Suppose xo. X1....., are distinct numbers in the interval [a,b] and f € C**[a,b). Then, for each x in [a, b]. a number 5(x) (generally unknown) between xo. X.....X, and hence in (a,b), exists with flas)(E(x)), (n+ 1)! f(x) = P(x) + *("r - x).. (Ix- x)(r-x)- (3.3) where P(x) is the interpolating polynomial given in Eq. (3.1).
Suppose xo. X1....., are distinct numbers in the interval [a,b] and f € C**[a,b). Then, for each x in [a, b]. a number 5(x) (generally unknown) between xo. X.....X, and hence in (a,b), exists with flas)(E(x)), (n+ 1)! f(x) = P(x) + *("r - x).. (Ix- x)(r-x)- (3.3) where P(x) is the interpolating polynomial given in Eq. (3.1).
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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![Suppose xo, x1....X, are distinct numbers in the interval [a, b] and f € Ca+ [a, b). Then,
for each x in [a, b]., a number (x) (generally unknown) between xp. X,...Xps and hence
in (a, b), exists with
fia+) ({(x)),
(n + 1)!
f(x) = P(x) +
*("r - x) .. (Ix- x)(ex- x)-
(3.3)
where P(x) is the interpolating polynomial given in Eq. (3.1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17b51c75-7ac6-4abf-8bca-f39eb6db7658%2F5ce5b0fe-a617-482e-9f5b-cf6be286b979%2Fqv4dtki_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose xo, x1....X, are distinct numbers in the interval [a, b] and f € Ca+ [a, b). Then,
for each x in [a, b]., a number (x) (generally unknown) between xp. X,...Xps and hence
in (a, b), exists with
fia+) ({(x)),
(n + 1)!
f(x) = P(x) +
*("r - x) .. (Ix- x)(ex- x)-
(3.3)
where P(x) is the interpolating polynomial given in Eq. (3.1).
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