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(A) If f(0) = 0.7,f(0.1) = 1, and S(0.2) = 0.2, use an appropriate 3-point formula to approximate f'(0). If IS"(x)| < 5.3 for all x, find a bound on the approximation error. %3D %3D (B) Find the error term and the order of the numerical differentiation formula given by g"'(x0) = G(xo – 2h) + S(xo – h) – f(xo + k) + (xo +2h)

(A) If f(0) = 0.7,f(0.1) = 1, and S(0.2) = 0.2, use an appropriate 3-point formula to approximate f'(0). If IS"(x)| < 5.3 for all x, find a bound on the approximation error. %3D %3D (B) Find the error term and the order of the numerical differentiation formula given by g"'(x0) = G(xo – 2h) + S(xo – h) – f(xo + k) + (xo +2h)

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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NUMERICAL ANALYSIS
(A) If f(0) = 0.7, f(0.1) = 1, and S(0.2) = 0.2, use an appropriate 3-point formula to approximate f'(0). If IS"(x)| < 5.3 for all x, find a bound on the approximation error. %3D %3D %3D (B) Find the error term and the order of the numerical differentiation formula given by s(x-2h)+ f(xo - h)- f(xo +h)+ S(xo +2h)
Transcribed Image Text:(A) If f(0) = 0.7, f(0.1) = 1, and S(0.2) = 0.2, use an appropriate 3-point formula to approximate f'(0). If IS"(x)| < 5.3 for all x, find a bound on the approximation error. %3D %3D %3D (B) Find the error term and the order of the numerical differentiation formula given by s(x-2h)+ f(xo - h)- f(xo +h)+ S(xo +2h)
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