Analisis numerico

Tarea #5


EJERCICIO 1

Interpolación polinomial 2 puntos

X0= 1 Y0=56.5
X1=5 Y1=113

Formula:

F0=A+BXo
F1=A+BX1

Sustituyendo:

56.5=A+B
113=A+5B

Por lotanto:

A= 42.374 B=14.125
USANDO A+Bx
Y=42.375+14.125x
Cuando x=2

y=70.625

EJERCICIO 2

puntos | x | y | x^2 | xy |
1 | 280 | 32.7 | 78400 | 9156 |
2 | 650 | 45.4 |422500 | 29510 |
3 | 1000 | 52.15 | 1000000 | 52150 |
4 | 1200 | 53.7 | 1440000 | 64440 |
5 | 1500 | 52.9 | 2250000 | 79350 |
6 | 1700 | 50.3 | 2890000 | 85510 |
sumatoria | 6330 | 287.15 |8080900 | 320116 |

Utilizando las formulas:

m=((6)(320116)-(6330)(287.15))/((6)(8080900)-(6330)^2)

m=0.0122



b=((8080900)(287.15)-(320116)(6330))/((6)(8080900)-(6330)^2)b=34.9428

Sustituyendo:

Y= 0.0122x+34.9428

EJERCICIO 3

Puntos | x | y | x^2 | xy |
1 | 0 | 600 | 0 | 0 |
2 | 3 | 550 | 9 | 1650 |
3 | 5 | 450 | 25 | 2250 |
4 | 7 | 312 | 49 |2184 |
5 | 8 | 240 | 64 | 1920 |
sumatoria | 23 | 2152 | 147 | 8004 |

Usando las formulas:

m=((5)(8004)-(23)(2152))/((5)(147)-(23)^2)

m=-46

b=((147)(2152)-(8004)(23))/((5)(147)-(23)^2)b=642

Sustituyendo:
Y=-46x+642
Cuando x=4 y=458
EJERCICIO 4

Xo= 0.0000257 fo=700
X1=0.0000298 f1=800

Sustituyendo:

a0= 700a1=(800-700)/(0.0000298-0.0000257)=24390243.9

P1(x)=700+24390243.9(x - 0.0000257)

CUANDO X=0.0000272 Y= 736.5854

EJERCICIO 5

Puntos | x | y | x^2 | xy |
1 | 0 | 92 | 0 | 0 |
2 | 1 | 85.5 | 1 | 85.5 |
3 | 2 | 79.5| 4 | 159 |
4 | 3 | 74.5 | 9 | 223.5 |
5 | 5 | 67 | 25 | 335 |
6 | 7 | 60.5 | 49 | 423.5 |
7 | 10 | 53.5 | 100 | 535 |
8 | 15 | 45 | 225 | 675 |
sumatoria | 43 | 557.5 | 413 | 2436.5 |SUSTITUYENDO EN LA FORMULA

m=((8)(2436.5)-(43)(557.5))/((8)(413)-(43)^2)= - 3.0794
b=((413)(557.5)-(2436.5)(43))/((8)(413)-(43)^2)= 86.2392

POR LO TANTO Y=mx+b

Y= -3.0794x+86.2392...