Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus
11th Edition
ISBN: 9780135902912
Author: Allyn J. Washington
Publisher: PEARSON
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Chapter 2.3, Problem 31E
To determine
To express: The area A of the large rectangle formed by the smaller rectangles in two ways and determine illustrated property by the result.
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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 2 Solutions
Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus
Ch. 2.1 - What is the measure of the complement of in Fig....Ch. 2.1 - Prob. 2PECh. 2.1 - In Exercises 1–4, answer the given questions about...Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...
Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 25–30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 41-46, solve the given problems
41. A...Ch. 2.1 - In Exercises 41–16, solve the given...Ch. 2.1 - In Exercises 41-46, solve the given problems
43. A...Ch. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.2 - Prob. 1PECh. 2.2 - Prob. 2PECh. 2.2 - Prob. 3PECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - Prob. 30ECh. 2.2 - In Exercises 31–58, solve the given problems.
31....Ch. 2.2 - In Exercises 31–58, solve the given problems.
32....Ch. 2.2 - In Exercises 31–58, solve the given problems.
33....Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given problems.
35....Ch. 2.2 - In Exercises 31–58, solve the given problems.
36....Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 50ECh. 2.2 - In Exercises 31–58, solve the given problems.
51....Ch. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.3 - Prob. 1PECh. 2.3 - Prob. 2PECh. 2.3 - Prob. 3PECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - In Exercises 21–24, set up a formula for the...Ch. 2.3 - In Exercises 25–46, solve the given...Ch. 2.3 - What conclusion can you make about the two...Ch. 2.3 - Find the area of a square whose diagonal is 24.0...Ch. 2.3 - Noting the quadrilateral in Fig. 2.67, determine...Ch. 2.3 - The sum S of the measures of the interior angles...Ch. 2.3 - Express the area A of the large rectangle in Fig....Ch. 2.3 - Express the area of the square in Fig. 2.69 in...Ch. 2.3 - Part of an electric circuit is wired in the...Ch. 2.3 - A walkway 3.0 m wide is constructed along the...Ch. 2.3 - An architect designs a rectangular window such...Ch. 2.3 - Find the area of the cross section of concrete...Ch. 2.3 - A beam support in a building is in the shape of a...Ch. 2.3 - Each of two walls (with rectangular windows) of an...Ch. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.4 - Prob. 1PECh. 2.4 - Prob. 2PECh. 2.4 - Prob. 3PECh. 2.4 - In Exercises 1-4, answer the given questions about...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 17 and 18, find the area of the...Ch. 2.4 - In Exercises 17 and 18, find the area of the...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 31–34, find a formula for the...Ch. 2.4 - In Exercises 31–34, find a formula for the...Ch. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - In Exercises 35–58, solve the given...Ch. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.5 - Prob. 1PECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - In Exercises 19–22, calculate the area of the...Ch. 2.6 - Prob. 1PECh. 2.6 - Prob. 2PECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - In Exercises 5–22, find the volume or area of each...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - In Exercises 5–22, find the volume or area of each...Ch. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - In Exercises 23–46, solve the given problems.
36....Ch. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - In Exercises 23–46, solve the given problems.
44....Ch. 2.6 - In Exercises 23–46, solve the given problems.
45....Ch. 2.6 - Prob. 46ECh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - In Exercises 19–26, find the perimeter or area of...Ch. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - In Exercises 27–32, find the volume of the...Ch. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - If the dimensions of a plane geometric figure are...Ch. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - In Exercises 55–84, solve the given problems.
69....Ch. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 1PTCh. 2 - Prob. 2PTCh. 2 - Prob. 3PTCh. 2 - Prob. 4PTCh. 2 - Prob. 5PTCh. 2 - Prob. 6PTCh. 2 - Prob. 7PTCh. 2 - Find the surface area of a tennis ball whose...Ch. 2 - Prob. 9PTCh. 2 - Prob. 10PTCh. 2 - Prob. 11PTCh. 2 - Prob. 12PTCh. 2 - Prob. 13PTCh. 2 - Prob. 14PT
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