1#+xG^ $"+x $/(fx = $(G(((( $"G1/ $#G8"( 1G988 "/G((((>> ) xfx2>> 76 >> )=1G>> f(=$/(>> 3453 x>> fx=1(+xG^ $/+xG^# !1#+xG^ $"+x $/(fx =1(+x^ $ /+x^# ! 1#+x^ $ "+x $ /(

>> 6fx=67fffx26fx =(+x^# $ +x^ ! 8+x $ ">> x=1G6fx=(+x^# $ +x^ ! 8+x $ "6fx = 1/G9/8>> &56&= $f(?)+6fx22&56& = (G"9>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> fx=1(+xG^ $/+xG^# !1#+xG^ $"+x $/(

>> )=1G&=1(=$/&=1#&1=$"&(=$/(>> %C&0B 6@ &3 *>> %L&3 * 3 3 0@f707@)@3 6@ 757 007@)@>> %P0@3 B5@70 7)@&)7>> 7=()=1G*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12(=-7 ) *1 *( FT.( = ( 1G(( 8G(9 (G1/ 1G#9(

>> 7=1)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*121=-7 ) *1 *( FT.1 =

1G(((( 1G#9( 8G((# (G(((" 1G#9(>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT. = G(((( 1G#9( 8G((#" (G(((( 1G#9(>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT


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>> V=-(1.V = ( 1G(( 8G(9 (G1/ 1G#9( 1G(((( 1G#9( 8G((# (G(((" 1G#9( G(((( 1G#9( 8G((#" (G(((( 1G#9(>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=1G#9(>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$

>> %EJERCICIO N°>> %G$ x^ $#x^# !"x^ $/x $(=(>> fx='+x^ $#+x^# !"+x^ $/+x $('fx =+x^ $#+x^# !"+x^ $/+x $(>> x=$1

x = $ $# $ $1 ( 1 # >> fx=+xG^ $#+xG^# !"+xG^ $/+x $(fx = 1"/ ( " $"( $( $ $8 19 /1(>> %EL INTERVALO ENCONTRADO ES -1 .>> x=1(G"x = 1G(((( 1G"(( 1G"((( 1G"(( G((((>> fx=+xG^ $#+xG^# !"+xG^ $/+x $(fx =

$G(((( $8/G/1# $8(G8"( $G"(( $8G((((>> )xfx2>> 76 >> x=(G"#x = G(((( G"(( G"((( G"(( #G((((>> fx=+xG^ $#+xG^# !"+xG^ $/+x $(fx = $8G(((( "G8"8# "(G8"( 11G1/" 19G((((>> )xfx2


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>> 76 >> )=G>> f(=$(>> 3453 x>> fx=+xG^ $#+xG^# !"+xG^ $/+x $(fx =+x^ $ #+x^# ! "+x^ $ /+x $ (>> 6fx=67fffx26fx =18+x^# $ 9+x^ ! 1(+x $ />> x=G6fx=18+x^# $ 9+x^ ! 1(+x $ /6fx = 1(G/(/(

>> &56&= $f(?)+6fx22&56& = (G8(>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6

>> fx=+xG^ $#+xG^# !"+xG^ $/+x $(>> )1=G&==$#&="&1=$/&(=$(>> %C&0B 6@ &3 *>> %P0@3 B5@70 7)@&)7>> 7=()=G*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12(=-7 ) *1 *( FT.( = ( G((( #1G(( $1G818 G119>> 7=1)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*121=-7 ) *1 *( FT.1 = 1G(((( G119 #1G8(/ (G("#9 G118>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT.

= G(((( G118 #1G8"1 $(G((1 G118>> 7=#)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12#=-7 ) *1 *( FT.# = #G(((( G118 #1G8"1/ (G(((( G118>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I =

7 ) *1 *( FT>> V=-(1#.V = ( G((( #1G(( $1G818 G119 1G(((( G119 #1G8(/ (G("#9 G118 G(((( G118 #1G8"1 $(G((1 G118 #G(((( G118 #1G8"1/ (G(((( G118>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=G118>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$


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>> %EJERCICIO N°/>> %/G$ "x^ $x^# !/x^ $"x $8"=(>> fx='"+x^ $+x^# !/+x^ $"+x $8"'fx =

"+x^ $+x^# !/+x^ $"+x $8">> x=$1x = $ $# $ $1 ( 1 # >> fx="+xG^ $+xG^# !/+xG^ $"+x $8"fx = 1/11 818 11# $( $8" $8 $19 (/ /">> %EL INTERVALO ENCONTRADO ES - #.>> x=(G"#x =

G(((( G"(( G"((( G"(( #G((((>> fx="+xG^ $+xG^# !/+xG^ $"+x $8"fx = $19G(((( 1G88( "/G#" 1G1/9 (/G((((>> )xfx2>> 76 >> )=G1">> f(=$8">> 3453 x>> fx="+xG^ $+xG^# !/+xG^ $"+x $8"

fx ="+x^ $ +x^# ! /+x^ $ "+x $ 8">> 6fx=67fffx26fx =(+x^# $ 1+x^ ! 18+x $ ">> x=G1"6fx=(+x^# $ 1+x^ ! 18+x $ "6fx = 1#1G(9"(>> &56&= $f(?)+6fx22&56& =


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(G#(8>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> fx="+xG^ $+xG^# !/+xG^ $"+x $8">> )=G1"&="=$&=/&1=$"&(=$8">> %C&0B 6@ &3 *>> %P0@3 B5@70 7)@&)7>> 7=()=G1"*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12(=-7 ) *1 *( FT.( = ( G1"(( 9G"# $1G"(11 G181>> 7=1)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*121=-7 ) *1 *( FT.1 = 1G(((( G181 #(G(91" (G(9" G181#>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT. = G(((( G181# #(G(# $(G((11 G181>> 7=#)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12#=-7 ) *1 *( FT.# = #G(((( G181 #(G(#/ (G(((( G181

>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1#.

V = ( G1"(( 9G"# $1G"(11 G181 1G(((( G181 #(G(91" (G(9" G181#

G(((( G181# #(G(# $(G((11 G181 #G(((( G181 #(G(#/ (G(((( G181>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=G181>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$

>> %EJERCICIO N°9>> %9G$ 1(x^ $9x^# !"x^ $/x $"=(


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>> fx='1(+x^ $9+x^# !"+x^ $/+x $"'fx =1(+x^ $9+x^# !"+x^ $/+x $">> x=$1x = $ $# $ $1 ( 1 # >> fx=1(+xG^ $9+xG^# !"+xG^ $/+x $"fx = #1# 1( 19# $# $" $ 1 "1# 19">> %EL INTERVALO ENCONTRADO ES -1 .>> x=1(G"x = 1G(((( 1G"(( 1G"((( 1G"(( G((((>> fx=1(+xG^ $9+xG^# !"+xG^ $/+x $"fx =

$G(((( $(G#"18 $""G"((( $/G1#/ 1G((((>> )xfx2

>> 76 >> )=1G91>> f(=$">> 3453 x>> fx=1(+xG^ $9+xG^# !"+xG^ $/+x $"fx =1(+x^ $ 9+x^# ! "+x^ $ /+x $ ">> 6fx=67fffx26fx =(+x^# $ +x^ ! 1(+x $ />> x=1G916fx=(+x^# $ +x^ ! 1(+x $ /

6fx = 191G#181>> &56&= $f(?)+6fx22&56& = (G(">> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> fx=1(+xG^ $9+xG^# !"+xG^ $/+x $">> )=1G91&=1(=$9&="&1=$/&(=$">> %C&0B 6@ &3 *>> %P0@3 B5@70 7)@&)7

>> 7=()=1G91*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12(=-7 ) *1 *( FT.( = ( 1G91(( #/G#9"/ $1G88( 1G91/9>> 7=1)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*121=-7 ) *1 *( FT.1 = 1G(((( 1G91/9 #9G111/ (G("1 1G91/8>> 7=)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12=-7 ) *1 *( FT. = G(((( 1G91/8 #9G(9(( $(G((1( 1G91/8>> 7=#)=FT*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12#=-7 ) *1 *( FT.


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# = #G(((( 1G91/8 #9G(9( (G(((( 1G91/8

>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1#.V = ( 1G91(( #/G#9"/ $1G88( 1G91/9 1G(((( 1G91/9 #9G111/ (G("1 1G91/8 G(((( 1G91/8 #9G(9(( $(G((1( 1G91/8 #G(((( 1G91/8 #9G(9( (G(((( 1G91/8>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=1G91/8>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$

>> %EJERCICIO N°1(>> %1(G$ 11x^ $1(x^# !/x^ $9x $>> fx= '11+x^ $1(+x^# !/+x^ $9+x $'fx =11+x^ $1(+x^# !/+x^ $9+x $>> x=$1x = $ $# $ $1 ( 1 #

>> fx= 11+xG^ $1(+xG^# !/+xG^ $9+x $fx = #"/ 11// # $# $ $ #/ "9 198>> %EL INTERVALO ENCONTRADO ES -1 .>> x=1(G"x = 1G(((( 1G"(( 1G"((( 1G"(( G((((>> fx= 11+xG^ $1(+xG^# !/+xG^ $9+x $fx = $G(((( $8#G"/ $"G"8" $1#G8"/ #/G((((


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>> )xfx2>> 76 >> )=1G/) = 1G/((>> )=1G/>> f(=$>> 3453 x>> fx= 11+xG^ $1(+xG^# !/+xG^ $9+x $fx =11+x^ $ 1(+x^# ! /+x^ $ 9+x $ >> 6fx=67fffx26fx =+x^# $ #(+x^ ! 18+x $ 9>> x=1G/6fx=+x^# $ #(+x^ ! 18+x $ 96fx = 1/8G(("(>> &56&= $f(?)+6fx22

&56& = (G1>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> fx= 11+xG^ $1(+xG^# !/+xG^ $9+x $>> )=1G/&=11=$1(&=/&1=$9&(=$>> %C&0B 6@ &3 *>> %P0@3 B570 7)@&)7>> 7=()=1G/*1=&+)!+)!&2+)!&12*(=*1+)!&(FT=) $ &56&+*(?*12 (=-7 ) *1 *( FT.( = ( 1G/(( #/G"( $1G" 1G//1>> 7=1 )=FT *1=&+)!+)!&2+)!&12 *(=*1+)!&( FT=) $ &56&+*(?*12 1=-7 ) *1 *( FT.

1 = 1G(((( 1G//1 #9G(/# (G(1 1G/9>> 7= )=FT *1=&+)!+)!&2+)!&12 *(=*1+)!&( FT=) $ &56&+*(?*12 =-7 ) *1 *( FT. = G(((( 1G/9 #9G#/9/ $(G(((/ 1G/9>> 7=# )=FT *1=&+)!+)!&2+)!&12 *(=*1+)!&( FT=) $ &56&+*(?*12 #=-7 ) *1 *( FT.# = #G(((( 1G/9 #9G#9(1 (G(((( 1G/9>> C=-'CUADRO DE CALCULO'.C =

CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1#.V = ( 1G/(( #/G"( $1G" 1G//1 1G(((( 1G//1 #9G(/# (G(1 1G/9 G(((( 1G/9 #9G#/9/ $(G(((/ 1G/9 #G(((( 1G/9 #9G#9(1 (G(((( 1G/9


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>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=1G/9>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$>> %EJERCICIO N°11

>> % 11G$ "x^ $1(x^# !x^ $"x $/=(>> fx= '"x^ $1(x^# !x^ $"x $/'

fx ="x^ $1(x^# !x^ $"x $/>> x=$1x = $ $# $ $1 ( 1 # >> fx= "+xG^ $1(+xG^# !+xG^ $"+x $/fx = 19( 81 118 $"" $/ $/" $8 1(1 8"(>> %EL INTERVALO ENCONTRADO ES - #.>> x=1G"#x =

>> x=(G"#x = G(((( G"(( G"((( G"(( #G((((>> fx= "+xG^ $1(+xG^# !+xG^ $"+x $/fx = $8G(((( $#G" $11G8/" #"G1"/ 1(1G((((>> )xfx2>> 76 >> )=G"8

>> f(=$/>> 3453 x>> fx= "+xG^ $1(+xG^# !+xG^ $"+x $/fx ="+x^ $ 1(+x^# ! +x^ $ "+x $ />> 6fx=67fffx26fx =(+x^# $ #(+x^ ! 1+x $ ">> x=G"86fx=(+x^# $ #(+x^ ! 1+x $ "6fx =


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189G8#>> &56&= $f(?)+6fx22&56& = (G1//>> %D@0&&6 & &3 & 05 0@f707@)@ 6@ 757 6&6>> fx= "+xG^ $1(+xG^# !+xG^ $"+x $/>> )=G"8&="=$1(&=&1=$"&(=$/>> %C&0B 6@ &3 *>> %P0@3 B5@70 7)@&)7>> 7=( )=G"8 *1=&+)!+)!&2+)!&12 *(=*1+)!&( FT=) $ &56&+*(?*12 (=-7 ) *1 *( FT.( = ( G"8(( #1G(1 $1G9/8 G"1/>> 7=1 )=FT *1=&+)!+)!&2+)!&12 *(=*1+)!&( FT=) $ &56&+*(?*12 1=-7 ) *1 *( FT.1 = 1G(((( G"1/ #1G91(1 (G(8"( G"1>> 7= )=FT *1=&+)!+)!&2+)!&12 *(=*1+)!&( FT=) $ &56&+*(?*12 =-7 ) *1 *( FT. = G(((( G"1 #1G//9( $(G((1 G"1

>> 7=# )=FT *1=&+)!+)!&2+)!&12 *(=*1+)!&( FT=) $ &56&+*(?*12 #=-7 ) *1 *( FT.# = #G(((( G"1 #1G//9" (G(((( G"1>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1#.V =

( G"8(( #1G(1 $1G9/8 G"1/ 1G(((( G"1/ #1G91(1 (G(8"( G"1 G(((( G"1 #1G//9( $(G((1 G"1 #G(((( G"1 #1G//9" (G(((( G"1>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=G"1>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$


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>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 ) *1 *( FT'.I = 7 ) *1 *( FT>> V=-(1.V = ( 1G(( /G/#/" (G#98 1G88/ 1G(((( 1G88/ /G8#8 (G((9 1G88 G(((( 1G88 /G8#"1 (G(((( 1G88>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=G"1>> %LA SOLUCION APROXIMADA DE LA ECUACION ES x+=1G88>> %PORUE SE CUMPLE CON LA CONDICION FX=1+1(^$

TRABAJO AUTONOMO #2

>>%METODO DE ;AUSS SEIDEL

>>%@3 B 5)6 7)@&)7 B)77&6 && @3@ 373)@5&3 6@ @0B&07@3 7@&@3G>> %EJERCICIO N°1>> %1G$ 11x !4 $# $ =11G">> %G$ #x !/4 $ $ =/G">> %#G$ x !#4 $1( !# =(G"

>> %G$ x !4 $" !/ =#(>>>> % 11> 37 11>$# 37 11>$1 37 )&) & 75@& @3 & @0B&07K B5@ B>> % /># 37 />$ 37 />$ 37 )&) & 3@B6& @3 & @0B&07K B5@ 63>> % &@6&6 & )@0@& @ & @0B&07K B5@ )@3>> % />1 37 /> 37 />$" 37 & )&) & 0B&)& @3 & @0B&07K B5@ >>>> % PROCESO NUMERICO ITERATIVO>>>> 7=( x=( 4=( =( =( X=11G"$+4!#+!2?11 =/G"$#+X$+!+2?/


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X$+!"+> 7=1 x=X 4= => 7=" x=X 4= => 7=/ x=X 4= =


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"G(((( (G"11 1G888 $(G#9( G#9# 8G(((( (G"1/ 1G88 $(G#// G#9# G(((( (G"1 1G881 $(G#/8 G#9#/ /G(((( (G"1 1G881 $(G#/8 G#9#/>> % L& 3B07 &x75&6& 6@ 373)@5& 6@ @0B&07@3 @3 x+=(G"1 4+=1G881 +=$(G#/8 +=G#9#/>> % B@ 3@ 0B5@ & 06707 x/$x=1+1($>> %EJERCICIO N°>> %1G$ 9x !"4 $# ! =1>> %G$ #x !1(4 $ !" ="#>> %#G$ x !#4 $/ !# =>> %G$ x !/4 $# !11 =89>> % 9>" 37 9>$# 37 9> 37 )&) & 75@& @3 & @0B&07 B5@ B>> % 1(># 37 1(>$ 37 1(>" 37 )&) & 3@B6& @3 & @0B&07 B5@ 63>> % &@6&6 & )@0@& @ & @0B&07 B5@ )@3>> % 11>1 37 11>/ 37 11>$# 37 & )&) & 0B&)& @3 & @0B&07 B5@ >> % PROCESO NUMERICO ITERATIVO>> 7=( x=( 4=( =( =( X=1$"+4!#+$+2?9 ="#$#+X!+$"+2?1( > 7=8 x=X 4= =


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/+!#+> % L& 3B07 &x75&6& 6@ 373)@5& 6@ @0B&07@3 @3 x+=1G/(" 4+=G9// +=#G1189 +=G/9>> % B@ 3@ 0B5@ & 06707 x11$x1(=1+1($#>> %EJERCICIO N°#>> %1G$ x !"4 $ $ =G"

>> %G$ x !1(4 $# $ =1"G">> %#G$ #x !4 $/ !# =$">> %G$ x !#4 $" !11 ="1>> % >" 37 >$1 37 >$1 37 )&) & 75@& @3 & @0B&07 B5@ B>> % 1(> 37 1(>$# 37 1(>$ 37 )&) & 3@B6& @3 & @0B&07 B5@ 63>> % /># 37 /> 37 /># 37 )&) & )@0@& @3 & @0B&07 B5@ )@3>> % &@6&6 & 0B&)& @3 & @0B&07 B5@ 0B&)>> 7=( x=( 4=( =( =( X=G"$"+4!!2? =1"G"$+X!#+!+2?1(


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>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 X < W'.I = 7 X < W>> V=-V(V1VV#VV"V8VV/V9V1(V11V1.V = ( (G#"1 1G/8 1G1/8 G1#8 1G(((( (G1#"8 G/( #G1" "G//8 G(((( $(G11 #G8#9# #G#"8 "G(9 #G(((( $1G(19 #G/(1 #G18( "G1# G(((( $1G18/ #G"#8 #G(#( "G1(/ "G(((( $1G18(# #G1"" #G(## "G1(8/ 8G(((( $1G1#1 #G(9 #G(1/ "G11(/ G(((( $1G18 #G1(( #G(88 "G111/ /G(((( $1G1 #G11/ #G(1 "G1118 9G(((( $1G1/8 #G1 #G(8 "G111

1(G(((( $1G19( #G11 #G(8 "G111 11G(((( $1G1/9 #G1( #G(8 "G111 1G(((( $1G1/9 #G1( #G(8 "G111>> % L& 3B07 &x75&6& 6@ 373)@5& 6@ @0B&07@3 @3 x+=$1G1/9 4+=#G1( +=#G(8 +="G111>> % B@ 3@ 0B5@ & 06707 x1$x11=1+1($>> %EJERCICIO N°>> %1G$ /x !#4 $ $# =8G">> %G$ #x !4 $ $ =1G">> %#G$ "x !4 $11 $# =$#/>> %G$ x !"4 $# !1( =8>> % /># 37 />$ 37 />$# 37 )&) & 75@& @3 & @0B&07 B5@ B

>> % ># 37 >$1 37 >$ 37 )&) & 3@B6& @3 & @0B&07 B5@ 63>> % 11>" 37 11> 37 11>$# 37 )&) & )@0@& @3 & @0B&07 B5@ )@3>> % &@6&6 & 0B&)& @3 & @0B&07 B5@ 0B&)>> % PROCESO NUMERICO ITERATIVO>> 7=( x=( 4=( =( =( X=8G"$#+4!+!#+2?/ =1G"$#+X!!+2? 7=1 x=X 4= => 7=# x=X 4= =


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>> 7= x=X 4= => 7=/ x=X 4= => I=-' 7 X < W'.I = 7 X < W>> V=-V(V1VV#VV"V8VV/.V = ( (G/1" G1"1/ G8(8# 8G#/1(

1G(((( #G""(( #G"9 G"/8( G8"9 G(((( G#98# #G9/ G"#8 "G(" #G(((( G""1 #G"(9 G"("9 G9" G(((( G919 #G99 G"(1 "G((/ "G(((( G"(#( #G"((# G"(( G99/ 8G(((( G99 #G999 G"((1 "G(((# G(((( G"(( #G"((( G"((( G9999 /G(((( G"((( #G"((( G"((( "G((((>> % L& 3B07 &x75&6& 6@ 373)@5& 6@ @0B&07@3 @3 x+=G" 4+=#G" +=G" +="G(>> % B@ 3@ 0B5@ & 06707 x/$x=1+1($

>> %EJERCICIO N°">> %1G$ 9x !4 $ $# =#>> %G$ #x !1(4 $ $ =(>> %#G$ x $"4 !9 $" =1>> %G$ #x $4 !" $1 =$">> % 9> 37 9>$1 37 9>$# 37 )&) & 75@& @3 & @0B&07 B5@ B>> % 1(># 37 1(>$1 37 1(>$ 37 )&) & 3@B6& @3 & @0B&07 B5@ 63>> % 9> 37 9>$" 37 9>$" 37 )&) & )@0@& @3 & @0B&07 B5@ )@3>> % &@6&6 & 0B&)& @3 & @0B&07 B5@ 0B&)>>


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>> C=-'CUADRO DE CALCULO'.C =CUADRO DE CALCULO>> I=-' 7 X < W'.I = 7 X < W>> V=-V(V1VV#VV"V8VV/V9V1(V11.V = ( #G"""8 (G9### $(G18(" "G(1(9 1G(((( G/1 G8# #G#88 8G1" G(((( #G91( #G81 G88( 8G189 #G(((( #G### #G9"## "G(( 8G1(# G(((( #G( G( "G("" 8G(# "G(((( #G(((( G(19# "G(9 8G((8( 8G(((( G99(# G((/# "G(1(1 "G999( G(((( G99 G((# "G((( "G99/8 /G(((( G99/( G(((# G999/ "G999# 9G(((( G9998 #G9999 G999 "G999/

1(G(((( #G(((( #G9999 G999/ 8G(((( 11G(((( #G(((1 #G9999 G9999 8G((((>> % L& 3B07K &x75&6& 6@ 373)@5& 6@ @0B&07@3 @3 x+=#G(((1 4+=#G9999 +=G9999 +=8G((((>> % B@ 3@ 0B5@ & 06707K x11$x1(=1+1($#>> %EJERCICIO N°8>> %1G$ "x !4 $ $ =$1>> %G$ x !94 $ $# =$/>> %#G$ #x !4 !11 $" =/>> %G$ x !#4 $" $1( =$#9>> % ">1 37 ">$1 37 ">$ 37 )&) & 75@& @3 & @0B&07K B5@ B>> % 9> 37 9>$ 37 9>$# 37 )&) & 3@B6& @3 & @0B&07K B5@ 63

>> % 11># 37 11> 37 11>$" 37 )&) & )@0@& @3 & @0B&07K B5@ )@3>> % &@6&6 & 0B&)& @3 & @0B&07K B5@ 0B&)>> % PROCESO NUMERICO ITERATIVO>> 7=( x=( 4=( =( =( X=$1$1+4!1+!+2?" =$/$+X!+!#+2?9 7=1 x=X 4= =


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+X$#+!"+> 7=" x=X 4= => 7=8 x=X 4= => % L& 3B07 &x75&6& 6@ 373)@5& 6@ @0B&07@3 @3 x+=$1 4+=1 += +=#>> % B@ 3@ 0B5@ & 06707 x/$x=1+1($

>> %EJERCICIO N°>> %1G$ x !4 $ $# =$1>> %G$ #x !114 $ $ =$">> %#G$ x !#4 $1# $" =$#/>> %G$ #x !4 $" !11 =>> % >1 37 >$ 37 >$# 37 )&) & 75@& @3 & @0B&07 B5@ B>> % 11># 37 11>$ 37 11>$ 37 )&) & 3@B6& @3 & @0B&07 B5@ 63>> % 1#> 37 1#># 37 1#>$" 37 )&) & )@0@& @3 & @0B&07 B5@ )@3>> % &@6&6 & 0B&)& @3 & @0B&07 B5@ 0B&)>> % PROCESO NUMERICO ITERATIVO


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>> 7=( x=( 4=( =( =( X=$1$1+4!+!#+2? =$"$#+X!+!+2?11 7=1 x=X 4= => 7= x=X 4= = 7=8 x=X 4= => 7= x=X 4= =


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>> 7=1 x=X 4= => %#x ! /4 $ $ =/G">> %x ! #4 $ 1( ! #=(G"


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>> %x ! 4 $ " ! /=#(>>>> %P0@3 B570 7)@&)7>> 7=(x=(4=(=(=(X=11G" $ +4 ! #+ ! 2?11=/G" $ #+x ! + ! +2?/> 7=#x=X4== 7=x=X4== 7="x=X4==> 7=8x=X4==


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8G(((( (G/"1 (G//( $G9# 1G/

>> 7=x=X4== 7=/x=X4== 7=9x=X4==> C=-'CUADRO DE CALCULO'.

C =

CUADRO DE CALCULO

>> I=-' 7 X < W'.

I =

7 X < W>> V=-(1#"8/91(.

V =

( 1G("" 1G(8" $G("(( #G"(( 1G(((( (G(9 1G(9"" $G8 1G/(8/ G(((( (G(/9 (G8/1 $G1" 1G9


53/89

#G(((( (G##/1 (G/"/# $G#/ G(#"/ G(((( (G9/# (G/8 $G##"8 1G/" "G(((( (G"/ (G/#11 $G/ 1G/1/ 8G(((( (G/"1 (G//( $G9# 1G/ G(((( (G/( (G/"(/ $G#((/ 1G/"( /G(((( (G (G/"/ $G9"" 1G/"1# 9G(((( (G/( (G/ $G98 1G/"/ 1(G(((( (G99 (G// $G91 1G/"81>> %L& 3B07K &x75&6& 6@ & @0B&07K @3 X+=(G99 +=(G// > %#x ! 1(4 $ ! "="#>> %x ! "4 $ / ! #=>> %x ! /4 $ # ! 11=89>>

>> %P0@3 B5@70 7)@&)7>> 7=(x=(4=(=(=(X=1 $ "+4 ! #+ ! +2?9="# $ #+x ! + $ "+2?1(> 7=1x=X4==> 7=x=X4==


54/89

>> 7="x=X4==> 7=9x=X4==> 7=1(x=X4==> 7=11x=X4==> 7=1x=X4==


55/89

>> 7=1#x=X4==> 7=18x=X4==> 7=1x=X4==> 7=1x=X4==


56/89

#+2?/W=89 $ x $ /+4 ! #+2?111=-7 X < W.

1 =

1G(((( /G#1" $(G"8(8 "G19" "G#9/1>> 7=x=X4==> 7=#x=X4==> 7=x=X4==> 7="x=X4==> 7=8x=X4==> 7=9x=X4==


57/89

9 =

9G(((( /G/1 $(G#1 "G("9 "G((9>> 7=#(x=X4==> 7=#1x=X4==> 7=#x=X4==> 7=##x=X4==> 7=#x=X4==> 7=#8x=X4==


58/89

# =

#G(((( /G"#8 $(G1#(8 "G19 "G91>> 7=#/x=X4==> 7=(x=X4==> 7=1x=X4==> 7=x=X4==> 7=#x=X4==


59/89

"G(((( /G8((( (G((## "G(1"8 8G(8//>> 7=8x=X4==> 7=/x=X4==> 7="(x=X4==> 7="1x=X4==


60/89


61/89

>> 7=8x=X4==> 7=8#x=X4==> 7=8x=X4==> 7=89x=X4==


62/89

#+2?/W=89 $ x $ /+4 ! #+2?11(=-7 X < W.

( =

(G(((( /G/" (G9/ G##1 8G818>> 7=1x=X4==> 7=x=X4==> 7=#x=X4==> 7=x=X4==> 7="x=X4==> 7=8x=X4==> 7=x=X4==> 7=/x=X4==


63/89

/ =

/G(((( /G/(9 (G G81 8G"8(>> 7=9x=X4==> 7=/1x=X4==> 7=/x=X4==


64/89

/8 =

/8G(((( /G9"9 (G19# G"( 8G"8/>> 7=/x=X4==> 7=//x=X4==> 7=/9x=X4==> 7=9(x=X4==


65/89

9G(((( G89# $(G/9 8G#99 G9"" 1(G(((( 9G1898 G(#1 G/#1 G91 11G(((( G9(1( $(G/"8 8G91" G## 1G(((( 9G# 1G/1# G98/ G/9# 1#G(((( /G(( $(G/# 8G1"8 G91 1G(((( 9G"( 1G88(" #G(/9 G/19 1"G(((( /G1#/# $(G8 8G(#9 "G(88 18G(((( 9G8 1G"#1/ #G("1 G#8 1G(((( /G11 $(G(( "G919" "G19 1/G(((( 9G"8 1G# #G#1 G8"(1 19G(((( /G8/ $(G8#(# "G/1" "G#(1" (G(((( 9G(( 1G##1/ #G11 G"8"" 1G(((( /G#1" $(G"8(8 "G19" "G#9/1 G(((( 9G1 1G"(# #G"( G/ #G(((( /G#"9 $(G9#" "G8#1# "G// G(((( 9G1" 1G1 #G"/1 G(9 "G(((( /G#/9" $(G99 "G"99 "G"8# 8G(((( 9G11( 1G111 #G88"( G##8#

G(((( /G(# $(G#( "G"( "G8#" /G(((( 9G(9( 1G("1# #G#89 G89 9G(((( /G/1 $(G#1 "G("9 "G((9 #(G(((( 9G(881 (G998# #G/(# G(9 #1G(((( /G## $(G8#1 "G# "G81 #G(((( 9G(#( (G9"9 #G/8# G1"(/ ##G(((( /G98# $(G1" "G/#" "G/188 #G(((( 9G(18 (G/99" #G9( G(99 #"G(((( /G"1 $(G11# "G9# "G/8 #8G(((( 9G((1 (G/"8/ #G9 G(9 #G(((( /G"#8 $(G1#(8 "G19 "G91

#/G(((( /G9/## (G/1" G((8 G(( #9G(((( /G""8 $(G(9#( "G1### "G9"/( (G(((( /G988# (G/1# G(8/ 8G988 1G(((( /G"1( $(G("/# "G(9(9 "G99/( G(((( /G9"( (G9 G1("8 8G9# #G(((( /G"/81 $(G(8 "G("1 8G(#/ G(((( /G9#8 (G11 G1# 8G//9( "G(((( /G8((( (G((## "G(1"8 8G(8// 8G(((( /G9/ (G8// G1/ 8G/"8 G(((( /G81/ (G(#(" G9/# 8G1((1

/G(((( /G91(" (G888 G(9/ 8G/8 9G(((( /G8 (G(""8 G9"18 8G1/9 "(G(((( /G/99 (G8#/" G#9# 8G9/ "1G(((( /G8#"8 (G(// G9## 8G1""" "G(((( /G/// (G818 G88 8G#1 "#G(((( /G8"8 (G1((1 G/9 8G1/(1 "G(((( /G/9( (G"9" G91" 8G98 ""G(((( /G8"9 (G119/ G/# 8G( "8G(((( /G/(1 (G"8/ G#18 8G/ "G(((( /G88#" (G1#/( G/"1( 8G#8


66/89

"/G(((( /G/819 (G""9 G##"9 8G(/ "9G(((( /G81# (G1" G/#(" 8G/ 8(G(((( /G/" (G"## G#""8 8G8/9# 81G(((( /G8/8 (G1(1 G/118 8G8(" 8G(((( /G/ (G"/" G## 8G8# 8#G(((( /G8/"# (G1/ G9 8G89 8G(((( /G/(9 (G"1/ G#9( 8G8"88 8"G(((( /G891" (G19" G/ 8G9( 88G(((( /G/#"( (G"( G("/ 8G81 8G(((( /G89 (G(98 G8# 8G#("9 8/G(((( /G/9" (G9(8 G(( 8G8/ 89G(((( /G(" (G(/ G9/ 8G#1/ (G(((( /G/" (G9/ G##1 8G818 1G(((( /G(# (G#11 G# 8G##(8 G(((( /G/19/ (G(( G" 8G8("1 #G(((( /G11/ (G(8 G"8 8G#1" G(((( /G/1"" (G8(9 G"8# 8G"98 "G(((( /G1"9 (G9# G19 8G#"1"

8G(((( /G/118 (G" G888 8G"/9 G(((( /G19 (G" G("( 8G#8(/ /G(((( /G/(9 (G G81 8G"8( 9G(((( /G# (G8/ G89"9 8G#89# /(G(((( /G/(8 (G#8 G// 8G"8/ /1G(((( /G8 (G1 G8/" 8G# /G(((( /G/(1" (G#1( G99 8G"8( /#G(((( /G9 (G/( G89/ 8G#/" /G(((( /G9/8 (G9 G"((# 8G""## /"G(((( /G# (G/#9 G8 8G#91 /8G(((( /G9"9 (G19# G"( 8G"8/

/G(((( /G# (G/9 G8881 8G#9 //G(((( /G9#" (G11 G"1#" 8G"(9 /9G(((( /G#( (G9 G88(( 8G(#1 9(G(((( /G91# (G(9# G"19# 8G"#"

>> %L& 3B07K &x75&6& 6@ & @0B&07K @3 X+=/G91# +=(G(9# > %x ! #4 $ " ! 11="1>> %P0@3 B570 7)@&)7>> 7=(x=(4=(=(=(X=G" $ "+4 ! ! 2?=1"G" $ +x ! #+ ! +2?1(


67/89


68/89

>> 7=9x=X4==> C=-'CUADRO DE CALCULO'.

C =

CUADRO DE CALCULO

>> I=-' 7 X < W'.

I =

7 X < W

>> V=-(1#"8/9.

V =

( (G#"1 1G""(( (G8"( G8#8 1G(((( (G((18 G"9## G//"1 G8"# G(((( $(G" #G#(/ G9/ "G(# #G(((( $(G/#81 #G"18 #G"( "G11/ G(((( $(G999( #G1" #G1 "G1" "G(((( $1G1(" #G9 #G1#"1 "G1##

8G(((( $1G1" #G#/ #G(8/ "G1 G(((( $1G1#9/ #G #G(88 "G11#8 /G(((( $1G1#" #G( #G(8# "G11/ 9G(((( $1G1#1 #G1 #G(9( "G1(9

>> %L& 3B07K &x75&6& 6@ & @0B&07K @3 X+=1G1#1 +=#G1 > %#x ! 4 $ $ =1G">> %"x ! 4 $ 11 $ #=$#/>> %x ! "4 $ # ! 1(=8>> %P0@3 B570 7)@&)7>> 7=(x=(4=(=(=(X=8G" $ #+4 ! + ! #+2?/=1G" $ #+x ! ! +2?


69/89

>> 7=1x=X4== 7=x=X4== 7=#x=X4==> 7=x=X4==


70/89

>> 7=9x=X4==> 7=11x=X4== 7=1x=X4==> 7=1x=X4==


71/89

( (G/1" G"((( #G"" 8G((( 1G(((( #G1#/8 G#9 G9/" "G/81 G(((( G(9 #G"8# G9(9" #G/(#9 #G(((( G" #G#989 G"88 "G1/ G(((( G("1 #G##/ G#1 "G18 "G(((( G(/8 #G( G8#8 G1# 8G(((( G"9 #G/" G"(81 "G11"# G(((( G""9 #G""19 G18 "G(9 /G(((( G( #G G"#9 G9#" 9G(((( G9#( #G98 G9/9 "G(#1( 1(G(((( G"1 #G"11 G/( "G((# 11G(((( G9( #G9#9 G"(/9 G9/" 1G(((( G9/9 #G998 G991 "G((/1 1#G(((( G"(#( #G"(8 G9 "G((( 1G(((( G9/ #G9/ G"( G9988

>> %L& 3B07K &x75&6& 6@ & @0B&07K @3 X+=G9/ +=#G9/ > %9x ! 4 $ $ #=#>> %#x ! 1(4 $ $ =(>> %x $ "4 ! 9 $ "=1>> %#x $ 4 ! " $ 1=$">> %P0@3 B570 7)@&)7>> 7=(x=(4=(=(=(X=# $ +4 ! ! #+2?9=( $ #+x ! ! +2?1(> 7=1x=X4== 7=x=X4== 7=#x=X4==


72/89

# =

#G(((( #G#9# #G8#8 G8# "G"#

>> 7=x=X4==> 7=x=X4== 7=/x=X4== 7=9x=X4==


73/89

1( =

1(G(((( #G(("( #G99" G9/9 "G99/

>> 7=11x=X4==> %L& 3B07K &x75&6& 6@ & @0B&07K @3 X+=#G((1 +=#G998 > %x ! 94 $ $ #=$/>> %#x ! 4 ! 11 $ "=/>> %x ! #4 $ " $ 1(=$#9>> %P0@3 B5@70 7)@&)7


74/89

>> 7=(x=(4=(=(=(X=$1 $ 4 ! ! +2?"=$/ $ +x ! + ! #+2?9> 7=1x=X4==> 7=x=X4== 7=x=X4==> 7="x=X4==> 7=8x=X4==


75/89

>> 7=x=X4== 7=9x=X4==> 7=1x=X4==> 7=1#x=X4==


76/89

>> 7=1x=X4==> 7=18x=X4==


77/89

1G(((( $1G(1"8 1G((" G""9 G#1" 1#G(((( $1G((8# 1G(## G"/ G(1 1G(((( $(G99"# 1G(8 G"/ G(1 1"G(((( $1G((8# 1G(#19 G""1( G9 18G(((( $1G(("( 1G(#8 G"88 G#/

>> %L& 3B07K &x75&6& 6@ & @0B&07K @3 X+=1G(("( +=1G(#8 > %EJERCICIO N°>> %x ! 4 $ $ #=$1>> %#x ! 114 $ $ =$">> %x ! #4 $ 1# $ "=$#/>> %#x ! 4 $ " ! 11=>> %P0@3 B570 7)@&)7>> 7=(x=(4=(=(=(X=$1 $ 4 ! + ! #+2?=$" $ #+x ! + ! +2?11> 7=1x=X4==


78/89

>> 7="x=X4== 7=x=X4== 7=9x=X4==


79/89

>> 7=1x=X4==> 7=1#x=X4== 7=1"x=X4==> 7=18x=X4== 7=1/x=X4==


80/89

>> C=-'CUADRO DE CALCULO'.

C =

CUADRO DE CALCULO

>> I=-' 7 X < W'.

I =

7 X < W

>> V=-(1#"8/91(1111#11"1811/.

V =

( $#G(((( $(G"" G9#1 G""

1G(((( (G181 1G/ 1G18 G88 G(((( (G/# 1G 1G"88# G###1 #G(((( $(G/8 (G"11 G/# G1/ G(((( $(G(""# 1G1(1/ 1G989 #G8# "G(((( (G1" 1G# 1G88 G981 8G(((( $(G(( (G/# G1#9 G8/"" G(((( $(G1#( (G988# G(9( #G1/ /G(((( (G1898 1G1(/ 1G9(# #G(8/1 9G(((( $(G(" (G98(9 G("( G/( 1(G(((( $(G("1 (G98( G(#1 #G(## 11G(((( (G("1/ 1G(#9( 1G98 #G("(

1G(((( (G(1( (G99/ 1G998 G9"1 1#G(((( $(G(##( (G9/( G(1/( G998 1G(((( (G(11( 1G(1(9 1G9919 #G( 1"G(((( (G(11 1G((# 1G999 G9/9 18G(((( $(G(118 (G991 G((8/ G99#( 1G(((( (G(((1 1G((19 1G9991 #G((91 1/G(((( (G(("9 1G((#1 1G9989 G99/9

>> %L& 3B07K &x75&6& 6@ & @0B&07K @3 X+=(G(("9 +=1G((#1 > %B@ 3@ 0B5@ & 06707K x1/ $ x1=1+1(^$


81/89

TRABAJO AUTONOMO #3

>> %METODO DE LOS MINIMOS CUADRADOS>> %PRIMER SISTEMA DE ECUACIONES>> %1G$>> % #x!4!"$=>> % x!/4$9!"=11>> % x!4$/$"=$9

>> % x!#4$$#=$/>> % "x!4$#$"=$1(>>>> %RESOLVIENDO EL SISTEMA>> A=-# " $1 / $9 "1 $/ $" # $ $#" $# $".

A =

# " $1 / $9 "

1 $/ $" # $ $# " $# $"

>> TA=A'

TA =

# 1 " / #

" $9 $/ $ $# $1 " $" $# $"

>> C=TA+A

C =

"" / $# $#" / 1/ $1#" $# $# $1#" 1/# 11

$#" $# 11 /"

>> IC=7C2

IC =

(G(9/ $(G("/" $(G(" (G(1 $(G("/" (G(/ (G("( $(G((/ $(G(" (G("( (G(19 $(G((( (G(1 $(G((/ $(G((( (G(18#


82/89

>> *=- 11 $9 $/ $1(.'

* =

11 $9 $/ $1(

>> x=IC+A'+*

x =

1G(((( G(((( #G((((

G((((

>> (G(1 $(G((/ $(G((( (G(18#

*=- 11 $9 $/ $1(.'

* =

11 $9

$/ $1(

x=IC+A'+*

x =

1G(((( G(((( #G((((

G((((

>>>> %RESOLVIENDO EL SISTEMA>> % 9x!1(4$/$"=$">> % x!114$!9=#8>> % x$"4$/!1(=$">> % x!4!"$11=$#>> % "x!94$11$/=$8>>


83/89

>> A=-9 1( $/ $" 11 $ 9 $" $/ 1( " $11" 9 $11 $/.

A =

9 1( $/ $" 11 $ 9 $" $/ 1( " $11 " 9 $11 $/

>> TA=A'

TA =

9 " 1( 11 $" 9 $/ $ $/ " $11 $" 9 1( $11 $/

>> C=TA+A

C =

( ( $1# $"9 ( ## $198 $11 $1# $198 ## $( $"9 $11 $( #91

>> IC=7C2

IC =

(G(1/ $(G((( (G((#9 (G(((/ $(G((( (G((9 (G((8 (G((# (G((#9 (G((8 (G((# (G(( (G(((/ (G((# (G(( (G((#9

>> *=-$" #8 $" $# $8.'

* =

$" #8 $" $# $8

>> x=IC+A'+*


84/89

x =

$G(((( #G(((( G(((( "G((((

>>>> %RESOLVIENDO EL # SISTEMA>> % x!/4$"$1(=$#>> % 9x!"4$#!9=(G">> % /x$4$#!11="G">> % "x!4$/$1=$8>> % #x!4$1($=$"1G">>>> A=- / $" $1(9 " $# 9/ $ $# 11" $/ $1# $1( $.

A =

/ $" $1( 9 " $# 9 / $ $# 11 " $/ $1 # $1( $

>> TA=A'

TA =

9 / " # / " $ $" $# $# $/ $1( $1( 9 11 $1 $

>> IC=7C2

IC =

(G(1/ $(G((( (G((#9 (G(((/

$(G((( (G((9 (G((8 (G((# (G((#9 (G((8 (G((# (G(( (G(((/ (G((# (G(( (G((#9

>> *=-$# (G" "G" $8 $"1G".'

* =

$#G(((( (G"(((


85/89

"G"((( $8G(((( $"1G"(((

>>>> x=IC+A'+*

x =

1"G"/99 $(G8 1#G18/ 11G/"#

>>>> %RESOLVIENDO EL SISTEMA>> % 11x!14$/!=$#>> % 9x$4!"$#=$1

>> % "x!4$9$=$#>> % x!1(4$$"=$#">> % "x!4$1($11=$9>>>>>> A=-11 1 $/ 9 $ " $#" $9 $ 1( $ $"" $1( $11.

A =

11 1 $/ 9 $ " $#

" $9 $ 1( $ $" " $1( $11

>> TA=A'

TA =

11 9 " " 1 $ 1(

$/ " $9 $ $1( $# $ $" $11

>> IC=7C2

IC =

(G(1/ $(G((( (G((#9 (G(((/ $(G((( (G((9 (G((8 (G((# (G((#9 (G((8 (G((# (G((


86/89

(G(((/ (G((# (G(( (G((#9

>> *=-$# $1 $# $#" $9.'

* =

$# $1 $# $#" $9

>> x=IC+A'+*

x =

$1G1("9 (G1#8

#G9(1 G9(>> %RESOLVIENDO EL " SISTEMA>> % x!4$11$/=$"1>> % "x!94$"$#=$1>> % 1(x!4$"!1(=8(>> % 9x$#4!$=1G">> % x!"4$$"=$1#G">>>> A=- $11 $/" 9 $" $#1( $" 1(9 $# $ " $ $".

A =

$11 $/ " 9 $" $# 1( $" 1( 9 $# $ " $ $"

>> TA=A'

TA =

" 1( 9 9 $# " $11 $" $" $ $/ $# 1( $ $"

>> IC=7C2

IC =


87/89


>> *=-$"1 $1 8( 1G" $1#G".'

* =

$"1G(((( $1G(((( 8(G(((( 1G"((( $1#G"(((

>> x=IC+A'+*

x =

/G/(8 (G(9/ G((9 "G/9

>>>> %RESOLVIENDO EL 8 SISTEMA>> % #x!4$$11=$9/>> % x!"4$$1=$11(

>> % "x!#4!$#=>> % #x!4$"$/=$>> % x!"4$$=$8>>>> A=-# $ $11 " $ $1" # $## $" $/ " $ $.

A =

# $ $11 " $ $1

" # $# # $" $/ " $ $

>> TA=A'

TA =

# " # " # "


88/89

$ $ $" $ $11 $1 $# $/ $

>> IC=7C2

IC =


>> *=-$9/ $11( $ $8.'

* =

$9/ $11(

$ $8

>> x=IC+A'+*

x =

G898 G"/1 1#G/1"(

1G811

>>>>>> %RESOLVIENDO EL SISTEMA>>>> % "x$4$#!=$>> % /x$1(!$"=$11>> % x!114$1($/=$##>> % x!"4$/$9=$"(

>> % #x!4!"$11=$1G">>>> A=-" $ $# / $1( $" 11 $1( $/ " $/ $9 # " $11.

A =

" $ $# / $1( $" 11 $1( $/ " $/ $9


89/89

# " $11

>> TA=A'

TA =

" / # $ $1( 11 " $# $1( $/ " $" $/ $9 $11

>> IC=7C2

IC =

(G(1/ $(G((( (G((#9 (G(((/ $(G((( (G((9 (G((8 (G((# (G((#9 (G((8 (G((# (G((

(G(((/ (G((# (G(( (G((#9

>> *=-$ $11 $## $"( $1G".'

* =

$G(((( $11G(((( $##G(((( $"(G(((( $1G"(((

>> x=IC+A'+*

x =

$1G/(8 G #G("#(

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