2 - According to table 1 values which one is the approximation of f(1.7) (just degree 1, P1 (1.7)) by using Lagrange interpolation ( You can find Lagrange polynomial formula below the table 1) Table 1 f(x) 1.0 0.7651977 1.3 0.6200860 1.6 0.4554022 1.9 0.2818186 2.2 0.1103623 Useful formula for Lagrange Interpolation: P(x) = f(x0)Ln,0(x) + + f(x,)Ln.a(x) = f(xx)Ln&(x). where, for each k = 0, 1I,.,n. (x – xo)(x – x) - -(x – xx-1)(x – Xx +1)*…· (x – x,) ("r – 1x) - - · (1+?x – 'r)(!-Ix – ?x) .. - (!x – ?x)(Or – !x) Las(x) =- (x - x) (x- x)

2 - According to table 1 values which one is the approximation of f(1.7) (just degree 1, P1 (1.7)) by using Lagrange interpolation ( You can find Lagrange polynomial formula below the table 1) Table 1 f(x) 1.0 0.7651977 1.3 0.6200860 1.6 0.4554022 1.9 0.2818186 2.2 0.1103623 Useful formula for Lagrange Interpolation: P(x) = f(x0)Ln,0(x) + + f(x,)Ln.a(x) = f(xx)Ln&(x). where, for each k = 0, 1I,.,n. (x – xo)(x – x) - -(x – xx-1)(x – Xx +1)*…· (x – x,) ("r – 1x) - - · (1+?x – 'r)(!-Ix – ?x) .. - (!x – ?x)(Or – !x) Las(x) =- (x - x) (x- x)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

2- According to table 1 values which one is the approximation of f(1.7) (just degree 1, P1 (1.7)) by using Lagrange
interpolation ( You can find Lagrange polynomial formula below the table 1)
Table 1
f(x)
1.0
0.7651977
1.3
0.6200860
1.6
0.4554022
1.9
0.2818186
2.2
0.1103623
Useful formula for Lagrange Interpolation:
P(x) = f(xo)Ln.0(x)+-… ·+ ƒ(xn)La„(x) = '
Ef(x)Ln&(x).
where, for each k = 0, 1, ... , n,
(x – xo)(x – x1) - (x – xi-1)(x – xk+1)•…·(x – xn)
("x- x) .. (1+?x – ?x)(1-?x – x) … . - ('x – ¥r)(Or – !r)_
LA(x) =
(x – x;)
(x2 – X;)
-0

a) O 0.7168271
b) O 0.1675144
c) O 0.397541
d) O 0.2818186
e) O 0.5102968

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