Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus
11th Edition
ISBN: 9780134434636
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 12.5, Problem 19E
To determine
To express: The
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Keity
x२
1. (i)
Identify which of the following subsets of R2 are open and which
are not.
(a)
A = (2,4) x (1, 2),
(b)
B = (2,4) x {1,2},
(c)
C = (2,4) x R.
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(ii)
Give an example of a bounded set in R2 which is not open.
[2 Marks]
(iii)
Give an example of an open set in R2 which is not bounded.
[2 Marks
2.
(i)
Which of the following statements are true? Construct coun-
terexamples for those that are false.
(a)
sequence.
Every bounded sequence (x(n)) nEN C RN has a convergent sub-
(b)
(c)
(d)
Every sequence (x(n)) nEN C RN has a convergent subsequence.
Every convergent sequence (x(n)) nEN C RN is bounded.
Every bounded sequence (x(n)) EN CRN converges.
nЄN
(e)
If a sequence (xn)nEN C RN has a convergent subsequence, then
(xn)nEN is convergent.
[10 Marks]
(ii)
Give an example of a sequence (x(n))nEN CR2 which is located on
the parabola x2 = x², contains infinitely many different points and converges
to the limit x = (2,4).
[5 Marks]
2.
(i) What does it mean to say that a sequence (x(n)) nEN CR2
converges to the limit x E R²?
[1 Mark]
(ii) Prove that if a set ECR2 is closed then every convergent
sequence (x(n))nen in E has its limit in E, that is
(x(n)) CE and x() x
x = E.
[5 Marks]
(iii)
which is located on the parabola x2 = = x
x4, contains a subsequence that
Give an example of an unbounded sequence (r(n)) nEN CR2
(2, 16) and such that x(i)
converges to the limit x = (2, 16) and such that x(i)
#
x() for any i j.
[4 Marks
Chapter 12 Solutions
Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus
Ch. 12.1 - Write in terms of j.
Ch. 12.1 - Simplify: 2.
Ch. 12.1 - Simplify: 2.
Ch. 12.1 - Prob. 4PECh. 12.1 - Prob. 5PECh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - In Exercises 1–4, perform the indicated operations...Ch. 12.1 - In Exercises 5–16, express each number in terms of...
Ch. 12.1 - In Exercises 5–16, express each number in terms of...Ch. 12.1 - In Exercises 5–16, express each number in terms of...Ch. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - In Exercises 17–32, simplify each of the given...Ch. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - In Exercises 17–32, simplify each of the given...Ch. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - In Exercises 33–50, perform the indicated...Ch. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - In Exercises 55–60, find the values of x and y...Ch. 12.1 - In Exercises 55–60, find the values of x and y...Ch. 12.1 - Prob. 61ECh. 12.1 - Prob. 62ECh. 12.1 - Prob. 63ECh. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Prob. 70ECh. 12.1 - Prob. 71ECh. 12.1 - Prob. 72ECh. 12.1 - Prob. 73ECh. 12.1 - Prob. 74ECh. 12.2 - Prob. 1PECh. 12.2 - Prob. 2PECh. 12.2 - Prob. 3PECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - In Exercises 1-4, perform the indicated operations...Ch. 12.2 - Prob. 4ECh. 12.2 - In Exercises 5–38, perform the indicated...Ch. 12.2 - Prob. 6ECh. 12.2 - In Exercises 5–38, perform the indicated...Ch. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - In Exercises 5–38, perform the indicated...Ch. 12.2 - In Exercises 5–38, perform the indicated...Ch. 12.2 - Prob. 14ECh. 12.2 - In Exercises 5–38, perform the indicated...Ch. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - In Exercises 5–38, perform the indicated...Ch. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - In Exercises 43–56, solve the given...Ch. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - In Exercises 61-64, answer or explain as...Ch. 12.2 - Prob. 62ECh. 12.2 - Prob. 63ECh. 12.2 - Prob. 64ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.4 - Prob. 1PECh. 12.4 - Prob. 2PECh. 12.4 - Prob. 3PECh. 12.4 - Prob. 1ECh. 12.4 - In Exercises 1 and 2, change the sign of the real...Ch. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - In Exercises 3-18, represent each complex number...Ch. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - In Exercises 19-36, represent each complex number...Ch. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - In Exercises 19-36, represent each complex number...Ch. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - In Exercises 19-36, represent each complex number...Ch. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - In Exercises 37–44, solve the given problems.
41....Ch. 12.4 - In Exercises 37–44, solve the given problems.
42....Ch. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.5 - Prob. 1PECh. 12.5 - Prob. 2PECh. 12.5 - Represent 3.00e2.66j in rectangular form.
Ch. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - In Exercises 3-22, express the given numbers in...Ch. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - In Exercises 23–30, express the given complex...Ch. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - In Exercises 23–30, express the given complex...Ch. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - In Exercises 31–34, perform the indicated...Ch. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - In Exercises 35–40, perform the indicated...Ch. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - In Exercises 35–40, perform the indicated...Ch. 12.6 - Prob. 1PECh. 12.6 - Prob. 2PECh. 12.6 - Find the polar form power: (3 cos 50°)8
Ch. 12.6 - Prob. 4PECh. 12.6 - Prob. 1ECh. 12.6 - Prob. 2ECh. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - Prob. 12ECh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12.6 - Prob. 25ECh. 12.6 - Prob. 26ECh. 12.6 - Prob. 27ECh. 12.6 - Prob. 28ECh. 12.6 - Prob. 29ECh. 12.6 - Prob. 30ECh. 12.6 - Prob. 31ECh. 12.6 - Prob. 32ECh. 12.6 - Prob. 33ECh. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12.6 - Prob. 37ECh. 12.6 - In Exercises 35–40, use DeMoivre’s theorem to find...Ch. 12.6 - Prob. 39ECh. 12.6 - Prob. 40ECh. 12.6 - Prob. 41ECh. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - In Exercises 41–46, find all of the roots of the...Ch. 12.6 - Prob. 46ECh. 12.6 - Prob. 47ECh. 12.6 - Prob. 48ECh. 12.6 - Prob. 49ECh. 12.6 - Prob. 50ECh. 12.6 - Prob. 51ECh. 12.6 - Prob. 52ECh. 12.6 - The electric power p (in W) supplied to an element...Ch. 12.6 - Prob. 54ECh. 12.6 - Prob. 55ECh. 12.6 - Prob. 56ECh. 12.7 - Prob. 1PECh. 12.7 - Prob. 1ECh. 12.7 - Prob. 2ECh. 12.7 - Prob. 3ECh. 12.7 - Prob. 4ECh. 12.7 - Prob. 5ECh. 12.7 - Prob. 6ECh. 12.7 - Prob. 7ECh. 12.7 - Prob. 8ECh. 12.7 - Prob. 9ECh. 12.7 - Prob. 10ECh. 12.7 - Prob. 11ECh. 12.7 - Prob. 12ECh. 12.7 - Prob. 13ECh. 12.7 - Prob. 14ECh. 12.7 - Prob. 15ECh. 12.7 - Prob. 16ECh. 12.7 - Prob. 17ECh. 12.7 - Prob. 18ECh. 12.7 - Prob. 19ECh. 12.7 - Prob. 20ECh. 12.7 - Prob. 21ECh. 12.7 - Prob. 22ECh. 12.7 - Prob. 23ECh. 12.7 - Prob. 24ECh. 12 - Prob. 1RECh. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - In Exercises 29–36, give the polar and exponential...Ch. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - In Exercises 37–48, give the rectangular form of...Ch. 12 - Prob. 46RECh. 12 - Prob. 47RECh. 12 - Prob. 48RECh. 12 - Prob. 49RECh. 12 - Prob. 50RECh. 12 - Prob. 51RECh. 12 - Prob. 52RECh. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Prob. 55RECh. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - Prob. 59RECh. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 72RECh. 12 - Prob. 73RECh. 12 - Prob. 74RECh. 12 - Prob. 75RECh. 12 - Prob. 76RECh. 12 - Prob. 77RECh. 12 - Prob. 78RECh. 12 - Prob. 79RECh. 12 - Prob. 80RECh. 12 - Prob. 81RECh. 12 - Prob. 82RECh. 12 - Prob. 85RECh. 12 - Prob. 86RECh. 12 - Prob. 87RECh. 12 - Prob. 88RECh. 12 - Prob. 89RECh. 12 - Prob. 90RECh. 12 - Prob. 91RECh. 12 - Prob. 92RECh. 12 - Prob. 93RECh. 12 - Prob. 94RECh. 12 - Prob. 95RECh. 12 - Prob. 96RECh. 12 - Prob. 97RECh. 12 - Prob. 98RECh. 12 - Prob. 99RECh. 12 - Prob. 100RECh. 12 - Prob. 1PTCh. 12 - Multiply, expressing the result in polar...Ch. 12 - Prob. 3PTCh. 12 - Prob. 4PTCh. 12 - Prob. 5PTCh. 12 - Prob. 6PTCh. 12 - Express 2.56(cos 125.2° + j sin 125.2°) in...Ch. 12 - Prob. 8PTCh. 12 -
Express 3.47 − 2.81j in exponential form.
Ch. 12 - Prob. 10PTCh. 12 - Prob. 11PTCh. 12 - Prob. 12PT
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