DISCRETE MATHEMATICS WITH APPLICATION (
5th Edition
ISBN: 9780357097717
Author: EPP
Publisher: CENGAGE L
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Chapter 12.2, Problem 26ES
To determine
(a)
To design an automaton with the given input alphabet that accepts the given set of strings.
To determine
(b)
A regular expression that defines the language accepted by the automaton.
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5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
1. Consider the following preference ballots:
Number of voters
Rankings 6 5 4 2
1st choice A DCB
DC
2nd choice B B D
3rd choice DCBD
4th choice CA
AAA
For each of the four voting systems we have studied, determine who would win the election
in each case. (Remember: For plurality with runoff, all but the top two vote-getters are
simultaneously eliminated at the end of round 1.)
Practice
k Help
ises
A
96
Anewer The probability that you get a sum of at least 10 is
Determine the number of ways that the specified event can occur when
two number cubes are rolled.
1. Getting a sum of 9 or 10
3. Getting a sum less than 5
2. Getting a sum of 6 or 7
4. Getting a sum that is odd
Tell whether you would use the addition principle or the multiplication
principle to determine the total number of possible outcomes for the
situation described.
5. Rolling three number cubes
6. Getting a sum of 10 or 12 after rolling three number cubes
A set of playing cards contains four groups of cards designated by color
(black, red, yellow, and green) with cards numbered from 1 to 14 in each
group. Determine the number of ways that the specified event can occur
when a card is drawn from the set.
7. Drawing a 13 or 14
9. Drawing a number less than 4
8. Drawing a yellow or green card
10. Drawing a black, red, or green car
The spinner is divided into equal parts.
Find the specified…
Chapter 12 Solutions
DISCRETE MATHEMATICS WITH APPLICATION (
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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