Answer to Question #8498 in Quantitative Methods for ahmed faraz

Question

let f(x)=cosx
xo=0,x1=.6,x2=.9
find linear and quadratic interpolation

Answer 1

y0=1
y1=0.8253
y2=0.6216

ai=(0.8253-1)/(0.6-0)=-0.2912

bi=1+0.2912*0=1

y=-0.2912x+1--- linear interpolation
(0^2)*ai+0*bi+ci=1
(0.6^2)*ai^2+0.6*bi+ci=0.8253
(0.9^2)*ai^2+0.9*bi+ci=0.6216

ci=1

(0.6^2)*ai+0.6bi=-0.1747
(0.9^2)*ai+0.9*bi=-0.3784

ai=-(0.6bi+0.1747)/(0.6^2)
-(0.9^2)*(0.6bi+0.1747)/(0.6^2)+0.9*bi=-0.3784

-1.35bi-0.3931=-0.3784
bi=-0,0109

ai=-(0.6bi+0.1747)/0.36=-0.4672

y=-0.4672*x^2-0,0109*x+1