7/26/2019 Raiz Quinta de Menos 5(Mtodo de Biseccin)
1/6
Encontrar Raiz quinta de menos cinco
x
-2 -270 5
Como f(-2)0
Por el teorema del valor intermedio
f(x) tiene un cero en el intervalo (-20)
Mtodo de biseccin
-2! "
Iteracin (n)# -2 0
2 -2 -1
$ -1.5 -1
% -1.5 -1.25
" -1.5 -1.375
& -1.4375 -1.375
! -1.40625 -1.375
' -1.390625 -1.375
-1.3828125 -1.375
#0 -1.3828125 -1.37890625## -1.380859375 -1.37890625
#2 -1.3798828125 -1.37890625
#$ -1.3798828125 -1.3793945313
#% -1.3798828125 -1.3796386719
#" -1.3797607422 -1.3796386719
#& -1.3797607422 -1.379699707
#! -1.3797302246 -1.379699707
#' -1.3797302246 -1.3797149658
# -1.3797302246 -1.3797225952
20 -1.3797302246 -1.37972640992# -1.3797302246 -1.3797283173
22 -1.3797302246 -1.3797292709
2$ -1.3797297478 -1.3797292709
2% -1.3797297478 -1.3797295094
2" -1.3797297478 -1.3797296286
2& -1.3797296882 -1.3797296286
2! -1.3797296882 -1.3797296584
2' -1.3797296733 -1.3797296584
2 -1.3797296658 -1.3797296584
$0 -1.3797296621 -1.3797296584$# -1.3797296621 -1.3797296602
$2 -1.3797296621 -1.3797296612
f(x) = x5 + 5
a1
b1
an
bn
7/26/2019 Raiz Quinta de Menos 5(Mtodo de Biseccin)
3/6
-2
Error soluto
-#,00000000000 4111 2
-#,"0000000000 -2.5!"75",0000000E-0# #,"
-#,2"000000000 1.!424222,"000000E-0# #,"
-#,$!"00000000 0.0511"5#,2"00000E-0# #,"
-#,%$!"0000000 -1.1"175&,2"00000E-02 #,%$!"
-#,%0&2"000000 -0.4!!"##7$,#2"0000E-02 #,%0&2"
-#,$0&2"00000 -0.2005#0##,"&2"000E-02 #,$0&2"
-#,$'2'#2"0000 -0.05#10!#!,'#2"000E-0$ #,$'2'#2"
-#,$!'0&2"000 0.014!02$,0&2"00E-0$ #,$'2'#2"
-#,$'0'"$!"00 -0.02050"4#,"$#2"0E-0$ #,$'0'"$'-#,$!''2'#2"0
-0.002775#,!&"&2"0E-0% #,$!''2'#
-#,$!$%"$#2" 0.00#0#!4%,''2'#2"E-0% #,$!''2'#
-#,$!&$'&!#'' 0.001#452,%%#%0&$E-0% #,$!''2'#
-#,$!!&0!%2# -0.0005#"2#,220!0$#E-0% #,$!!&0!%
-#,$!&!0!0$ 0.0005427&,#0$"#"&E-0" #,$!!&0!%
-#,$!!$022% -1.02$-005$,0"#!"!'E-0" #,$!!$022
-#,$!!#%&"'2 0.0002##"#,"2"'!'E-0" #,$!!$022
-#,$!!22""2# 0.00012!,&2$%"E-0& #,$!!$022
-#,$!!2&%0# 5.!2$-005$,'#%&!$E-0& #,$!!$022
-#,$!!2'$#!2& 2.4"#$-005#,0!$%'&E-0&
#,$!!$022-#,$!!22!0% 7.07#$-00#,"$&!%$2E-0! #,$!!$022
-#,$!!2!%!!! -1.5#$-00#%,!&'$!#&E-0! #,$!!2!"
-#,$!!2"0$" 2.75#$-00#2,$'%#'"'E-0! #,$!!2!"
-#,$!!2&2'"& 5.!#1$-007#,#202E-0! #,$!!2!"
-#,$!!2&''#! -4.4$-007",&0%&%"E-0' #,$!!2&
-#,$!!2&"'$! 5.#10$-002,'02$22E-0' #,$!!2&
-#,$!!2&!$2! -2.14$-007#,%0##E-0' #,$!!2&!
-#,$!!2&&"'2 -7.!$-00!,%"0"'0&E-0 #,$!!2&!
-#,$!!2&&20 -1.14$-00$,!2"20$E-0 #,$!!2&&
-#,$!!2&&02$ 2.2"5$-00#,'&2&%"#E-0
#,$!!2&&-#,$!!2& 5.472$-00!,$#$22"!E-#0
#,$!!2&&
-#,$!!2&&2 -2.!7$-00!111 0
pn
f(pn) %b
n&1-a
n&1% %a
n&1%
a#
'
#
p1=a
1+
b1a
1
2
