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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![6. Consider the function f (x)
1
, x > 0.
%3D
x + 2
(a) Find the interpolating polynomial P2(x) that agrees with f at the points
X1 = 0, x2 = 1, x3 = 2. (You may use Lagrange's interpolation formula or
Newton's divided differences formula).
(b) Use the above polynomial P2(x) to approximate f(1.5).
(c) Find an upper bound for the error |f(1.5) – P2(1.5)| using the appropriate
error formula and compare your result with the actual error.](https://content.bartleby.com/qna-images/question/3e085104-fb6a-40f0-89db-c0353a727e3b/d00fbded-ed99-4c73-9cf9-bc8361548d60/cj74bcc_thumbnail.jpeg)
Transcribed Image Text:6. Consider the function f (x)
1
, x > 0.
%3D
x + 2
(a) Find the interpolating polynomial P2(x) that agrees with f at the points
X1 = 0, x2 = 1, x3 = 2. (You may use Lagrange's interpolation formula or
Newton's divided differences formula).
(b) Use the above polynomial P2(x) to approximate f(1.5).
(c) Find an upper bound for the error |f(1.5) – P2(1.5)| using the appropriate
error formula and compare your result with the actual error.
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