Mathematics: A Discrete Introduction
3rd Edition
ISBN: 9780840049421
Author: Edward A. Scheinerman
Publisher: Cengage Learning
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Textbook Question
Chapter 1.1, Problem 1.1E
Simplify the following algebraic expression:
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Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b).
x-a
f(x)=
1 - cos (4x-4)
3(x-1)²
; a = 1
a. Use a graphing utility to graph f. Select the correct graph below..
A.
W
→
✓
Each graph is displayed in a [- 1,3] by [0,5] window.
B.
in
✓
○ C.
und
☑
Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x-1
○ A. The limit appears to be approximately ☐ .
(Round to the nearest tenth as needed.)
B. The limit does not exist.
b. Evaluate f(x) for values of x near 1 to support your conjecture.
X
0.9
0.99
0.999
1.001
1.01
1.1
f(x)
○ D.
+
☑
(Round to six decimal places as needed.)
Does the table from the previous step support your conjecture?
A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…
x²-19x+90
Let f(x) =
.
Complete parts (a) through (c) below.
x-a
a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x→a+
○ A.
a=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no values of a for which the limit equals a finite number.
b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A.
(Type integers or simplified fractions)
C. There are no values of a that satisfy lim f(x) = ∞.
+
x-a
c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A. Either a
(Type integers or simplified fractions)
B.
Sketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions.
f(2)=0
f(4) is undefined
lim f(x)=1
X-6
lim f(x) = -∞
x-0+
lim f(x) = ∞
lim f(x) = ∞
x-4
_8
Chapter 1 Solutions
Mathematics: A Discrete Introduction
Ch. 1.1 - Simplify the following algebraic expression:...Ch. 1.2 - Prob. 2.1ECh. 1.3 - Prob. 3.1ECh. 1.3 - Prob. 3.2ECh. 1.3 - Prob. 3.3ECh. 1.3 - Prob. 3.4ECh. 1.3 - Prob. 3.5ECh. 1.3 - Prob. 3.6ECh. 1.3 - Prob. 3.7ECh. 1.3 - Prob. 3.8E
Ch. 1.3 - Prob. 3.9ECh. 1.3 - Prob. 3.10ECh. 1.3 - Prob. 3.11ECh. 1.3 - Prob. 3.12ECh. 1.3 - Prob. 3.13ECh. 1.3 - Prob. 3.14ECh. 1.4 - Prob. 4.1ECh. 1.4 - Prob. 4.2ECh. 1.4 - Prob. 4.3ECh. 1.4 - Prob. 4.4ECh. 1.4 - Prob. 4.5ECh. 1.4 - Prob. 4.6ECh. 1.4 - Prob. 4.7ECh. 1.4 - Prob. 4.8ECh. 1.4 - Prob. 4.9ECh. 1.4 - Prob. 4.10ECh. 1.4 - Prob. 4.11ECh. 1.4 - Prob. 4.12ECh. 1.5 - Prove that the sum of two odd integers is even.Ch. 1.5 - Prove that the sum of an odd integer and an even...Ch. 1.5 - Prove that if n is an odd integer, then n is also...Ch. 1.5 - Prove that the product of two even integers is...Ch. 1.5 - Prove that the product of an even integer and an...Ch. 1.5 - Prove that the product of two odd integers is odd.Ch. 1.5 - Prove that the square of an odd integer is odd.Ch. 1.5 - Prove that the cube of an odd integer is odd.Ch. 1.5 - Suppose a, b, and c are integers. Prove that if ab...Ch. 1.5 - Suppose a, b, and c are integers. Prove that if...Ch. 1.5 - Suppose a, b, d, x, and y are integers. Prove that...Ch. 1.5 - Suppose a, b, c, and d are integers. Prove that if...Ch. 1.5 - Let x be an integer. Prove that x is odd if and...Ch. 1.5 - Let x be an integers. Prove that x is odd if and...Ch. 1.5 - Let x be an integer. Prove that 0x if and only if...Ch. 1.5 - Let a and b be integers. Prove that ab if and only...Ch. 1.5 - Let a be a number with a1. Prove that a number x...Ch. 1.5 - Prove that the difference between consecutive...Ch. 1.5 - Let a be a perfect square. Prove that a is the...Ch. 1.5 - For real numbers a and b, prove that if 0ab, then...Ch. 1.5 - Prove that the difference between distinct,...Ch. 1.5 - Prove that an integer is odd if and only if it is...Ch. 1.5 - Suppose you are asked to prove a statement of the...Ch. 1.5 - Suppose you are asked to prove a statement of the...Ch. 1.6 - Disprove: If a and b are integers with ab, then...Ch. 1.6 - Disprove: If a and b are nonnegative integers with...Ch. 1.6 - Disprove: If a, b, and c are positive integers...Ch. 1.6 - Disprove: If a, b, and c are positive integers,...Ch. 1.6 - Disprove: If p and q are prime, then p+q is...Ch. 1.6 - Disprove: If p is prime, then 2p1 is also prime.Ch. 1.6 - Prob. 6.7ECh. 1.6 - An integer is a palindrome if it reads the same...Ch. 1.6 - Prob. 6.9ECh. 1.6 - Prob. 6.10ECh. 1.6 - Prob. 6.11ECh. 1.6 - Prob. 6.12ECh. 1.6 - Prob. 6.13ECh. 1.7 - Prob. 7.1ECh. 1.7 - Prob. 7.2ECh. 1.7 - Prob. 7.3ECh. 1.7 - Prob. 7.4ECh. 1.7 - Prob. 7.5ECh. 1.7 - Prob. 7.6ECh. 1.7 - Prob. 7.7ECh. 1.7 - Prob. 7.8ECh. 1.7 - Prob. 7.9ECh. 1.7 - Prob. 7.10ECh. 1.7 - Prob. 7.11ECh. 1.7 - Prob. 7.12ECh. 1.7 - Prob. 7.13ECh. 1.7 - Prob. 7.14ECh. 1.7 - Prob. 7.15ECh. 1.7 - Prob. 7.16ECh. 1.7 - Prob. 7.17ECh. 1.7 - Prob. 7.18ECh. 1.7 - Prove that xy can be reexpressed in terms of just ...Ch. 1.7 - Prob. 7.20ECh. 1 - Prob. 1STCh. 1 - Prob. 2STCh. 1 - Prob. 3STCh. 1 - Prob. 4STCh. 1 - Prob. 5STCh. 1 - Prob. 6STCh. 1 - Prob. 7STCh. 1 - Prob. 8STCh. 1 - Prob. 9STCh. 1 - Prob. 10STCh. 1 - Prob. 11STCh. 1 - Prob. 12STCh. 1 - Prob. 13STCh. 1 - Prob. 14STCh. 1 - Prob. 15STCh. 1 - Prob. 16STCh. 1 - Prob. 17STCh. 1 - Prob. 18STCh. 1 - Prob. 19STCh. 1 - Prob. 20ST
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