Advanced Engineering Mathematics
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.
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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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