Prealgebra & Introductory Algebra (5th Edition) (What's New in Developmental Math)
5th Edition
ISBN: 9780134707631
Author: Elayn Martin-Gay
Publisher: PEARSON
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Chapter 16.2, Problem 4VRVC
To determine
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The process of solving a
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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 16 Solutions
Prealgebra & Introductory Algebra (5th Edition) (What's New in Developmental Math)
Ch. 16.1 - Prob. 1PCh. 16.1 - Prob. 2PCh. 16.1 - Prob. 3PCh. 16.1 - Prob. 4PCh. 16.1 - Prob. 5PCh. 16.1 - Prob. 6PCh. 16.1 - Prob. 7PCh. 16.1 - Prob. 8PCh. 16.1 - Prob. 9PCh. 16.1 - Prob. 1E
Ch. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.1 - Prob. 6ECh. 16.1 - Prob. 7ECh. 16.1 - Prob. 8ECh. 16.1 - Prob. 9ECh. 16.1 - Prob. 10ECh. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Prob. 16ECh. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Prob. 20ECh. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.1 - Prob. 27ECh. 16.1 - Prob. 28ECh. 16.1 - Prob. 29ECh. 16.1 - Prob. 30ECh. 16.1 - Prob. 31ECh. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Prob. 34ECh. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Prob. 39ECh. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.1 - Prob. 43ECh. 16.1 - Prob. 44ECh. 16.1 - Prob. 45ECh. 16.1 - Prob. 46ECh. 16.1 - Prob. 47ECh. 16.1 - Prob. 48ECh. 16.1 - Prob. 49ECh. 16.1 - Prob. 50ECh. 16.1 - Prob. 51ECh. 16.1 - Prob. 52ECh. 16.1 - Prob. 53ECh. 16.1 - Prob. 54ECh. 16.1 - Prob. 55ECh. 16.1 - Prob. 56ECh. 16.1 - Prob. 57ECh. 16.1 - Prob. 58ECh. 16.1 - Prob. 59ECh. 16.1 - Prob. 60ECh. 16.1 - Prob. 61ECh. 16.1 - Prob. 62ECh. 16.1 - Prob. 63ECh. 16.1 - Prob. 64ECh. 16.1 - Prob. 65ECh. 16.1 - Prob. 66ECh. 16.1 - Prob. 67ECh. 16.1 - Prob. 68ECh. 16.1 - Prob. 69ECh. 16.1 - Prob. 70ECh. 16.1 - Prob. 71ECh. 16.1 - Prob. 72ECh. 16.1 - Prob. 73ECh. 16.1 - Prob. 74ECh. 16.2 - Prob. 1PCh. 16.2 - Prob. 2PCh. 16.2 - Prob. 3PCh. 16.2 - Prob. 4PCh. 16.2 - Prob. 5PCh. 16.2 - Prob. 1VRVCCh. 16.2 - Prob. 2VRVCCh. 16.2 - Prob. 3VRVCCh. 16.2 - Prob. 4VRVCCh. 16.2 - Prob. 5VRVCCh. 16.2 - Prob. 6VRVCCh. 16.2 - Prob. 7VRVCCh. 16.2 - Prob. 8VRVCCh. 16.2 - Prob. 9VRVCCh. 16.2 - Prob. 10VRVCCh. 16.2 - Prob. 11VRVCCh. 16.2 - Prob. 12VRVCCh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - Prob. 19ECh. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Prob. 32ECh. 16.2 - Prob. 33ECh. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Prob. 38ECh. 16.2 - Prob. 39ECh. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Prob. 42ECh. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Prob. 48ECh. 16.2 - Prob. 49ECh. 16.2 - Prob. 50ECh. 16.2 - Prob. 51ECh. 16.2 - Prob. 52ECh. 16.3 - Prob. 1CCCh. 16.3 - Prob. 1PCh. 16.3 - Prob. 2PCh. 16.3 - Prob. 3PCh. 16.3 - Prob. 4PCh. 16.3 - Prob. 5PCh. 16.3 - Prob. 6PCh. 16.3 - Prob. 1VRVCCh. 16.3 - Prob. 2VRVCCh. 16.3 - Prob. 3VRVCCh. 16.3 - Prob. 4VRVCCh. 16.3 - Prob. 5VRVCCh. 16.3 - Prob. 6VRVCCh. 16.3 - Prob. 7VRVCCh. 16.3 - Prob. 8VRVCCh. 16.3 - Prob. 9VRVCCh. 16.3 - Prob. 10VRVCCh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Prob. 14ECh. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Prob. 20ECh. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Prob. 24ECh. 16.3 - Prob. 25ECh. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - Prob. 28ECh. 16.3 - Prob. 29ECh. 16.3 - Prob. 30ECh. 16.3 - Prob. 31ECh. 16.3 - Prob. 32ECh. 16.3 - Prob. 33ECh. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Prob. 38ECh. 16.3 - Prob. 39ECh. 16.3 - Prob. 40ECh. 16.3 - Prob. 41ECh. 16.3 - Prob. 42ECh. 16.3 - Prob. 43ECh. 16.3 - Prob. 44ECh. 16.3 - Prob. 45ECh. 16.3 - Prob. 46ECh. 16.3 - Prob. 47ECh. 16.3 - Prob. 48ECh. 16.3 - Prob. 49ECh. 16.3 - Prob. 50ECh. 16.3 - Prob. 51ECh. 16.3 - Prob. 52ECh. 16.3 - Prob. 53ECh. 16.3 - Prob. 54ECh. 16.3 - Prob. 55ECh. 16.3 - Prob. 56ECh. 16.3 - Prob. 57ECh. 16.3 - Prob. 58ECh. 16.3 - Prob. 59ECh. 16.3 - Prob. 60ECh. 16.3 - Prob. 61ECh. 16.3 - Prob. 62ECh. 16.3 - Prob. 63ECh. 16.3 - Prob. 64ECh. 16.3 - Prob. 65ECh. 16.3 - Prob. 66ECh. 16.3 - Prob. 67ECh. 16.3 - Prob. 68ECh. 16.3 - Prob. 69ECh. 16.3 - Prob. 70ECh. 16.3 - Prob. 71ECh. 16.3 - Prob. 72ECh. 16.3 - Prob. 73ECh. 16.3 - Prob. 74ECh. 16.3 - Prob. 75ECh. 16.3 - Prob. 76ECh. 16.IR - Prob. 1PCh. 16.IR - Prob. 2PCh. 16.IR - Prob. 3PCh. 16.IR - Prob. 1IRCh. 16.IR - Prob. 2IRCh. 16.IR - Prob. 3IRCh. 16.IR - Prob. 4IRCh. 16.IR - Prob. 5IRCh. 16.IR - Prob. 6IRCh. 16.IR - Prob. 7IRCh. 16.IR - Prob. 8IRCh. 16.IR - Prob. 9IRCh. 16.IR - Prob. 10IRCh. 16.IR - Prob. 11IRCh. 16.IR - Prob. 12IRCh. 16.IR - Prob. 13IRCh. 16.IR - Prob. 14IRCh. 16.IR - Prob. 15IRCh. 16.IR - Prob. 16IRCh. 16.IR - Prob. 17IRCh. 16.IR - Prob. 18IRCh. 16.IR - Prob. 19IRCh. 16.IR - Prob. 20IRCh. 16.IR - Prob. 21IRCh. 16.IR - Prob. 22IRCh. 16.IR - Prob. 23IRCh. 16.IR - Prob. 24IRCh. 16.IR - Prob. 25IRCh. 16.IR - Prob. 26IRCh. 16.IR - Prob. 27IRCh. 16.IR - Prob. 28IRCh. 16.IR - Prob. 29IRCh. 16.IR - Prob. 30IRCh. 16.IR - Prob. 31IRCh. 16.IR - Prob. 32IRCh. 16.IR - Prob. 33IRCh. 16.IR - Prob. 34IRCh. 16.IR - Prob. 35IRCh. 16.IR - Prob. 36IRCh. 16.IR - Prob. 37IRCh. 16.IR - Prob. 38IRCh. 16.IR - Prob. 39IRCh. 16.IR - Prob. 40IRCh. 16.IR - Prob. 41IRCh. 16.4 - Prob. 1CCCh. 16.4 - Prob. 2CCCh. 16.4 - Prob. 1PCh. 16.4 - Prob. 2PCh. 16.4 - Prob. 3PCh. 16.4 - Prob. 4PCh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - 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Prob. 3CRCh. 16.CR - Prob. 4CRCh. 16.CR - Prob. 5CRCh. 16.CR - Prob. 6CRCh. 16.CR - Prob. 7CRCh. 16.CR - Prob. 8CRCh. 16.CR - Prob. 9CRCh. 16.CR - Prob. 10CRCh. 16.CR - Prob. 11CRCh. 16.CR - Prob. 12CRCh. 16.CR - Prob. 13CRCh. 16.CR - Prob. 14CRCh. 16.CR - Prob. 15CRCh. 16.CR - Prob. 16CRCh. 16.CR - Prob. 17CRCh. 16.CR - Prob. 18CRCh. 16.CR - Prob. 19CRCh. 16.CR - Prob. 20CRCh. 16.CR - Prob. 21CRCh. 16.CR - Prob. 22CRCh. 16.CR - Prob. 23CRCh. 16.CR - Prob. 24CRCh. 16.CR - Prob. 25CRCh. 16.CR - Prob. 26CRCh. 16.CR - Prob. 27CRCh. 16.CR - Prob. 28CRCh. 16.CR - Prob. 29CRCh. 16.CR - Prob. 30CRCh. 16.CR - Prob. 31CRCh. 16.CR - Prob. 32CRCh. 16.CR - Prob. 33CRCh. 16.CR - Prob. 34CRCh. 16.CR - Prob. 35CRCh. 16.CR - Prob. 36CRCh. 16.CR - Prob. 37CRCh. 16.CR - Prob. 38CRCh. 16.CR - Prob. 39CRCh. 16.CR - Prob. 40CRCh. 16.CR - Prob. 41CRCh. 16.CR - Prob. 42CRCh. 16.CR - Prob. 43CRCh. 16.CR - Prob. 44CRCh. 16.CR - Prob. 45CRCh. 16.CR - Prob. 46CRCh. 16.CR - Prob. 47CRCh. 16.CR - Prob. 48CRCh. 16.CR - Prob. 49CRCh. 16.CR - Prob. 50CRCh. 16.CR - Prob. 51CRCh. 16.CR - Prob. 52CRCh. 16.CR - Prob. 53CRCh. 16.CR - Prob. 54CRCh. 16.CR - Prob. 55CRCh. 16.CR - Prob. 56CRCh. 16.CR - Prob. 57CRCh. 16.CR - Prob. 58CRCh. 16.CR - Prob. 59CRCh. 16.CR - Prob. 60CRCh. 16.CR - Prob. 61CRCh. 16.CR - Prob. 62CRCh. 16.CR - Prob. 63CRCh. 16.CR - Prob. 64CRCh. 16.CR - Prob. 65CRCh. 16.CR - Prob. 66CRCh. 16.CR - Prob. 67CRCh. 16.CR - Prob. 68CRCh. 16.CR - Prob. 69CRCh. 16.CR - Prob. 70CRCh. 16.CR - Prob. 71CRCh. 16.CR - Prob. 72CRCh. 16.GRT - Prob. 1GRTCh. 16.GRT - Prob. 2GRTCh. 16.GRT - Prob. 3GRTCh. 16.GRT - Prob. 4GRTCh. 16.GRT - Prob. 5GRTCh. 16.GRT - Prob. 6GRTCh. 16.GRT - Prob. 7GRTCh. 16.GRT - Prob. 8GRTCh. 16.GRT - Prob. 9GRTCh. 16.GRT - Prob. 10GRTCh. 16.CT - Prob. 1CTCh. 16.CT - Prob. 2CTCh. 16.CT - Prob. 3CTCh. 16.CT - Prob. 4CTCh. 16.CT - Prob. 5CTCh. 16.CT - Prob. 6CTCh. 16.CT - Prob. 7CTCh. 16.CT - Prob. 8CTCh. 16.CT - Prob. 9CTCh. 16.CT - Prob. 10CTCh. 16.CT - Prob. 11CTCh. 16.CT - Prob. 12CTCh. 16.CT - 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