Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Chapter 13.1, Problem 20E

a.

To determine

To estimate: The value of the limit of function f(x) from graph.

a.

Expert Solution
Check Mark

Answer to Problem 20E

The value of the limit is 2 .

Explanation of Solution

Given information:

Limit is limx3f(x)

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 13.1, Problem 20E , additional homework tip  1

Concept used:

When function is continuous and differentiable at the point the limit exists.

Limit is limx3f(x)

  limx3f(x) to be continuous it should follow

  limx3f(x)=limx3f(x)=limx3+f(x)

From graph it can be observed that value of y − coordinate of x − coordinate which is slightly less than 3 is 2 and slightly more than 3 is 2 and exactly 3 is also 2

So, limx3+f(x)=limx3f(x)=limx3f(x)

So, the limit value of limx3f(x) is 2

b.

To determine

To estimate: The value of the limit.

b.

Expert Solution
Check Mark

Answer to Problem 20E

The value of the limit is doesn’t exist.

Explanation of Solution

Given information:

Limit is limx1f(x)

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 13.1, Problem 20E , additional homework tip  2

Concept used:

When function is continuous and differentiable at point the limit exists.

Limit is limx1f(x)

  limx1f(x) to be continuous it should follow

  limx1f(x)=limx1f(x)=limx1+f(x)

From graph it can be observed that value of y − coordinate of x − coordinate which is slightly less than 1 is 1 , slightly greater than 1 is 1 nearly and exactly 1 is 1

So, limx1f(x)=limx1+f(x)limx1f(x)

Therefore, limit doesn’t exists.

c.

To determine

To estimate: The value of the limit.

c.

Expert Solution
Check Mark

Answer to Problem 20E

The value of limit of the limit doesn’t exit.

Explanation of Solution

Given information:

Limit is limx3f(x)

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 13.1, Problem 20E , additional homework tip  3

Concept used:

When function is continuous and differentiable at the point the limit exist.

Limit is limx3f(x)

  limx3f(x) to be continuous it should follow

  limx3+f(x)=limx3f(x)=limx3f(x)

As explained in above subparts

  limx3+f(x)=1   limx3f(x)=1 and

  limx3f(x)=undefined

So, limx3+f(x)=limx3f(x)limx3f(x)

Therefore limit doesn’t exist.

d.

To determine

To estimate: The value of the limit.

d.

Expert Solution
Check Mark

Answer to Problem 20E

The value of limit is 1 .

Explanation of Solution

Given information:

Limit is limx2f(x)

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 13.1, Problem 20E , additional homework tip  4

Limit is limx2f(x)

From graph it can be observed that y − coordinate which is slightly less than 2 is 1 .

So, the limit value of limx2f(x) is 1

e.

To determine

To estimate: The value of the limit.

e.

Expert Solution
Check Mark

Answer to Problem 20E

The value of limit is 2 .

Explanation of Solution

Given information:

Limit is limx2+f(x)

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 13.1, Problem 20E , additional homework tip  5

Limit is limx2+f(x)

From graph it can be observed that the value of y − coordinate of x − coordinate which is slightly greater than 2 is 2

So, the value of limx2+f(x)=2

f.

To determine

To estimate: The value of the limit.

f.

Expert Solution
Check Mark

Answer to Problem 20E

The value of limit of the limit doesn’t exit.

Explanation of Solution

Given information:

Limit is limx2f(x)

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 13.1, Problem 20E , additional homework tip  6

Concept used:

When function is continuous and differentiable at the point the limit exist.

Limit is limx2f(x)

  limx2f(x) to be continuous it should follow

  limx2+f(x)=limx2f(x)=limx2f(x)

From above subpart d and e

  limx2f(x)=1   limx2f(x)=2

And at x=2f(x)=1

So, limx2f(x)=limx2f(x)limx2+f(x)

Therefore limit doesn’t exist.

Chapter 13 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 29ECh. 13.1 - Prob. 30ECh. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.2 - Suppose the following limits exist:...Ch. 13.2 - If f is a polynomial or a rational function and a...Ch. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Prob. 25ECh. 13.2 - Prob. 26ECh. 13.2 - Prob. 27ECh. 13.2 - Prob. 28ECh. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.3 - The derivative of a function f at a number a is...Ch. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - Inflating a Balloon A spherical balloon is being...Ch. 13.3 - Temperature Change A roast turkey is taken from an...Ch. 13.3 - Heart Rate A cardiac monitor is used to measure...Ch. 13.3 - Prob. 33ECh. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - Prob. 37ECh. 13.4 - Let f be a function defined on some interval (a,...Ch. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Prob. 11ECh. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Prob. 21ECh. 13.4 - Prob. 22ECh. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Prob. 31ECh. 13.4 - Prob. 32ECh. 13.4 - Prob. 33ECh. 13.4 - Prob. 34ECh. 13.4 - Salt Concentration (a) A tank contains 5000 L of...Ch. 13.4 - Prob. 36ECh. 13.4 - Prob. 37ECh. 13.5 - The graph of a function f is shown below. 1. To...Ch. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 18ECh. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Prob. 22ECh. 13 - Prob. 1RCCCh. 13 - Prob. 2RCCCh. 13 - Prob. 3RCCCh. 13 - Prob. 4RCCCh. 13 - Prob. 5RCCCh. 13 - Prob. 6RCCCh. 13 - Prob. 7RCCCh. 13 - Prob. 8RCCCh. 13 - Prob. 9RCCCh. 13 - Prob. 10RCCCh. 13 - Prob. 11RCCCh. 13 - Prob. 1RECh. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - Prob. 39RECh. 13 - Prob. 40RECh. 13 - Prob. 41RECh. 13 - Prob. 42RECh. 13 - Prob. 43RECh. 13 - Prob. 44RECh. 13 - Prob. 45RECh. 13 - Prob. 46RECh. 13 - Prob. 47RECh. 13 - Prob. 48RECh. 13 - Prob. 1TCh. 13 - For the piecewise-defined function f whose graph...Ch. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - Prob. 5TCh. 13 - Prob. 6TCh. 13 - Prob. 7TCh. 13 - Work Done by a Winch A motorized winch is being...Ch. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - Prob. 5PCh. 13 - Prob. 1CRTCh. 13 - Prob. 2CRTCh. 13 - Prob. 3CRTCh. 13 - Prob. 4CRTCh. 13 - Prob. 5CRTCh. 13 - Prob. 6CRTCh. 13 - Prob. 7CRTCh. 13 - Prob. 8CRTCh. 13 - Prob. 9CRTCh. 13 - Prob. 10CRT
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