A Interpolação de Lagrange

[pic 1]Resposta: -8,31

FX= - 0,7      AX0= -1   BX1= 0   CX2= 3

 (X0)= -10   F(X1) = -5   F(X2) = -1  

Lo (X)=      =    = 0,6475 [pic 2][pic 3]

ʄ (x0) L0 (x) = -10 (0.65) = - 6,475

L1 (x)=      =  = 0,3700 aprox. 0,4[pic 4][pic 5]

ʄ (x1) L1 (x) = -5 (0,4) = - 2,00

L2 (x)=      =   = -0,0175 [pic 6][pic 7]

ʄ (x2) L2 (x) = -1 (-0,175) = 0,0175

ʄ (x0) L0 (x) + ʄ (x1) L1 (x) + ʄ (x2) L2 (x)= (-6,4750) + (-1,8500) + 0,0175=  -8,3

[pic 8]

Resposta: 5,92

FX= - 1,82      AX0= -6   BX1=-2 CX2 = -1

 D(X0) = 3   EF(X1) = 5   FF(X2) = 11 

L0 (X)=      =    = -0,00738[pic 9][pic 10]

ʄ (x0) L0 (x) = 3 (-0,0074) = - 0,0222

L1 (x)=      =  = 0,8569[pic 11][pic 12]

ʄ (x1) L1 (x) = 5 (0,8569) = 4,2845 = 4,3

L2 (x)=      =   =0.15048[pic 13][pic 14]

ʄ (x2) L2 (x) = 11 (0,15048) =  1,65528 = 1,66

ʄ (x0) L0 (x) + ʄ (x1) L1 (x) + ʄ (x2) L2 (x)= -0,02214 + 4,2845 + 1,65528= 5,9

[pic 15]

Resposta: 14,80

FX= (2,81)      X0=2   X1= 5   X2= 8

 (X0 )=-15   F(X1) =-12   F(X2) = -3  

L0 (X)=      =    =  0,63145[pic 16][pic 17]

ʄ (x0) L0 (x) = -15 (0,63415) = - 9,47175

L1 (x)=      =  = 0,4671[pic 18][pic 19]

ʄ (x1) L1 (x) = -12 (0,4671) = -5,6052

L2 (x)=      =   = -0.9855[pic 20][pic 21]

ʄ (x2) L2 (x) = -3 (-0,9855) =  0,29565

ʄ (x0) L0 (x) + ʄ (x1) L1 (x) + ʄ (x2) L2 (x)= -9,47175 - 5,6052 + 0,29565=  14,7813

[pic 22]

Resposta: 6,35

(Fx)= 5,17      X0=2   X1= 4   X2=8

 (X0)= -3  F(X1) =4   F(X2) =  7 

L0 (X)=      =    =  - 0,2755925[pic 23][pic 24]

ʄ (x0) L0 (x) = -3 (-O,2755925) = 0,827775

L1 (x)=      =  = 1,1213875[pic 25][pic 26]

ʄ (x1) L1 (x) = 4 (1,1213875) = 4,48555

L2 (x)=      =   = 0,1545375[pic 27][pic 28]

ʄ (x2) L2 (x) = 7 (0,1545375) =  1,0817625

ʄ (x0) L0 (x) + ʄ (x1) L1 (x) + ʄ (x2) L2 (x)= 0,827775 + 4,48555 +1,0817625 =  6,38775

[pic 29] 

[pic 30]

Resposta:

[pic 31]

FX= 3,5      X0=-1   X1= 2  X2= 5 X3 = 9

 (X0 )= 1   F(X1) =7  F(X2) = 97   F(X3) = 609

Resposta: 33,62

L0 (X)=      =    =  0,38671875[pic 32][pic 33]

ʄ (x0) L0 (x) = 1 (0,38671875) = 0,38671875

L1 (x)=      =  = 0,982142[pic 34][pic 35]

ʄ (x1) L1 (x) = 7 (0,982142) = 6,874994

L2 (x)=      =   = 0,4296875[pic 36][pic 37]