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Consider the interpolating polynomial for f(x) = 15 with interpolation nodes x = 0, 2, 4, 6, 8, 10. x+5 (a) Find an upper bound for the interpolation error at x = 1. (b) Find an upper bound for the interpolation error at x = 5. (c) Find an upper bound for the interpolation error for 0 < x < 10.

Consider the interpolating polynomial for f(x) = 15 with interpolation nodes x = 0, 2, 4, 6, 8, 10. x+5 (a) Find an upper bound for the interpolation error at x = 1. (b) Find an upper bound for the interpolation error at x = 5. (c) Find an upper bound for the interpolation error for 0 < x < 10.

Advanced Engineering Mathematics
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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Consider the interpolating polynomial for \( f(x) = \frac{1}{x+5} \) with interpolation nodes \( x = 0, 2, 4, 6, 8, 10 \). (a) Find an upper bound for the interpolation error at \( x = 1 \). (b) Find an upper bound for the interpolation error at \( x = 5 \). (c) Find an upper bound for the interpolation error for \( 0 \leq x \leq 10 \).
Transcribed Image Text:Consider the interpolating polynomial for \( f(x) = \frac{1}{x+5} \) with interpolation nodes \( x = 0, 2, 4, 6, 8, 10 \). (a) Find an upper bound for the interpolation error at \( x = 1 \). (b) Find an upper bound for the interpolation error at \( x = 5 \). (c) Find an upper bound for the interpolation error for \( 0 \leq x \leq 10 \).
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