1. Xi f(Xi) f'(Xi) X(i+1) Xi f(xi) f''(Xi)
1 -0.01846518 -0.1849452 0.90015866 1 -0.01846518 -0.00026294
0.90015866 -0.01662868 -0.18496866 0.81025867 -69.226367 -25.9878513 0.00074302
0.81025867 -0.01497314 -0.18498773 0.7293174 34906.7514 -7.1125E+13 -9.7399E+33
0.7293174 -0.01348118 -0.18500323 0.65644742 34906.7514 -7.1125E+13 -9.7399E+33
0.65644742 -0.01213698 -0.18501582 0.59084775 34906.7514 -7.1125E+13 -9.7399E+33
0.59084775 -0.01092614 -0.18502605 0.53179587 34906.7514 -7.1125E+13 -9.7399E+33
0.53179587 -0.00983561 -0.18503435 0.47864029 34906.7514 -7.1125E+13 -9.7399E+33
0.47864029 -0.00885357 -0.18504109 0.43079377 34906.7514 -7.1125E+13 -9.7399E+33
0.43079377 -0.00796933 -0.18504656 0.38772717 34906.7514 -7.1125E+13 -9.7399E+33
0.38772717 -0.00717321 -0.18505099 0.34896378 34906.7514 -7.1125E+13 -9.7399E+33
0.34896378 -0.00645648 -0.18505459 0.3140742 34906.7514 -7.1125E+13 -9.7399E+33
0.3140742 -0.00581126 -0.18505751 0.28267174 34906.7514 -7.1125E+13 -9.7399E+33
0.28267174 -0.00523045 -0.18505987 0.25440818 34906.7514 -7.1125E+13 -9.7399E+33
0.25440818 -0.00470764 -0.18506179 0.22897 34906.7514 -7.1125E+13 -9.7399E+33
0.22897 -0.00423704 -0.18506335 0.20607492 34906.7514 -7.1125E+13 -9.7399E+33
0.20607492 -0.00381346 -0.18506461 0.18546883 34906.7514 -7.1125E+13 -9.7399E+33
0.18546883 -0.0034322 -0.18506563 0.16692297 34906.7514 -7.1125E+13 -9.7399E+33
0.16692297 -0.00308905 -0.18506646 0.15023142 34906.7514 -7.1125E+13 -9.7399E+33
0.15023142 -0.00278019 -0.18506713 0.13520882 34906.7514 -7.1125E+13 -9.7399E+33
0.13520882 -0.0025022 -0.18506768 0.12168834 34906.7514 -7.1125E+13 -9.7399E+33
0.12168834 -0.00225201 -0.18506812 0.10951979 34906.7514 -7.1125E+13 -9.7399E+33
En esta primera iteracion En la segunda realizamos
Metodo Newton
Metodo Newton
Raphson
Raphson
aplicamos el metodo de el metodo utilizando de
forma tradicional sin la segunda derivada en
alterar la formulacion vez de la primera, donde
del metodo el valor si converge en la
tercera iteracion pero en
funcion de el valor de
f(x)

2. X(i+1) Xi f(xi) f''(Xi) X(i+1) Xi f'(xi)
-69.226367 1 -0.01846518 -0.00026294 -69.226367 29 -0.14774472
34906.7514 -69.226367 -25.9878513 0.00074302 34906.7514 18.0295028 -0.15998881
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -4.69329033 -0.18198938
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 174.179507 -16.6590845
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 58.717223 -0.36641024
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 48.8399257 -0.23047613
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 40.7239649 -0.17254591
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 32.8212599 -0.14997112
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 23.4693241 -0.15141027
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 8.39475203 -0.17769881
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -57.6995945 0.67690603
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -18.2213735 -0.12734502
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 51.6162525 -0.26056247
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 43.1481608 -0.18562151
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 35.3270954 -0.15419792
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 26.6673166 -0.14845466
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 14.2752606 -0.16713717
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -17.9127124 -0.12952419
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 52.3954856 -0.27007642
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 43.8070154 -0.18975813
34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 35.9848724 -0.15572251
ealizamos En este recuadro En este metododo
Metodo Newton
Metodo Newton
Raphson
Raphson
ando de encontramos que si la remplazamos a f(x) por
vada en funcion la hacemos f'(xi) y a f'(x) por
ra, donde utilizando la segunda f''(xi), de igual manera
erge en la derivada en vez de la los resultados no son los
n pero en primera pero en funcion esperados para ninguna
alor de de Xi, el valor es combinacion, exepto la
divergente segunda q por obvias
monotonicamente razones no es la correcta

3. f''(x) X(i+1)
-0.01346746 18.0295028
-0.0070409 -4.69329033
0.00101742 174.179507
-0.14428161 58.717223
-0.0370962 48.8399257
-0.02839789 40.7239649
-0.02183378 32.8212599
-0.01603637 23.4693241
-0.01004408 8.39475203
-0.00268856 -57.6995945
-0.01714632 -18.2213735
0.00182344 51.6162525
-0.03076992 43.1481608
-0.02373353 35.3270954
-0.01780622 26.6673166
-0.01197983 14.2752606
-0.00519253 -17.9127124
0.00184223 52.3954856
-0.03144639 43.8070154
-0.0242591 35.9848724
-0.0182816 27.46688
tododo
os a f(x) por
ual manera
dos no son los
para ninguna
on, exepto la
por obvias
es la correcta

4. X g(x) Error X
1 6 0 2
6 -344 101.744186 1.29099445
-344 40233906 100.000855 1.37477412
40233906 -6.5129E+22 100 1.36401734
-6.5129E+22 2.7627E+68 100 1.36538433
2.7627E+68 -2.109E+205 100 1.36521038
-2.109E+205 #NUM! #NUM! 1.36523251
#NUM! #NUM! #NUM! 1.3652297
#NUM! #NUM! #NUM! 1.36523005
#NUM! #NUM! #NUM! 1.36523001
1.36523001
1.36523001
1.36523001
Se quiere aproximar una raíz de la 1.36523001
ecuación x3 - 30x2 + 2400 = 0, que 1.36523001
sabemos se encuentra en el intervalo 1.36523001
1.36523001
(10,15), mediante el método del 1.36523001
punto fijo. ¿Cuál de las siguientes 1.36523001
funciones utilizarías para poder 1.36523001
1.36523001
esperar convergencia en el proceso de 1.36523001
iteración? Justifique su respuesta. 1.36523001

5. h(x) Error
1.29099445 0
1.37477412 6.09406791
1.36401734 0.78860996
1.36538433 0.10011736
1.36521038 0.01274138
1.36523251 0.00162102
1.3652297 0.00020624
1.36523005 2.624E-05
1.36523001 3.3385E-06
1.36523001 4.2476E-07
1.36523001 5.4042E-08
1.36523001 6.8757E-09
1.36523001 8.7479E-10
1.36523001 1.113E-10
1.36523001 1.4166E-11
1.36523001 1.8053E-12
1.36523001 2.277E-13
1.36523001 3.2529E-14
1.36523001 0
1.36523001 0
1.36523001 0
1.36523001 0
1.36523001 0

6. f(Xi)*f(Xs)= -100
Biseccion
Iteraciones Xi Xr Xs f(Xi) f(Xr)
1 0 50 100 1 -50
2 0 25 50 1 -25
3 0 12.5 25 1 -12.5
4 0 6.25 12.5 1 -6.24999627
5 0 3.125 6.25 1 -3.12306955
6 0 1.5625 3.125 1 -1.51856307
7 0 0.78125 1.5625 1 -0.57163861
8 0 0.390625 0.78125 1 0.06720836
9 0.390625 0.5859375 0.78125 0.06720836 -0.27615195
10 0.390625 0.48828125 0.5859375 0.06720836 -0.1116778
11 0.390625 0.439453125 0.48828125 0.06720836 -0.0242163
12 0.390625 0.415039063 0.43945313 0.06720836 0.02097616
13 0.415039063 0.427246094 0.43945313 0.02097616 -0.00174688
14 0.415039063 0.421142578 0.42724609 0.02097616 0.00958255
15 0.421142578 0.424194336 0.42724609 0.00958255 0.00390986
Grafica Biseccion
Biseccion
120
100
80
60
Error vs Iteraciones
40
20
0
0 5 10 15 20
Secante
Iteracion Xi f(Xi) f(Xi-1) Xi+1 Error
0 110 -110
1 100 -100 -110 0 0
2 0 1 -100 0.99009901 #DIV/0!
3 0.99009901 -0.85205711 1 0.53459421 100
4 0.534594211 -0.1913072 -0.85205711 0.40271171 85.205711
5 0.402711712 0.044186946 -0.1913072 0.42745749 32.7486126

7. 6 0.427457486 -0.00213813 0.04418695 0.42631535 5.78906073
7 0.426315346 -2.3333E-05 -0.00213813 0.42630274 0.26790971
8 0.426302744 1.23969E-08 -2.3333E-05 0.42630275 0.00295596
9 0.426302751 -7.1942E-14 1.2397E-08 0.42630275 1.5697E-06
Grafico Secante
Secante
120
100
80
60
Error vs Iteraciones
40
20
0
0 2 4 6 8 10
-20
Punto Fijo
Iteracion Xi f(x) Error
1 100 1.3839E-87 0
2 1.3839E-87 1 7.226E+90 8E+90
3 1 0.135335283 100
4 0.135335283 0.762867769 638.90561 7E+90
5 0.762867769 0.217461047 82.2596669 6E+90
6 0.217461047 0.647315095 250.806629
5E+90
7 0.647315095 0.273999173 66.4056888
8 0.273999173 0.57810582 136.247098 4E+90
9 0.57810582 0.314676031 52.603976
3E+90
10 0.314676031 0.532936999 83.7146025
11 0.532936999 0.344426695 40.9543657 2E+90
12 0.344426695 0.502151511 54.7316182 1E+90
13 0.502151511 0.366299849 31.4098061
14 0.366299849 0.480657799 37.0875562 0
15 0.480657799 0.382389484 23.7919682 -1E+90 0
16 0.382389484 0.465436796 25.6984881
17 0.465436796 0.394209182 17.8428765
18 0.394209182 0.454563181 18.0684819
19 0.454563181 0.402876038 13.277362
20 0.402876038 0.446751809 12.82954

8. 21 0.446751809 0.40921949 9.82106159
22 0.40921949 0.441119714 9.1716841
23 0.441119714 0.413855074 7.2316479
24 0.413855074 0.437048918 6.58796803
25 0.437048918 0.417238267 5.30692176
26 0.417238267 0.43410166 4.74804282
27 0.43410166 0.419704948 3.8846644
28 0.419704948 0.431965353 3.43019816
29 0.431965353 0.421502022 2.83828423
30 0.421502022 0.430415592 2.48239164
31 0.430415592 0.422810503 2.07092188
32 0.422810503 0.429290684 1.79869933
33 0.429290684 0.42376282 1.50950888
34 0.42376282 0.42847382 1.30447115
35 0.42847382 0.424455699 1.09948375
36 0.424455699 0.42788047 0.94665268

9. Falsa Posicion f(Xi)*f(Xs)=
f(Xi)*f(Xr) Error Iteraciones Xi Xr
-50 0 1 0 0.99009901
-25 100 2 0 0.534594211
-12.5 100 3 0 0.44874589
-6.24999627 100 4 0 0.431007689
-3.12306955 100 5 0 0.427291289
-1.51856307 100 6 0 0.426510545
-0.57163861 100 7 0 0.426346434
0.06720836 100 8 0 0.426311934
-0.01855972 33.3333333 9 0 0.426304682
-0.00750568 20 10 0 0.426303157
-0.00162754 11.1111111 11 0 0.426302836
0.00140977 5.88235294 12 0 0.426302769
-3.6643E-05 2.85714286 13 0 0.426302755
0.000201 1.44927536 14 0 0.426302752
3.7466E-05 0.71942446 15 0 0.426302751
Grafica Falsa Posicion
90
80
70
60
50
40
Error vs Iteraciones
30
20
10
0
0 5
Newton Raphson
Iteracion Xi f(Xi)
1 100 -100
2 0 1
3 0.33333333 0.180083786
4 0.42218312 0.007646564
5 0.42629493 1.44945E-05
6 0.42630275 5.21899E-11

10. 7 0.42630275 0
8 0.42630275 0
9 0.42630275 0
10 0.42630275 0
Grafica Newton Raphson
Newton Raphson
120
100
80
60
Error vs Iteraciones
40
20
0
0 2 4 6 8
-20
Punto Fijo
Error vs Iteraciones
10 20 30 40

12. Xs f(Xi) f(Xr) f(Xs) f(Xi)*f(Xr) Error
100 1 -0.85205711 -100 -0.85205711 0
0.99009901 1 -0.1913072 -0.85205711 -0.1913072 85.205711
0.53459421 1 -0.04115518 -0.1913072 -0.04115518 19.1307203
0.44874589 1 -0.00869758 -0.04115518 -0.00869758 4.11551845
0.43100769 1 -0.00183054 -0.00869758 -0.00183054 0.86975798
0.42729129 1 -0.00038492 -0.00183054 -0.00038492 0.18305385
0.42651055 1 -8.0926E-05 -0.00038492 -8.0926E-05 0.03849237
0.42634643 1 -1.7013E-05 -8.0926E-05 -1.7013E-05 0.00809262
0.42631193 1 -3.5767E-06 -1.7013E-05 -3.5767E-06 0.00170132
0.42630468 1 -7.5192E-07 -3.5767E-06 -7.5192E-07 0.00035767
0.42630316 1 -1.5808E-07 -7.5192E-07 -1.5808E-07 7.5192E-05
0.42630284 1 -3.3232E-08 -1.5808E-07 -3.3232E-08 1.5808E-05
0.42630277 1 -6.9864E-09 -3.3232E-08 -6.9864E-09 3.3232E-06
0.42630275 1 -1.4687E-09 -6.9864E-09 -1.4687E-09 6.9864E-07
0.42630275 1 -3.0877E-10 -1.4687E-09 -3.0877E-10 1.4687E-07
Falsa Posicion
Error vs Iteraciones
10 15 20
f'(Xi) Xi+1 Error
-1 0 0
-3 0.33333333 #DIV/0!
-2.02683424 0.42218312 100
-1.85965936 0.42629493 21.0453192
-1.85261884 0.42630275 0.96454564
-1.8526055 0.42630275 0.00183526

13. -1.8526055 0.42630275 6.6082E-09
-1.8526055 0.42630275 0
-1.8526055 0.42630275 0
-1.8526055 0.42630275 0
Newton Raphson
Error vs Iteraciones
8 10 12
Biseccion
120
100
80
Newton Raphson
60 Secante
40 Falsa Posicion
Biseccion
20
0
0 5 10 15 20
-20