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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 9, Problem 33RE
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section
Problem 1RE
Problem 2RE
Problem 3RE
Problem 4RE
Problem 5RE
Problem 6RE
Problem 7RE
Problem 8RE
Problem 9RE
Problem 10RE
Problem 11RE
Problem 12RE
Problem 13RE
Problem 14RE
Problem 15RE
Problem 16RE
Problem 17RE
Problem 18RE
Problem 19RE
Problem 20RE
Problem 21RE
Problem 22RE
Problem 23RE
Problem 24RE
Problem 25RE
Problem 26RE
Problem 27RE
Problem 28RE
Problem 29RE
Problem 30RE
Problem 31RE
Problem 32RE
Problem 33RE
Problem 34RE
Problem 35RE
Problem 36RE
Problem 37RE
Problem 38RE
Problem 39RE
Problem 40RE
Problem 41RE
Problem 42RE
Problem 43RE
Problem 44RE
Problem 45RE
Problem 46RE
Problem 47RE
Problem 48RE
Problem 49RE
Problem 50RE
Problem 51RE
Problem 52RE
Problem 53RE
Problem 54RE
Problem 55RE
Problem 56RE
Problem 57RE
Problem 58RE
Problem 59RE
Problem 60RE
Problem 61RE
Problem 62RE
Problem 63RE
Problem 64RE
Problem 65RE
Problem 66RE
Problem 67RE
Problem 68RE
Problem 69RE
Problem 70RE
Problem 71RE
Problem 72RE
Problem 73RE
Problem 74RE
Problem 75RE
Problem 76RE
Problem 77RE
Problem 78RE
Problem 79RE
Problem 80RE
Problem 81RE
Problem 82RE
Problem 83RE
Problem 84RE
Problem 85RE
Problem 86RE
Problem 87RE
Problem 88RE
Problem 89RE
Problem 90RE
Problem 91RE
Problem 92RE
Problem 93RE
Problem 94RE
Problem 95RE
Problem 96RE
Problem 97RE
Problem 98RE
Problem 99RE
Problem 100RE
Problem 101RE
Problem 102RE
Problem 103RE
Problem 104RE
Problem 105RE
Problem 106RE
Problem 107RE
Problem 108RE
Problem 1T
Problem 2T
Problem 3T
Problem 4T
Problem 5T
Problem 6T
Problem 7T
Problem 8T
Problem 9T
Problem 10T
Problem 11T
Problem 12T
Problem 13T
Problem 14T
Problem 15T
Problem 1EAGP1
Problem 2EAGP1
Problem 3EAGP1
Problem 4EAGP1
Problem 1EAGP2
Problem 2EAGP2
Problem 3EAGP2
Problem 4EAGP2
Problem 5EAGP2
Problem 6EAGP2
Problem 7EAGP2
Problem 8EAGP2
Problem 9EAGP2
Problem 10EAGP2
Problem 1EAGP3
Problem 2EAGP3
Problem 3EAGP3
Problem 4EAGP3
Problem 5EAGP3
Problem 6EAGP3
Problem 7EAGP3
Problem 8EAGP3
Problem 9EAGP3
Problem 10EAGP3
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

For the functions in Problems 31-34, determine which are continuous. Identify discontinuities for those that are not continuous.

f ( x ) = { x + 2  if  x ≤ 2 5 x − 6  if  x > 2

To determine

Whether the function, f(x)={x+2    if x≤25x−6   if x>2, is continuous or discontinuous with the points of discontinuities.

Explanation

Given Information:

The provided function is f(x)={x+2    if x≤25x−6   if x>2.

Explanation:

Consider the provided function,

f(x)={x+2    if x≤25x−6   if x>2

There are two different values of the function, f(x)=x+2 for all x≤2 and f(x)=5x−6 for all x>2.

A function, f, is continuous at x=c if f(c) exists, limx→cf(x) exists and limx→cf(x)=f(c).

The function is continuous at x=2 if all the three conditions are satisfied for x=2.

To check whether the value of f(2) exists, substitute 2 for x in the function,

f(2)=2+2=4

Thus, the value of f(2) is defined, which means the first condition is satisfied, and is equal to 4.

To check whether the limit, limx→2f(x), exists, find the values of the left hand limit and the right hand limit. If the values of the left hand limit and right hand limit are equal, then the limit exists.

The limit from the left is represented by limx→2−f(x), that is, the values of f(2) but c≤2

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Sect-9.1 P-1CPSect-9.1 P-2CPSect-9.1 P-3CPSect-9.1 P-4CPSect-9.1 P-5CPSect-9.1 P-6CPSect-9.1 P-7CPSect-9.1 P-8CPSect-9.1 P-9CPSect-9.1 P-10CP
Sect-9.1 P-2ESect-9.1 P-1ESect-9.1 P-4ESect-9.1 P-3ESect-9.1 P-6ESect-9.1 P-5ESect-9.1 P-8ESect-9.1 P-7ESect-9.1 P-10ESect-9.1 P-9ESect-9.1 P-11ESect-9.1 P-12ESect-9.1 P-13ESect-9.1 P-14ESect-9.1 P-16ESect-9.1 P-15ESect-9.1 P-18ESect-9.1 P-17ESect-9.1 P-20ESect-9.1 P-19ESect-9.1 P-22ESect-9.1 P-21ESect-9.1 P-24ESect-9.1 P-23ESect-9.1 P-25ESect-9.1 P-26ESect-9.1 P-27ESect-9.1 P-28ESect-9.1 P-29ESect-9.1 P-30ESect-9.1 P-31ESect-9.1 P-32ESect-9.1 P-33ESect-9.1 P-34ESect-9.1 P-35ESect-9.1 P-36ESect-9.1 P-37ESect-9.1 P-38ESect-9.1 P-39ESect-9.1 P-40ESect-9.1 P-41ESect-9.1 P-42ESect-9.1 P-43ESect-9.1 P-44ESect-9.1 P-45ESect-9.1 P-46ESect-9.1 P-47ESect-9.1 P-48ESect-9.1 P-49ESect-9.1 P-50ESect-9.1 P-51ESect-9.1 P-52ESect-9.1 P-53ESect-9.1 P-54ESect-9.1 P-55ESect-9.1 P-56ESect-9.1 P-57ESect-9.1 P-58ESect-9.1 P-59ESect-9.1 P-60ESect-9.1 P-61ESect-9.1 P-62ESect-9.1 P-63ESect-9.1 P-64ESect-9.1 P-65ESect-9.1 P-66ESect-9.1 P-67ESect-9.1 P-68ESect-9.1 P-69ESect-9.1 P-70ESect-9.2 P-1CPSect-9.2 P-2CPSect-9.2 P-3CPSect-9.2 P-1ESect-9.2 P-2ESect-9.2 P-3ESect-9.2 P-4ESect-9.2 P-5ESect-9.2 P-6ESect-9.2 P-7ESect-9.2 P-8ESect-9.2 P-9ESect-9.2 P-10ESect-9.2 P-11ESect-9.2 P-12ESect-9.2 P-13ESect-9.2 P-14ESect-9.2 P-15ESect-9.2 P-16ESect-9.2 P-17ESect-9.2 P-18ESect-9.2 P-19ESect-9.2 P-20ESect-9.2 P-21ESect-9.2 P-22ESect-9.2 P-23ESect-9.2 P-24ESect-9.2 P-25ESect-9.2 P-26ESect-9.2 P-27ESect-9.2 P-28ESect-9.2 P-29ESect-9.2 P-30ESect-9.2 P-31ESect-9.2 P-32ESect-9.2 P-33ESect-9.2 P-34ESect-9.2 P-35ESect-9.2 P-36ESect-9.2 P-37ESect-9.2 P-38ESect-9.2 P-39ESect-9.2 P-40ESect-9.2 P-41ESect-9.2 P-42ESect-9.2 P-43ESect-9.2 P-44ESect-9.2 P-45ESect-9.2 P-46ESect-9.2 P-47ESect-9.2 P-48ESect-9.2 P-49ESect-9.2 P-50ESect-9.2 P-51ESect-9.2 P-52ESect-9.2 P-54ESect-9.3 P-1CPSect-9.3 P-2CPSect-9.3 P-3CPSect-9.3 P-4CPSect-9.3 P-1ESect-9.3 P-2ESect-9.3 P-3ESect-9.3 P-4ESect-9.3 P-5ESect-9.3 P-6ESect-9.3 P-7ESect-9.3 P-8ESect-9.3 P-9ESect-9.3 P-10ESect-9.3 P-11ESect-9.3 P-12ESect-9.3 P-13ESect-9.3 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P-39ESect-9.5 P-40ESect-9.5 P-41ESect-9.5 P-42ESect-9.5 P-43ESect-9.5 P-44ESect-9.5 P-45ESect-9.5 P-46ESect-9.5 P-47ESect-9.5 P-48ESect-9.5 P-49ESect-9.5 P-50ESect-9.5 P-51ESect-9.5 P-52ESect-9.5 P-53ESect-9.5 P-54ESect-9.5 P-55ESect-9.5 P-56ESect-9.6 P-1CPSect-9.6 P-2CPSect-9.6 P-1ESect-9.6 P-2ESect-9.6 P-3ESect-9.6 P-4ESect-9.6 P-5ESect-9.6 P-6ESect-9.6 P-7ESect-9.6 P-8ESect-9.6 P-9ESect-9.6 P-10ESect-9.6 P-11ESect-9.6 P-12ESect-9.6 P-13ESect-9.6 P-14ESect-9.6 P-15ESect-9.6 P-16ESect-9.6 P-17ESect-9.6 P-18ESect-9.6 P-19ESect-9.6 P-20ESect-9.6 P-21ESect-9.6 P-22ESect-9.6 P-23ESect-9.6 P-24ESect-9.6 P-25ESect-9.6 P-26ESect-9.6 P-27ESect-9.6 P-28ESect-9.6 P-29ESect-9.6 P-30ESect-9.6 P-31ESect-9.6 P-32ESect-9.6 P-33ESect-9.6 P-34ESect-9.6 P-35ESect-9.6 P-36ESect-9.6 P-37ESect-9.6 P-38ESect-9.6 P-39ESect-9.6 P-40ESect-9.6 P-41ESect-9.6 P-42ESect-9.6 P-43ESect-9.6 P-44ESect-9.6 P-45ESect-9.6 P-46ESect-9.6 P-47ESect-9.6 P-48ESect-9.6 P-49ESect-9.6 P-50ESect-9.6 P-51ESect-9.6 P-52ESect-9.6 P-53ESect-9.6 P-54ESect-9.6 P-55ESect-9.6 P-56ESect-9.7 P-1CPSect-9.7 P-2CPSect-9.7 P-3CPSect-9.7 P-1ESect-9.7 P-2ESect-9.7 P-3ESect-9.7 P-4ESect-9.7 P-5ESect-9.7 P-6ESect-9.7 P-7ESect-9.7 P-8ESect-9.7 P-9ESect-9.7 P-10ESect-9.7 P-11ESect-9.7 P-12ESect-9.7 P-13ESect-9.7 P-14ESect-9.7 P-15ESect-9.7 P-16ESect-9.7 P-17ESect-9.7 P-18ESect-9.7 P-19ESect-9.7 P-20ESect-9.7 P-21ESect-9.7 P-22ESect-9.7 P-23ESect-9.7 P-24ESect-9.7 P-25ESect-9.7 P-26ESect-9.7 P-27ESect-9.7 P-28ESect-9.7 P-29ESect-9.7 P-30ESect-9.7 P-31ESect-9.7 P-32ESect-9.7 P-33ESect-9.7 P-34ESect-9.7 P-35ESect-9.7 P-36ESect-9.7 P-37ESect-9.7 P-38ESect-9.7 P-39ESect-9.7 P-40ESect-9.7 P-41ESect-9.7 P-42ESect-9.7 P-43ESect-9.7 P-44ESect-9.7 P-45ESect-9.8 P-1CPSect-9.8 P-2CPSect-9.8 P-3CPSect-9.8 P-4CPSect-9.8 P-1ESect-9.8 P-2ESect-9.8 P-3ESect-9.8 P-4ESect-9.8 P-5ESect-9.8 P-6ESect-9.8 P-7ESect-9.8 P-8ESect-9.8 P-9ESect-9.8 P-10ESect-9.8 P-11ESect-9.8 P-12ESect-9.8 P-13ESect-9.8 P-14ESect-9.8 P-15ESect-9.8 P-16ESect-9.8 P-17ESect-9.8 P-18ESect-9.8 P-19ESect-9.8 P-20ESect-9.8 P-21ESect-9.8 P-22ESect-9.8 P-23ESect-9.8 P-24ESect-9.8 P-25ESect-9.8 P-26ESect-9.8 P-27ESect-9.8 P-28ESect-9.8 P-29ESect-9.8 P-30ESect-9.8 P-31ESect-9.8 P-32ESect-9.8 P-33ESect-9.8 P-34ESect-9.8 P-35ESect-9.8 P-36ESect-9.8 P-37ESect-9.8 P-38ESect-9.8 P-39ESect-9.8 P-40ESect-9.8 P-41ESect-9.8 P-42ESect-9.8 P-43ESect-9.8 P-44ESect-9.8 P-47ESect-9.9 P-1CPSect-9.9 P-2CPSect-9.9 P-3CPSect-9.9 P-4CPSect-9.9 P-5CPSect-9.9 P-6CPSect-9.9 P-7CPSect-9.9 P-1ESect-9.9 P-2ESect-9.9 P-3ESect-9.9 P-4ESect-9.9 P-5ESect-9.9 P-6ESect-9.9 P-7ESect-9.9 P-8ESect-9.9 P-9ESect-9.9 P-10ESect-9.9 P-11ESect-9.9 P-12ESect-9.9 P-13ESect-9.9 P-14ESect-9.9 P-15ESect-9.9 P-16ESect-9.9 P-17ESect-9.9 P-18ESect-9.9 P-19ESect-9.9 P-20ESect-9.9 P-21ESect-9.9 P-22ESect-9.9 P-23ESect-9.9 P-24ESect-9.9 P-25ESect-9.9 P-26ESect-9.9 P-27ESect-9.9 P-28ESect-9.9 P-29ESect-9.9 P-30ESect-9.9 P-31ESect-9.9 P-32ESect-9.9 P-33ESect-9.9 P-34ESect-9.9 P-35ESect-9.9 P-36ESect-9.9 P-37ESect-9.9 P-38ECh-9 P-1RECh-9 P-2RECh-9 P-3RECh-9 P-4RECh-9 P-5RECh-9 P-6RECh-9 P-7RECh-9 P-8RECh-9 P-9RECh-9 P-10RECh-9 P-11RECh-9 P-12RECh-9 P-13RECh-9 P-14RECh-9 P-15RECh-9 P-16RECh-9 P-17RECh-9 P-18RECh-9 P-19RECh-9 P-20RECh-9 P-21RECh-9 P-22RECh-9 P-23RECh-9 P-24RECh-9 P-25RECh-9 P-26RECh-9 P-27RECh-9 P-28RECh-9 P-29RECh-9 P-30RECh-9 P-31RECh-9 P-32RECh-9 P-33RECh-9 P-34RECh-9 P-35RECh-9 P-36RECh-9 P-37RECh-9 P-38RECh-9 P-39RECh-9 P-40RECh-9 P-41RECh-9 P-42RECh-9 P-43RECh-9 P-44RECh-9 P-45RECh-9 P-46RECh-9 P-47RECh-9 P-48RECh-9 P-49RECh-9 P-50RECh-9 P-51RECh-9 P-52RECh-9 P-53RECh-9 P-54RECh-9 P-55RECh-9 P-56RECh-9 P-57RECh-9 P-58RECh-9 P-59RECh-9 P-60RECh-9 P-61RECh-9 P-62RECh-9 P-63RECh-9 P-64RECh-9 P-65RECh-9 P-66RECh-9 P-67RECh-9 P-68RECh-9 P-69RECh-9 P-70RECh-9 P-71RECh-9 P-72RECh-9 P-73RECh-9 P-74RECh-9 P-75RECh-9 P-76RECh-9 P-77RECh-9 P-78RECh-9 P-79RECh-9 P-80RECh-9 P-81RECh-9 P-82RECh-9 P-83RECh-9 P-84RECh-9 P-85RECh-9 P-86RECh-9 P-87RECh-9 P-88RECh-9 P-89RECh-9 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