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Pk) = )(K- (-) = a. A table of values for f(r) = sin(xx) is: 1. * f(x) 1.0 0.0 1.5 -1.0 2.0 0.0 Use quadratic interpolation to estimate f(1.6). Rk) = (K-2) 4x²_12x +8 (15-1) (15-2) (16) = 0.6 (-0,4) ) = (-0 6.5 (-05) '(4)=(-0,96 b. Use the Lagrange error formula to obtain a reasonable bound on the error in your estimate pa(1.6) of f(1.6). -t' car (1€) 3! 0,124 c. Calculate the exact error f(1.6) - Pa(1.6).

Pk) = )(K- (-) = a. A table of values for f(r) = sin(xx) is: 1. * f(x) 1.0 0.0 1.5 -1.0 2.0 0.0 Use quadratic interpolation to estimate f(1.6). Rk) = (K-2) 4x²_12x +8 (15-1) (15-2) (16) = 0.6 (-0,4) ) = (-0 6.5 (-05) '(4)=(-0,96 b. Use the Lagrange error formula to obtain a reasonable bound on the error in your estimate pa(1.6) of f(1.6). -t' car (1€) 3! 0,124 c. Calculate the exact error f(1.6) - Pa(1.6).

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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1. a. A table of values for f(x) = sin(xx) is: * f(x) 1.0 0.0 1.5 -1.0 2.0 0.0 Use quadratic interpolation to estimate f(1.6). 3 4x²_12x +8 (1,5-1)(15-2) A (.6) = 0.6 (-0,4) 6) =(-0,96 6. 5 (-0s) %3D b. Use the Lagrange error formula to obtain a reasonable bound on the error in your estimate p2(1.6) of f(1.6). -t° car(1€), 3 3! E (o,024) 0, 124 c. Calculate the exact error f(1.6) – P2(1.6). F(46) = sin(1.6) = -0,951 = -095) - (-096) =C0,009
Transcribed Image Text:1. a. A table of values for f(x) = sin(xx) is: * f(x) 1.0 0.0 1.5 -1.0 2.0 0.0 Use quadratic interpolation to estimate f(1.6). 3 4x²_12x +8 (1,5-1)(15-2) A (.6) = 0.6 (-0,4) 6) =(-0,96 6. 5 (-0s) %3D b. Use the Lagrange error formula to obtain a reasonable bound on the error in your estimate p2(1.6) of f(1.6). -t° car(1€), 3 3! E (o,024) 0, 124 c. Calculate the exact error f(1.6) – P2(1.6). F(46) = sin(1.6) = -0,951 = -095) - (-096) =C0,009
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