Raices de ecuaciones lineales
of 8
-
Upload
ivan-sandoval -
Category
Documents
-
view
220 -
download
0
Transcript of Raices de ecuaciones lineales
-
8/15/2019 Raices de ecuaciones lineales
1/8
f (x) = 0
f (x) = 0
f (x)
Lineales
N o lineales
Algebraicas
Racionales
Irracionales
T rascendentes
ax + b = 0
=
• 9x3x−1 = 2 +
33x−1
•
x√ 2.1
−0.5x
(1−x)√ 1.1−0.5x −3.69 =0 0 < x
-
8/15/2019 Raices de ecuaciones lineales
2/8
f (x) = e−x − x
f (0.57) = e−0.57− 0.57 = −0.0045
f (x) = 0 α
α
f (α) = 0
-
8/15/2019 Raices de ecuaciones lineales
3/8
f (a) . f (b) < 0
ξ
xi = (a+b)
2
f (xi) f (xi) = 0 xi
f (a) . f (xi) f (a) . f (xi) < 0 xi
xi
f (a) . f (xi) f (a) . f (xi) > 0 xi
xi
|xi−xi−1xi
| < ξ xi
x1 = a+b2 ∈ [a1, b1] x2 ∈ [a2, b2] x3 ∈ [a3, b3] [an, bn]
b1 − a1 = b−a2
b2 − a2 = b2−a2
2 = b−a
4
bn − an = ... = b−a2n
a ≤ a1 ≤ a2 ≤ ... ≤ bb ≥ b1 ≥ b2 ≥ ... ≥ a
an y bn
-
8/15/2019 Raices de ecuaciones lineales
4/8
limann →∞
limbnn →∞
|bn − an| ≤
b−a2n → 0
limann →∞
= limbnn →∞
= α
an bn ≤ f
(α) ≤ 0
α α
xn = (an−1+bn−1)
2
|α − xn| ≤ bn−1−an−1
2n = b−a2n
ξ a
ξ a = |xi−xi−1
xi| . 100%
xi xi−1
ξ a ξ a
ξ
xn
f (x) = e−x − x
10−3
f (0) . f (1) < 0
ξ = 10−3
-
8/15/2019 Raices de ecuaciones lineales
5/8
ξ
xi = 0.5673828
-
8/15/2019 Raices de ecuaciones lineales
6/8
(a, f (a))
(b, f (b))
y−
f (
a) =
f (b)−f (a)
b−a (x1 −
a)
x1
x1 = a − f (a)(b−a)f (b)−f (a)
f (a) . f (b) < 0
ξ
xi = a − f (a)(b−a)f (b)−f (a)
-
8/15/2019 Raices de ecuaciones lineales
7/8
f (xi) f (xi) = 0 xi
f (a) . f (xi) f (a) . f (xi) < 0 xi
xi
f (a) . f (xi) f (a) . f (xi) > 0 xi
xi
|xi−xi−1
xi| < ξ
xi
f (x) = e−x − x
10−3
f (0) . f (1) < 0
ξ = 10−3
ξ
xi = 0.5672055
ξ
ξ n
ξ = b−a2n
ξ n
n = log( b−a
ξ )
log(2)
-
8/15/2019 Raices de ecuaciones lineales
8/8
