ADVANCED ENGINEERING MATHEMATICS
ADVANCED ENGINEERING MATHEMATICS
10th Edition
ISBN: 9781119664697
Author: Kreyszig
Publisher: WILEY
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4. 5. 6. Let X be a set and let f: XX be a function. We say that f is an involution if fof idx and that f is idempotent if f f = f. (a) If f is an involution, must it be invertible? Why or why not?2 (b) If f is idempotent, must it be invertible? Why or why not? (c) If f is idempotent and x E range(f), prove that f(x) = x. Prove that [log3 536] 5. You proof must be verifiable by someone who does not have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7). Define the sequence {a} by a = 2-i for i≥ 1. (a) Give the first five terms of the sequence. (b) Prove that the sequence is increasing.
1. 2. Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x². (a) Calculate (go f)(2). (b) Find an explicit formula for the function gof. Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1. Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.
Suppose that two toothpaste companies compete for customers in a fixed market in which each customer uses either Brand A or Brand B. Suppose also that a market analysis shows that the buying habits of the customers fit the following pattern in the quarters that were analyzed: each quarter (three-month period), 30% of A users will switch to B, while the rest stay with A. Moreover, 40% of B users will switch to A in a given quarter, while the remaining B users will stay with B. Finally assume that this pattern does not vary from quarter to quarter. (a) If A initially has all of the customers, what are the market shares 2 quarters later? (b) If A initially has all of the customers, what are the market shares 20 quarters later? (c) If B initially has all of the customers, what are the market shares 2 quarters later? (d) If B initially has all of the customers, what are the market shares 20 quarters later?

Chapter 14 Solutions

ADVANCED ENGINEERING MATHEMATICS

Ch. 14.1 - Prob. 11PCh. 14.1 - Prob. 12PCh. 14.1 - Prob. 13PCh. 14.1 - Prob. 14PCh. 14.1 - Prob. 15PCh. 14.1 - Prob. 16PCh. 14.1 - Prob. 17PCh. 14.1 - Prob. 18PCh. 14.1 - Prob. 19PCh. 14.1 - Prob. 20PCh. 14.1 - Prob. 21PCh. 14.1 - Prob. 22PCh. 14.1 - Prob. 23PCh. 14.1 - Prob. 24PCh. 14.1 - Prob. 25PCh. 14.1 - Prob. 26PCh. 14.1 - Prob. 27PCh. 14.1 - Prob. 28PCh. 14.1 - Prob. 29PCh. 14.1 - Prob. 30PCh. 14.1 - Prob. 32PCh. 14.1 - Prob. 33PCh. 14.1 - Prob. 35PCh. 14.2 - Prob. 1PCh. 14.2 - Prob. 2PCh. 14.2 - Prob. 3PCh. 14.2 - Prob. 4PCh. 14.2 - Prob. 5PCh. 14.2 - Prob. 6PCh. 14.2 - Prob. 7PCh. 14.2 - Prob. 9PCh. 14.2 - Prob. 10PCh. 14.2 - Prob. 11PCh. 14.2 - Prob. 12PCh. 14.2 - Prob. 13PCh. 14.2 - Prob. 14PCh. 14.2 - Prob. 15PCh. 14.2 - Prob. 16PCh. 14.2 - Prob. 17PCh. 14.2 - Prob. 18PCh. 14.2 - Prob. 19PCh. 14.2 - Prob. 20PCh. 14.2 - Prob. 21PCh. 14.2 - Prob. 22PCh. 14.2 - Prob. 23PCh. 14.2 - Prob. 24PCh. 14.2 - Prob. 25PCh. 14.2 - Prob. 26PCh. 14.2 - Prob. 27PCh. 14.2 - Prob. 28PCh. 14.2 - Prob. 29PCh. 14.2 - Prob. 30PCh. 14.3 - Prob. 1PCh. 14.3 - Prob. 2PCh. 14.3 - Prob. 3PCh. 14.3 - Prob. 4PCh. 14.3 - Prob. 5PCh. 14.3 - Prob. 6PCh. 14.3 - Prob. 7PCh. 14.3 - Prob. 8PCh. 14.3 - Prob. 11PCh. 14.3 - Prob. 12PCh. 14.3 - Prob. 13PCh. 14.3 - Prob. 14PCh. 14.3 - Prob. 15PCh. 14.3 - Prob. 16PCh. 14.3 - Prob. 17PCh. 14.3 - Prob. 18PCh. 14.3 - Prob. 19PCh. 14.3 - Prob. 20PCh. 14.4 - Prob. 1PCh. 14.4 - Prob. 2PCh. 14.4 - Prob. 3PCh. 14.4 - Prob. 4PCh. 14.4 - Prob. 5PCh. 14.4 - Prob. 6PCh. 14.4 - Prob. 7PCh. 14.4 - Prob. 8PCh. 14.4 - Prob. 9PCh. 14.4 - Prob. 10PCh. 14.4 - Prob. 11PCh. 14.4 - Prob. 12PCh. 14.4 - Prob. 13PCh. 14.4 - Prob. 14PCh. 14.4 - Prob. 15PCh. 14.4 - Prob. 16PCh. 14.4 - Prob. 17PCh. 14.4 - Prob. 18PCh. 14.4 - Prob. 19PCh. 14 - Prob. 1RQCh. 14 - Prob. 2RQCh. 14 - Prob. 3RQCh. 14 - Prob. 4RQCh. 14 - Prob. 5RQCh. 14 - Prob. 6RQCh. 14 - Prob. 7RQCh. 14 - Prob. 8RQCh. 14 - Prob. 9RQCh. 14 - Prob. 10RQCh. 14 - Prob. 11RQCh. 14 - Prob. 12RQCh. 14 - Prob. 13RQCh. 14 - Prob. 14RQCh. 14 - Prob. 15RQCh. 14 - Prob. 16RQCh. 14 - Prob. 17RQCh. 14 - Prob. 18RQCh. 14 - Prob. 19RQCh. 14 - Prob. 20RQCh. 14 - Prob. 21RQCh. 14 - Prob. 22RQCh. 14 - Prob. 23RQCh. 14 - Prob. 24RQCh. 14 - Prob. 25RQCh. 14 - Prob. 26RQCh. 14 - Prob. 27RQCh. 14 - Prob. 28RQCh. 14 - Prob. 29RQCh. 14 - Prob. 30RQ
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