Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 11.2, Problem 66E

a.

To determine

To graph: the function C(x)=80−3[−(x−1)] for 0<x≤10 .

a.

Expert Solution
Check Mark

Explanation of Solution

Given information:

The function,

  C(x)=80−3[−(x−1)]

where x is the distance in miles.

Make a table to sketch the graph.

  xC(x)1802833864895926957988101910410107

Graph:

The graph becomes,

  Precalculus with Limits: A Graphing Approach, Chapter 11.2, Problem 66E

b.

To determine

To identify: The value of C(x) in the following table

  x55.35.45.55.65.76C(x)

And also find limx→5.5C(x) .

b.

Expert Solution
Check Mark

Answer to Problem 66E

  x55.35.45.55.65.76C(x)92959595959595limx→5.5C(x)=95

Explanation of Solution

Given information:

The function,

  C(x)=80−3[−(x−1)]

where x is the distance in miles.

Concept Involved:

Greatest integer function defined as:

For each real number x, the greatest integer function is the largest integer that is less than or equal to x.

Such that [1.9]=1,[−2.5]=−3,[3]=3

Take x=5 ,

  C(5)=80−3[−(5−1)]=80−3[−4]=80−3×(−4)=80+12=92

Take x=5.3 ,

  C(5.3)=80−3[−(5.3−1)]=80−3[−4.3]=80−3×(−5)=80+15=95

Take x=5.4 ,

  C(5.4)=80−3[−(5.4−1)]=80−3[−4.4]=80−3×(−5)=80+15=95

Take x=5.5 ,

  C(5.5)=80−3[−(5.5−1)]=80−3[−4.5]=80−3×(−5)=80+15=95

Take x=5.6 ,

  C(5.6)=80−3[−(5.6−1)]=80−3[−4.6]=80−3×(−5)=80+15=95

Take x=5.7 ,

  C(5.7)=80−3[−(5.7−1)]=80−3[−4.7]=80−3×(−5)=80+15=95

Take x=6 ,

  C(6)=80−3[−(6−1)]=80−3[−5]=80−3×(−5)=80+15=95

From the above, shows that the value of C is constant when 5<x≤6 .

And the value of limx→5.5C(x) from the table is

  limx→5.5C(x)=95

Conclusion:

  x55.35.45.55.65.76C(x)92959595959595limx→5.5C(x)=95

c.

To determine

To identify: The value of C(x) in the following table

  x44.54.955.15.56C(x)

And also find limx→5C(x) .

c.

Expert Solution
Check Mark

Answer to Problem 66E

  x44.54.955.15.56C(x)89929292959595

Explanation of Solution

Given information:

The function,

  C(x)=80−3[−(x−1)]

where x is the distance in miles.

Concept Involved:

Greatest integer function defined as:

For each real number x, the greatest integer function is the largest integer that is less than or equal to x.

Such that [1.9]=1,[−2.5]=−3,[3]=3

Take x=4 ,

  C(4)=80−3[−(4−1)]=80−3[−3]=80−3×(−3)=80+9=89

Take x=4.5 ,

  C(4.5)=80−3[−(4.5−1)]=80−3[−3.5]=80−3×(−4)=80+12=92

Take x=4.9 ,

  C(4.9)=80−3[−(4.9−1)]=80−3[−3.9]=80−3×(−4)=80+12=92

Take x=5 ,

  C(5)=80−3[−(5−1)]=80−3[−4]=80−3×(−4)=80+12=92

Take x=5.1 ,

  C(5.1)=80−3[−(5.1−1)]=80−3[−4.1]=80−3×(−5)=80+15=95

Take x=5.5 ,

  C(5.5)=80−3[−(5.5−1)]=80−3[−4.5]=80−3×(−5)=80+15=95

Take x=6 ,

  C(6)=80−3[−(6−1)]=80−3[−5]=80−3×(−5)=80+15=95

From the above, shows that the value of C is constant when 4<x≤5 .

And the value of limx→5C(x) from the table is

  limx→5C(x)=92

And

  limx→5−C(x)=92limx→5+C(x)=95

So, the limx→5C(x) does not exist.

Conclusion:

  x44.54.955.15.56C(x)89929292959595

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Chapter 11.2, Problem 65E
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Chapter 11.2, Problem 67E

Chapter 11 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 11.1 - Prob. 1ECh. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
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