Question

Using Lagrange's interpolation formula find y(0.25) from the following table: x0.4 0.6 0.81 y 0.48 0.12 3.2 Write 3-decimal plates

Answer 1

Lagrange is Interpolation formula xo x23 y : yol y 8.Т. 3 using Lagrange formula you-f(x) = (oc - X, )(x-xg) (x-*3) (X-XI) (x,-)g) 060-33) yo + (x-xo)(x-Xg 26-23) (x,-Xo) (6-4) (-23) y, + (-to) (-21) (x-x3) (ng-20) (x2-x) (362-23) 9,2 + (x-10) (1-21) fl-ig) (az-x)(8C3-X17623-89) 93 Ques х 0.4 Or61 0.8 y 10.48 0.1 2 3.2 xo - 019 2=0.6 MC2 = 0.8 &z=1 yos 0.48 di -01 ya *3 = 3.2 find y(0.25)

( 8.o) (h.o) (9. ) 7€ X (55.0-) (5€.0-) (s1.0-) + (0:4) (0.2) 60:2) XQ xoil +60:15)(-0-35)(-0.75) (h.o-)(7.0-) (2.0) (9.0-) (6.0-) (7.0-) (SL.07 (95.0-) (S10-) + (84.0)x (51:02) (55.0-) (SEO-) (57.05€! ( 8.0-1) 19.0-1) (4.0-1) T.ex (8.0 - 92.0) (9.0 - $2.0) (6.0-S2.0) + 8 * (1-8.0) (9.0-8.0) (h.0-8.0) (1-92.0) (9.0-97.0) Ch.0-51.0 + Хо•1 0. (1-9.0) (8.0-9.0) (h.0-4.0) (1-4.0) (8.0-6.0) (9.0-6.0) (1-92-9) (8.0-52.0) (6.0-52.0) +86.0 X(1-52.0) (8.0-97.0) (9.0-92.O) -(92.0

y = 0.0693 01048 0.0061875 + 0 0 7875 htbo.o 0.016 0.016 8 horo y (0.25)- 1.44375 0.38671 +4.92187 - 1.925 90-25)- 4.05391 4.054 And