Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 56, Problem 12A

Determine the unknown value for each of the following exercises. Round the answers to 3 decimal places.
Chapter 56, Problem 12A, Determine the unknown value for each of the following exercises. Round the answers to 3 decimal
Arc length A B C = 620.700 mmand ∠1 = 69.30°. Find r.

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1.6. By manipulating Taylor series, determine the constant C for an error expansion of (1.3) of the form wj−u' (xj) ~ Ch¼u (5) (x;), where u (5) denotes the fifth derivative. Based on this value of C and on the formula for u(5) (x) with u(x) = esin(x), determine the leading term in the expansion for w; - u'(x;) for u(x) = esin(x). (You will have to find maxε[-T,T] |u(5) (x)| numerically.) Modify Program 1 so that it plots the dashed line corresponding to this leading term rather than just N-4. This adjusted dashed line should fit the data almost perfectly. Plot the difference between the two on a log-log scale and verify that it shrinks at the rate O(h6).
Define sinc(x) = sin(x)/x, except with the singularity removed.  Differentiate sinc(x) once and twice.
1.4. Run Program 1 to N = 216 instead of 212. What happens to the plot of error vs. N? Why? Use the MATLAB commands tic and toc to generate a plot of approximately how the computation time depends on N. Is the dependence linear, quadratic, or cubic?

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