Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 6, Problem 11A

Find the value of the complex fractions in Exercises 10 through 12.

10.
a. 1 3 + 5 6 3 3 4
b. 6 3 4 2 7 8 3 1 2 + 1 1 16
c. 10 1 2 × 1 2 4 ÷ 2 1 4

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Use Taylor Series to derive the entries to the pentadiagonal and heptadiagonal (septadiagonal?) circulant matrices
1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to this behavior?
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).
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