Essentials of Discrete Mathematics
Essentials of Discrete Mathematics
3rd Edition
ISBN: 9781284056242
Author: David J. Hunter
Publisher: Jones & Bartlett Learning
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Chapter 3.3, Problem 4E
To determine

A recursive definition for the set Y of all binary strings with more 0’s than 1’s.

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Evaluate the following integrals, showing all your working
Consider the function f(x) = 2x³-4x2-x+1. (a) Without doing a sketch, show that the cubic equation has at least one solution on the interval [0,1]. Use a theorem discussed in lectures, or see Section 1.8 of Calculus (7th ed) by Stewart. Ensure that the conditions of the theorem are satisfied (include this in your solution) (b) Now, by sketching the cubic (by hand or by computer), you should see that there is, in fact, exactly one zero in the interval [0,1]. Use Newton's method to find this zero accurate to 3 decimal places. You should include a sketch of the cubic, Newton's iteration formula, and the list of iterates. [Use a computer if possible, e.g., a spreadsheet or MatLab.]
Evaluate the following integrals, showing all your working
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