Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 4, Problem 21SE
To determine
To find: The number of paths of lengths 1, 2, 3 and 4 from
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
not use ai please
A graph of the function f is given below:
Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1
Of is defined at a.
If is not defined at x = a.
Of is continuous at x = a.
If is discontinuous at x = a.
Of is smooth at x = a.
Of is not smooth at = a.
If has a horizontal tangent line at = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
If has no tangent line at x = a.
f(a + h) - f(a)
lim
is finite.
h→0
h
f(a + h) - f(a)
lim
h->0+
and lim
h
h->0-
f(a + h) - f(a)
h
are infinite.
lim
does not exist.
h→0
f(a+h) - f(a)
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
The graph below is the function f(z)
4
3
-2
-1
-1
1
2
3
-3
Consider the function f whose graph is given above.
(A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter
"DNE". If a limit can be represented by -∞o or ∞o, then do so.
lim f(z)
+3
lim f(z)
1-1
lim f(z)
f(1)
= 2
=
-4
= undefined
lim f(z) 1
2-1
lim f(z):
2-1+
lim f(x)
2+1
-00
= -2
= DNE
f(-1) = -2
lim f(z) = -2
1-4
lim f(z)
2-4°
00
f'(0)
f'(2)
=
=
(B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left-
continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If
there are none, enter "none".
Discontinuous at z =
Left-continuous at x =
Invalid use of a comma.syntax incomplete.
Right-continuous at z =
Invalid use of a comma.syntax incomplete.
(C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list,
if needed (eg. -2, 3, 5).…
Chapter 4 Solutions
Discrete Mathematics
Ch. 4.1 - In Exercises 1–4, list the set of edges and set of...Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - In Exercises 5–8, draw a diagram representing the...Ch. 4.1 - Prob. 7ECh. 4.1 - In Exercises 5–8, draw a diagram representing the...Ch. 4.1 - Prob. 9ECh. 4.1 - In Exercises 9–14, determine whether a graph is...
Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Draw the graph with ν = {1, 2, … , 10} as its set...Ch. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Show that there are an even number of vertices...Ch. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - In Exercises 26–29, find the adjacency matrix and...Ch. 4.1 - Prob. 29ECh. 4.1 - In Exercises 30 and 31, construct the graph for...Ch. 4.1 - Prob. 31ECh. 4.1 - In Exercises 32 and 33, construct the graph for...Ch. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - In Exercises 35-37, can each matrix be an...Ch. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Are the pairs of graphs in (a), (b), and (c)...Ch. 4.1 - Are the pairs of graphs in (a), (b), and (c)...Ch. 4.1 - Draw all the non isomorphic graphs with three...Ch. 4.1 - Prob. 45ECh. 4.1 - Draw all the nonisomorphic graphs with five...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Suppose a graph has n vertices, each with degree...Ch. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Suppose Mr. and Mrs. Lewis attended a bridge party...Ch. 4.1 - Prove that if a graph has at least two vertices,...Ch. 4.2 - In Exercises 1–4, determine whether the multigraph...Ch. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - In Exercises 9 and 10, perform the following...Ch. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - In Exercises 18–23, determine whether the...Ch. 4.2 - Prob. 19ECh. 4.2 - In Exercises 18–23, determine whether the...Ch. 4.2 - Prob. 21ECh. 4.2 - In Exercises 18–23, determine whether the...Ch. 4.2 - Prob. 23ECh. 4.2 - In Exercises 24–29, determine whether the...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - An old childhood game asks children to trace a...Ch. 4.2 - Prob. 39ECh. 4.2 - In 1859, Sir William Rowan Hamilton, a famous...Ch. 4.2 - Give examples of connected graphs satisfying each...Ch. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Are the following two graphs isomorphic? Justify...Ch. 4.2 - Prob. 51ECh. 4.2 - A bipartite graph is a graph in which the vertices...Ch. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.3 - In Exercises 1–4, use the breadth-first search...Ch. 4.3 - In Exercises 1–4, use the breadth-first search...Ch. 4.3 - Prob. 3ECh. 4.3 - In Exercises 1–4, use the breadth-first search...Ch. 4.3 - In Exercises 5–8, determine the distance from S to...Ch. 4.3 - In Exercises 5–8, determine the distance from S to...Ch. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - For the following graph, determine the number of...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.4 - In Exercises 1–8, find the chromatic number of the...Ch. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - It might be supposed that if a graph has a large...Ch. 4.4 - Prob. 13ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Suppose is a graph with three vertices. How many...Ch. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Show that it is possible to assign one of the...Ch. 4.4 - Prob. 35ECh. 4.4 - Prove Theorem 4.9 by mathematical induction on the...Ch. 4.4 - Suppose that each vertex of a graph is such that...Ch. 4.5 - In Exercises 1–4, list the vertices and directed...Ch. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 49ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Write a breadth-first search algorithm for...Ch. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - In Exercises 67–70, determine the distance from S...Ch. 4.5 - In Exercises 67–70, determine the distance from S...Ch. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Determine whether the following pairs of directed...Ch. 4.5 - Determine whether the following pairs of directed...Ch. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4 - Prob. 1SECh. 4 - Prob. 2SECh. 4 - Prob. 3SECh. 4 - Prob. 4SECh. 4 - Prob. 5SECh. 4 - Prob. 6SECh. 4 - Prob. 7SECh. 4 - Prob. 8SECh. 4 - Prob. 9SECh. 4 - Prob. 10SECh. 4 - Prob. 11SECh. 4 - Prob. 12SECh. 4 - Prob. 13SECh. 4 - Prob. 14SECh. 4 - Is the property “is connected” a graph isomorphism...Ch. 4 - Prob. 16SECh. 4 - Prob. 17SECh. 4 - Prob. 18SECh. 4 - Prob. 19SECh. 4 - Prob. 20SECh. 4 - Prob. 21SECh. 4 - Prob. 22SECh. 4 - Prob. 23SECh. 4 - Prob. 24SECh. 4 - Prob. 25SECh. 4 - Prob. 26SECh. 4 - Prob. 28SECh. 4 - Prob. 29SECh. 4 - Prob. 30SECh. 4 - Prob. 31SECh. 4 - Prob. 32SECh. 4 - Prob. 34SECh. 4 - Prob. 35SECh. 4 - Prob. 36SECh. 4 - Prob. 37SECh. 4 - Prob. 38SECh. 4 - Prob. 39SECh. 4 - Prob. 40SECh. 4 - Prob. 6CPCh. 4 - Prob. 9CPCh. 4 - Prob. 14CP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- A graph of the function f is given below: Study the graph of f at the value given below. Select each of the following that applies for the value a = -4. f is defined at = a. f is not defined at 2 = a. If is continuous at x = a. Of is discontinuous at x = a. Of is smooth at x = a. f is not smooth at x = a. If has a horizontal tangent line at x = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. Of has no tangent line at x = a. f(a + h) − f(a) h lim is finite. h→0 f(a + h) - f(a) lim is infinite. h→0 h f(a + h) - f(a) lim does not exist. h→0 h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.arrow_forwardFind the point of diminishing returns (x,y) for the function R(X), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars). R(x) = 10,000-x3 + 42x² + 700x, 0≤x≤20arrow_forward[3] Use a substitution to rewrite sn(x) as 8n(x) = 1 2π C sin 2n+1 sin f(x+u)du.arrow_forward
- Differentiate the following functions. (a) y(x) = x³+6x² -3x+1 (b) f(x)=5x-3x (c) h(x) = sin(2x2)arrow_forwardx-4 For the function f(x): find f'(x), the third derivative of f, and f(4) (x), the fourth derivative of f. x+7arrow_forwardIn x For the function f(x) = find f'(x). Then find f''(0) and f''(9). 11x'arrow_forward
- Let f(x) = √√x+3 and g(x) = 6x − 2. Find each of the following composite functions and state the domain: (a) fog (b) gof, (c) fof (d) gogarrow_forwardCompute the following: (a) 8x³ + 3x dx (b) cos(2u) du (c) f² ebx dxarrow_forwardFind the following limits. (a) lim 3(x-1)² x→2 x (b) lim 0+x (c) lim 3x2-x+1 x²+3 x²+x-12 x-3 x-3arrow_forward
- For f(x) = (x+3)² - 2 sketch f(x), f(x), f(x − 2), and f(x) — 2. State the coordi- nates of the turning point in each graph.arrow_forwardif the b coloumn of a z table disappeared what would be used to determine b column probabilitiesarrow_forwardConstruct a model of population flow between metropolitan and nonmetropolitan areas of a given country, given that their respective populations in 2015 were 263 million and 45 million. The probabilities are given by the following matrix. (from) (to) metro nonmetro 0.99 0.02 metro 0.01 0.98 nonmetro Predict the population distributions of metropolitan and nonmetropolitan areas for the years 2016 through 2020 (in millions, to four decimal places). (Let x, through x5 represent the years 2016 through 2020, respectively.) x₁ = x2 X3 261.27 46.73 11 259.59 48.41 11 257.96 50.04 11 256.39 51.61 11 tarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Sequences and Series Introduction; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=m5Yn4BdpOV0;License: Standard YouTube License, CC-BY
Introduction to sequences; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=VG9ft4_dK24;License: Standard YouTube License, CC-BY