EBK ADVANCED ENGINEERING MATHEMATICS
6th Edition
ISBN: 9781284127003
Author: ZILL
Publisher: JONES+BARTLETT LEARNING,LLC (CC)
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Chapter 1.2, Problem 30E
(a)
To determine
To verify:
(b)
To determine
The explicit solution of the given differential equation by using one parameter family of solutions and to explain the reason due to which the solution is not defined in the interval
(c)
To determine
The largest interval for the solution of the initial value problem.
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7.
Define the sequence {b} by
bo = 0
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= 2
8.
bn=4bn-1-4bn-2 for n ≥ 2
(a) Give the first five terms of this sequence.
(b) Prove: For all n = N, bn = 2nn.
Let a Rsuch that a 1, and let nЄ N. We're going to derive a formula for
Σoa without needing to prove it by induction. Tip: it can be helpful to use C1+C2+...+Cn
notation instead of summation notation when working this out on scratch paper.
(a) Take a a² and manipulate it until it is in the form Σ.a.
i=0
(b) Using this, calculate the difference between a Σ0 a² and Σ0 a², simplifying away the
summation notation.
i=0
(c) Now that you know what (a – 1) Σ0 a² equals, divide both sides by a − 1 to derive the
formula for
a².
(d) (Optional, just for induction practice) Prove this formula using induction.
3.
Let A, B, and C be sets and let f: A B and g BC be functions. For
each of the following, draw arrow diagrams that illustrate the situation, and then prove the
proposition.
(a) If ƒ and g are injective, then go f is injective.
(b) If ƒ and g are surjective, then go f is surjective.
(c) If gof is injective then f is injective. Make sure your arrow diagram shows that 9 does
not need to be injective!
(d) If gof is surjective then g is surjective. Make sure your arrow diagram shows that f
does not need to be surjective!
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.
Chapter 1 Solutions
EBK ADVANCED ENGINEERING MATHEMATICS
Ch. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10E
Ch. 1.1 - Prob. 11ECh. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Prob. 37ECh. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Prob. 51ECh. 1.1 - Prob. 52ECh. 1.1 - Prob. 53ECh. 1.1 - Prob. 54ECh. 1.1 - Prob. 55ECh. 1.1 - Prob. 56ECh. 1.1 - Prob. 57ECh. 1.1 - Prob. 58ECh. 1.1 - Prob. 59ECh. 1.1 - Prob. 60ECh. 1.1 - Prob. 61ECh. 1.1 - Prob. 62ECh. 1.2 - Prob. 1ECh. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.3 - Prob. 1ECh. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1 - Prob. 1CRCh. 1 - Prob. 2CRCh. 1 - Prob. 3CRCh. 1 - Prob. 4CRCh. 1 - Prob. 5CRCh. 1 - Prob. 6CRCh. 1 - Prob. 7CRCh. 1 - Prob. 8CRCh. 1 - Prob. 9CRCh. 1 - Prob. 10CRCh. 1 - Prob. 11CRCh. 1 - Prob. 12CRCh. 1 - Prob. 13CRCh. 1 - Prob. 14CRCh. 1 - Prob. 15CRCh. 1 - Prob. 16CRCh. 1 - Prob. 17CRCh. 1 - Prob. 18CRCh. 1 - Prob. 19CRCh. 1 - Prob. 20CRCh. 1 - Prob. 21CRCh. 1 - Prob. 22CRCh. 1 - Prob. 23CRCh. 1 - Prob. 24CRCh. 1 - Prob. 25CRCh. 1 - Prob. 26CRCh. 1 - Prob. 27CRCh. 1 - Prob. 28CRCh. 1 - Prob. 29CRCh. 1 - Prob. 30CRCh. 1 - Prob. 31CRCh. 1 - Prob. 32CRCh. 1 - Prob. 33CRCh. 1 - Prob. 34CRCh. 1 - Prob. 35CRCh. 1 - Prob. 36CRCh. 1 - Prob. 37CRCh. 1 - Prob. 38CRCh. 1 - Prob. 39CRCh. 1 - Prob. 40CRCh. 1 - Prob. 41CRCh. 1 - Prob. 42CRCh. 1 - Prob. 43CR
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