Ejemplo 01.

F ( x )=x3−2 x X* [-1,2]

Obtener una solución con 2 cifras ex

Se deja de iterar si |x i−x i−1|≤0.5∗10−1

i=0 [a0 , b0 ]=[−1,2]

x0=0.5

f (−1 ) f (0.5 )<0−→a1=−1b1=0.5

i=1 [a1 , b1 ]=[−1 ,0.5 ]

x1=−0.25

|x1−x0|≤0.5∗10−1−→falso

f (−1 ) f (−0.25 )>0a2=−0.25b2=0.5

i=2[a2 , b2 ]=[−0.25 ,0.5]

x2=0.125

|x2−x1|≤0.5∗10−1−→falso

f (−0.25 ) f (0.125 )<0−→a3=−0.25b3=0.125

i=3[a3 , b3 ]=[−0.25 ,0.125]

x3=−0.0625

|x3−x2|≤0.5∗10−1−→falso

f (−0.25 ) f (−0.0625 )>0−→a4=−0.0625b4=0.125

i=4[a4 , b4 ]=[−0.0 .625 ,0.125]

x4=−0.03125

|x4−x3|≤0.5∗10−1−→verdadero x lo tan¿ aca termina

X* = -0.03125

Ejemplo 02.

F ( x )=3 x2−2 X* [-2,1]

Obtener una solución con 2 cifras ex

Se deja de iterar si ,|x i−x i−1|≤0.5∗10−1

i=0 ; [a0 , b0 ]=[−2,1]

x0=−0.5

f (−2 ) f (−0.5 )<0−→a1=−2b1=−0.5

i=1 ; [a1 , b1 ]=[−2 ,−0.5]

x1=−1.25

|x1−x0|≤0.5∗10−1−→falso

f (−2 ) f (−1.25 )<0a2=−2b2=−1.25

i=2[a2 , b2 ]=[−2 ,−1.25]

x2=−1.625

|x2−x1|≤0.5∗10−1−→falso

f (−2 ) f (−1.625 )<0−→a3=−2b3=−1.625

i=3[a3 , b3 ]=[−2 ,−1.625]

x3=−1.8125

|x3−x2|≤0.5∗10−1−→falso

f (−2 ) f (−1.8125 )<0−→a4=−2b4=−1.8125

i=4[a4 , b4 ]=[−2 ,−1.8125]

x4=−1.90625

|x4−x3|≤0.5∗10−1−→falso

f (−2 ) f (−1.90625 )<0−→a4=−2b4=−1.90625

i=5 [a5 , b5 ]=[−2 ,−1.90625]

x5=−1.953125

|x5−x4|≤0.5∗10−1−→verdadero x lo tantoaca termina

X* = -1.953125