Discrete Mathematics With Applications
5th Edition
ISBN: 9781337694193
Author: EPP, Susanna S.
Publisher: Cengage Learning,
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Textbook Question
Chapter 12.1, Problem 11ES
In 10—12, use the rules about order of precedence to eliminate the parentheses in the given regular expression.
11.
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4.
The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
a) Find the average rate of change of revenue when the production is increased from 1000 to 1001 units.
MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
1
If ye y = sin x, find dy/dx and dy/dx²
at (0, 0).
Chapter 12 Solutions
Discrete Mathematics With Applications
Ch. 12.1 - If x and y are strings, the concatenation of x and...Ch. 12.1 - Prob. 2TYCh. 12.1 - Prob. 3TYCh. 12.1 - Prob. 4TYCh. 12.1 - Prob. 5TYCh. 12.1 - Prob. 6TYCh. 12.1 - Prob. 7TYCh. 12.1 - Use of a single dot in a regular expression stands...Ch. 12.1 - Prob. 9TYCh. 12.1 - If r is a regular expression, the notation r +...
Ch. 12.1 - Prob. 11TYCh. 12.1 - Prob. 12TYCh. 12.1 - Prob. 1ESCh. 12.1 - Prob. 2ESCh. 12.1 - Prob. 3ESCh. 12.1 - In 4—6, describe L1L2,L1L2, and (L1L2)*for the...Ch. 12.1 - Prob. 5ESCh. 12.1 - Prob. 6ESCh. 12.1 - Prob. 7ESCh. 12.1 - Prob. 8ESCh. 12.1 - In 7—9, add parentheses to emphasize the order of...Ch. 12.1 - Prob. 10ESCh. 12.1 - In 10—12, use the rules about order of precedence...Ch. 12.1 - Prob. 12ESCh. 12.1 - In 13—15, use set notation to derive the language...Ch. 12.1 - Prob. 14ESCh. 12.1 - Prob. 15ESCh. 12.1 - Prob. 16ESCh. 12.1 - In 16—18, write five strings that belong to the...Ch. 12.1 - Prob. 18ESCh. 12.1 - Prob. 19ESCh. 12.1 - Prob. 20ESCh. 12.1 - In 19—21, use words to describe the language...Ch. 12.1 - Prob. 22ESCh. 12.1 - In 22—24, indicate whether the given strings...Ch. 12.1 - Prob. 24ESCh. 12.1 - Prob. 25ESCh. 12.1 - Prob. 26ESCh. 12.1 - In 25—27, find a regular expression that defines...Ch. 12.1 - Let r, s, and t be regular expressions over...Ch. 12.1 - Prob. 29ESCh. 12.1 - Prob. 30ESCh. 12.1 - Prob. 31ESCh. 12.1 - In 31—39, write a regular expression to define the...Ch. 12.1 - Prob. 33ESCh. 12.1 - Prob. 34ESCh. 12.1 - Prob. 35ESCh. 12.1 - Prob. 36ESCh. 12.1 - Prob. 37ESCh. 12.1 - Prob. 38ESCh. 12.1 - Prob. 39ESCh. 12.1 - Prob. 40ESCh. 12.1 - Write a regular expression to define the set of...Ch. 12.2 - The five objects that make up a finite-state...Ch. 12.2 - The next-state table for an automaton shows the...Ch. 12.2 - In the annotated next-state table, the initial...Ch. 12.2 - A string w consisting of input symbols is accepted...Ch. 12.2 - The language accepted by a finite-state automaton...Ch. 12.2 - If N is the next-stale function for a finite-state...Ch. 12.2 - One part of Kleene’s theorem says that given any...Ch. 12.2 - The second part of Kleene’s theorem says that...Ch. 12.2 - A regular language is .__________Ch. 12.2 - Given the language consisting of all strings of...Ch. 12.2 - Find the state of the vending machine in Example...Ch. 12.2 - Prob. 2ESCh. 12.2 - Prob. 3ESCh. 12.2 - Prob. 4ESCh. 12.2 - Prob. 5ESCh. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 2—7, a finite-state automaton is given by a...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - In 8 and 9, a finite-state automaton is given by...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - A finite-state automaton A given by the transition...Ch. 12.2 - Prob. 12ESCh. 12.2 - Consider again the finite-state automaton of...Ch. 12.2 - In each of 14—19, (a) find the language accepted...Ch. 12.2 - Prob. 15ESCh. 12.2 - Prob. 16ESCh. 12.2 - Prob. 17ESCh. 12.2 - Prob. 18ESCh. 12.2 - Prob. 19ESCh. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - Prob. 21ESCh. 12.2 - Prob. 22ESCh. 12.2 - Prob. 23ESCh. 12.2 - Prob. 24ESCh. 12.2 - Prob. 25ESCh. 12.2 - Prob. 26ESCh. 12.2 - In each of 20—28, (a) design an automaton with the...Ch. 12.2 - Prob. 28ESCh. 12.2 - Prob. 29ESCh. 12.2 - Prob. 30ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 32ESCh. 12.2 - Prob. 33ESCh. 12.2 - Prob. 34ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 36ESCh. 12.2 - Prob. 37ESCh. 12.2 - Prob. 38ESCh. 12.2 - Prob. 39ESCh. 12.2 - Prob. 40ESCh. 12.2 - Prob. 41ESCh. 12.2 - Prob. 42ESCh. 12.2 - Prob. 43ESCh. 12.2 - Prob. 44ESCh. 12.2 - Prob. 45ESCh. 12.2 - In 29—47, design a finite-state automaton to...Ch. 12.2 - Prob. 47ESCh. 12.2 - Prob. 48ESCh. 12.2 - Write a computer algorithm that simulates the...Ch. 12.2 - Prob. 50ESCh. 12.2 - Prob. 51ESCh. 12.2 - Prob. 52ESCh. 12.2 - Prob. 53ESCh. 12.2 - a. Let A be a finite-state automaton with input...Ch. 12.3 - Given a finite-state automaton A with...Ch. 12.3 - Prob. 2TYCh. 12.3 - Given states s and t in a finite-state automaton...Ch. 12.3 - Prob. 4TYCh. 12.3 - Prob. 5TYCh. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaton A given by the...Ch. 12.3 - Consider the finite-state automaon A discussed in...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Consider the finite-state automaton given by the...Ch. 12.3 - Prob. 7ESCh. 12.3 - Prob. 8ESCh. 12.3 - Prob. 9ESCh. 12.3 - Prob. 10ESCh. 12.3 - Prob. 11ESCh. 12.3 - Prob. 12ESCh. 12.3 - Prob. 13ESCh. 12.3 - Prob. 14ESCh. 12.3 - Prob. 15ESCh. 12.3 - Prob. 16ESCh. 12.3 - Prob. 17ESCh. 12.3 - Prob. 18ES
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