6. Consider the function f(x) = 1 x > 0. x +2 (a) Find the interpolating polynomial P2(x) that agrees with f at the points ¤1 = 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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. Consider the function f(x)
1
, x > 0.
x + 2
(a) Find the interpolating polynomial P2(x) that agrees with f at the points
x1 = 0, x2 = 1, xz = 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.
Transcribed Image Text:6. Consider the function f(x) 1 , x > 0. x + 2 (a) Find the interpolating polynomial P2(x) that agrees with f at the points x1 = 0, x2 = 1, xz = 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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