Metodos Numericos

f(x)=-0.5x^2+2.5x+4.5

5.1 Determine las raices reales de f(x)= -0.5x2+2.5x+4.5: a)gráficamente b)empleando la formula cuadrada c)usando el metodo debiseccion con tres interaciones para determinar la grande.

Emplee como valores iniciales xl =5 y xu=10. calcule el error estimado Ea verdadero Et para cadainteracion.

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

f(x) -20.5 -13.5 -7.5 -2.5 1.5 4.5 6.5 7.5 7.5 6.5 4.5 1.5 -2.5 -7.5 -13.5 -20.5

f(x)
10 5 0 -6 -5 -4 -3 -2-1 0 -5 -10 -15 -20 -25

1

2

3

4

5

6

7

8

a b c

-0.5 2.5 4.5

x2 x

Interación 1 2 3 4 5 6 7 8

Xi 5 5 6.25 6.25 6.25 6.256.328125 6.3671875

Xs 10 7.5 7.5 6.875 6.5625 6.40625 6.40625 6.40625

Xr 7.5 6.25 6.875 6.5625 6.40625 6.328125 6.3671875 6.38671875

Ea% 20 9.090909094.76190476 2.43902439 1.2345679 0.61349693 0.3058104

Et%

9 10 11 12 13 14 15

6.38671875 6.39648438 6.40136719 6.40380859 6.4050293 6.4050293 6.40502936.40625 6.40625 6.40625 6.40625 6.40625 6.40563965 6.40533447

6.39648438 6.40136719 6.40380859 6.4050293 6.40563965 6.40533447 6.40518188

0.152671760.07627765 0.03812429 0.01905851 0.00952835 0.0047644 0.00238226

.5x2+2.5x+4.5:

nteraciones para determinar la raiz mas

10. calcule el error estimado Ea y elerror

8

9 10 11 f(x)

X1= x2=

0 5

f(Xi) 4.5 4.5 0.59375 0.59375 0.59375 0.59375 0.29772949 0.14743042

f(Xs) -20.5 -4.875 -4.875 -1.9453125-0.62695313 -0.00439453 -0.00439453 -0.00439453

f(Xr) -4.875 0.59375 -1.9453125 -0.62695313 -0.00439453 0.29772949 0.14743042 0.07170868

Prueba (f(Xi)*f(Xr)