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Q2 (a) The following table gives the values of an experiment at various sample z Zi 0.3 0.4 0.5 0.6 0.7 0.8 fi 1.1880/a 1.2990ld | 1.4777ld 1.6488ld| 2.1555ld | 2.6666/d Check your solution with f(z) = 2e3z“ . Find the approximation values of f'(0.5) and f"(0.5) using : (i) 2-point forward difference (ii) 3-point central. (iii) 3-point backward.

Q2 (a) The following table gives the values of an experiment at various sample z Zi 0.3 0.4 0.5 0.6 0.7 0.8 fi 1.1880/a 1.2990ld | 1.4777ld 1.6488ld| 2.1555ld | 2.6666/d Check your solution with f(z) = 2e3z“ . Find the approximation values of f'(0.5) and f"(0.5) using : (i) 2-point forward difference (ii) 3-point central. (iii) 3-point backward.

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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Q2 (a) The following table gives the values of an experiment at various sample z Zi 0.3 0.4 0.5 0.6 0.7 0.8 fi 1.1880la 1.2990ld 1.4777ld 1.6488ld| 2.1555ld | 2.66661a Check your solution with f(z) = 2e3z . Find the approximation values of f'(0.5) %3D and f"(0.5) using : (i) 2-point forward difference (ii) 3-point central. (iii) 3-point backward. (iv) 3-point central for second derivative. (v) 5-point central difference for second derivative. (b) Explain which formula gives better approximation in Q2(a).
Transcribed Image Text:Q2 (a) The following table gives the values of an experiment at various sample z Zi 0.3 0.4 0.5 0.6 0.7 0.8 fi 1.1880la 1.2990ld 1.4777ld 1.6488ld| 2.1555ld | 2.66661a Check your solution with f(z) = 2e3z . Find the approximation values of f'(0.5) %3D and f"(0.5) using : (i) 2-point forward difference (ii) 3-point central. (iii) 3-point backward. (iv) 3-point central for second derivative. (v) 5-point central difference for second derivative. (b) Explain which formula gives better approximation in Q2(a).
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