i 2 3 Xi 0.5 1 1.5 f(x;) -1 -0.625 1.5 7.625 P(x)= ? P(x) = L, (x)fo +L (x)f¡ + L,(x)f, + L;(x)f; +.... (x- x, )(x – x1)...(x – x,-1)(x – x;41)....(x – x,) L, (x; - x,)(x; - x,) .(x; - x;-1 )(x; - x41) .(x, – x, )

i 2 3 Xi 0.5 1 1.5 f(x;) -1 -0.625 1.5 7.625 P(x)= ? P(x) = L, (x)fo +L (x)f¡ + L,(x)f, + L;(x)f; +.... (x- x, )(x – x1)...(x – x,-1)(x – x;41)....(x – x,) L, (x; - x,)(x; - x,) .(x; - x;-1 )(x; - x41) .(x, – x, )

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 52E

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Question

Using the data in the table, with the help of Lagrange Interpolation Polynomials, 3.
Obtain a polynomial of degrees P (0.75) =? , P (1.25) =? , P (1.5) =? values
Find.

i
1
2
3
0.5
1
1.5
f(x;)
-1
-0.625
1.5
7.625
P(x)= ?
P(x) = L, (x)fo +L (x)f; + L,(x)f, + L;(x)f; +....
(x – x,)(x – x,)...(x – x,-1 )(x – X;41)....(x – x, )
L,
i+1
(x; - xo)(x; – x,)..(x; - x;1)(x; - Xj41). .(x; - x„)

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