1. Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h) to estimate the first derivative of HE f(x) - 1+cos(2) at z=0.25 using a step size h = 0.125, Compute the percent relative true error for each approximation. (Note: Round off your approximations to 9 decimal places. Percentage errors must be rounded-off to 3 decimal places.) Interpret your results.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
1. Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h) to estimate the first derivative of
f(x)= NE
1+cos(2)
at z=0.25 using a step size h = 0.125, Compute the percent relative true error for each approximation. (Note: Round off your approximations to 9
decimal places. Percentage errors must be rounded-off to 3 decimal places.) Interpret your results.
Transcribed Image Text:1. Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h) to estimate the first derivative of f(x)= NE 1+cos(2) at z=0.25 using a step size h = 0.125, Compute the percent relative true error for each approximation. (Note: Round off your approximations to 9 decimal places. Percentage errors must be rounded-off to 3 decimal places.) Interpret your results.
f(x) =
(x)soo+[
Transcribed Image Text:f(x) = (x)soo+[
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