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1. Compute forward and backward difference approximations of O(h) and O(h²), and central π difference approximations of O(h²) and O(h*) for the first derivative of y=sin x at x = 4 T using a value of h=- Given the true value is 0.7071. Estimate the true percent relative 12 error &, for each approximation.

1. Compute forward and backward difference approximations of O(h) and O(h²), and central π difference approximations of O(h²) and O(h*) for the first derivative of y=sin x at x = 4 T using a value of h=- Given the true value is 0.7071. Estimate the true percent relative 12 error &, for each approximation.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter58: Achievement Review—section Five
Section: Chapter Questions
Problem 30AR: Determine dimension x to 3 decimal places.
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Tutorial 11: Numerical Differentiation 1. Compute forward and backward difference approximations of O(h) and O(h²), and central difference approximations of O(h²) and O(h*) for the first derivative of y = sin x at x = - 4 using a value of h = Given the true value is 0.7071. Estimate the true percent relative 12 error ɛ, for each approximation.
Transcribed Image Text:Tutorial 11: Numerical Differentiation 1. Compute forward and backward difference approximations of O(h) and O(h²), and central difference approximations of O(h²) and O(h*) for the first derivative of y = sin x at x = - 4 using a value of h = Given the true value is 0.7071. Estimate the true percent relative 12 error ɛ, for each approximation.
Use high-accuracy differentiation formula O(h*) to estimate the first derivative of f(x) = log x. Evaluate at x= 20 with h =2. Use centered diffrence anproximation to estimate the first and second derivatives of
Transcribed Image Text:Use high-accuracy differentiation formula O(h*) to estimate the first derivative of f(x) = log x. Evaluate at x= 20 with h =2. Use centered diffrence anproximation to estimate the first and second derivatives of
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