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(Finite Difference Calculus) Example 1: Given the function f(x)=(Inx)*, find f'(2) numerically to three decimals accuracy. (Begin with h = 0.1) ANS: f'(2) =0.517327 = 0.517.

(Finite Difference Calculus) Example 1: Given the function f(x)=(Inx)*, find f'(2) numerically to three decimals accuracy. (Begin with h = 0.1) ANS: f'(2) =0.517327 = 0.517.

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 Differentiation (Finite Difference Calculus) Example 1: Given the function f(x)=(lnx)*, find f'(2) numerically to three decimals accuracy. (Begin with h = 0.1) ANS: f'(2) = 0.517327 = 0.517. Example 2: The curve y = f(x) passes through the three points (1,3), (2,8.5), and (3,44). Estimate, as accurate as possible, dy/ dx at x= 1.5. Example 3: The function f(x) has the following properties at x,: Af Vf =0.23751 and =0.24369, where h=0.1. Find f "(x,) and h f"(x,) using central differences with error of O(h)'.
Transcribed Image Text:Numerical Differentiation (Finite Difference Calculus) Example 1: Given the function f(x)=(lnx)*, find f'(2) numerically to three decimals accuracy. (Begin with h = 0.1) ANS: f'(2) = 0.517327 = 0.517. Example 2: The curve y = f(x) passes through the three points (1,3), (2,8.5), and (3,44). Estimate, as accurate as possible, dy/ dx at x= 1.5. Example 3: The function f(x) has the following properties at x,: Af Vf =0.23751 and =0.24369, where h=0.1. Find f "(x,) and h f"(x,) using central differences with error of O(h)'.
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