Calculo Numerico Atividade 3

Prévia do material em texto

P(X) = L0.f(X0) + L1.f(X1) + L2.f(X2) + L3.f(X3) 
X0 = 20, X1 = 25, X2 = 30, X3 = 35 
 
L0 = (X-X1). (X-X2). (X-X3) -> (X-25).(X-30).(X-35) -> -(X 3 – 90X 2 + 2675X – 26250) (X0-X1). (X0-
X2). (X0-X3) -> (20-25).(20-30).(20-35) -> 750 
 
L1 = (X-X0). (X-X2). (X-X3) -> (X-20).(X-30).(X-35) -> X + 2 2 0 3 – 85X 2 350X – 100 (X1-X0). (X1-
X2). (X1-X3) -> (25-20).(25-30).(25-35) -> 250 
 
L2 = (X-X0). (X-X1). (X-X3) -> (X-20).(X-25).(X-35) -> -(X + 2075X 17500) 3 – 80X 2 – (X2-X0). (X2-
X1). (X2-X3) -> (30-20).(30-25).(30-35) -> 250 
 
L3 = (X-X0). (X-X1). (X-X2) -> (X-20).(X-25).(X-30) -> X + 1850X 3 – 75X 2 – 1500 (X3-X0). (X3-X1). 
(X3-X2) -> (35-20).(35-25).(35-30) -> 750 
 
f(X) – Calor específico 
 f(X0) f(X1) f(X2) f(X3) 
0,99907 0,99852 0,99826 0,99818 
750 250 250 750 -> MMC = 750 
 
P(X) = 0,99907. -(X 90X 3 – 2 + 2675X – 26250) + 0,99852. (X + 2350X 21000) + 3 – 85X 2 – 
0,99826. -(X 3 – 80X 2 + 2075X – 17500) + 0,99818. (X + 1850X 3 – 75X 2 – 1500) 
P(X) = 0,99907. -(X 90X 3 – 2 + 2675X – 26250) + 3. {0,99852. (X 3 – 85X 2 + 2350X – 21000)} + 
3. {0,99826. -(X 3 – 80X 2 + 2075X – 17500)} + 3. {0,99818. (X 3 – 75X 2 + 1850X – 1500)} 
750 
P(X) = 1,99625 X 149,71 X + 3657,37X + 11263,37 
 750 
P¹(X) = Y0 + Y1 – Y0 (X – X0) 
X1 – X0 
P¹(X) = 0,99852 + 0,99826 – 0,99852 (X – 25) = 0,00026X + 4,991 
 
P¹ (27,5) = -0,00026. 27,5 + 4,991 = 0,99677