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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Limits
When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…
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Chapter 11.1, Problem 80E

a.

To determine

To find: To find the function f(0) exists in the given graph.

a.

Expert Solution
Check Mark

Answer to Problem 80E

The function f(0) exists in the given graph.

Explanation of Solution

Given:

  Precalculus with Limits: A Graphing Approach, Chapter 11.1, Problem 80E , additional homework tip 1

From the graph we can observe that there is a hole and a solid dot at x=0 .

The solid dot means f(0) is been defined.

  f(0)=1

Therefore we can conclude that the function f(0) is defined and exists.

b.

To determine

To find: To find the function limx→0f(x) exists in the given graph.

b.

Expert Solution
Check Mark

Answer to Problem 80E

The function limx→0f(x) does not exist in the given graph.

Explanation of Solution

Given:

  Precalculus with Limits: A Graphing Approach, Chapter 11.1, Problem 80E , additional homework tip 2

From the observation of the graph,

From the left hand side, limx→0f(x) approaches f(x)→4 at x→0 .

From the right hand side, limx→0f(x) approaches f(x)→1 at x→0 .

The function f(x) approaches two different values at x→0 .

Therefore the function limx→0f(x) does not exist.

c.

To determine

To find: To find the function f(2) exists in the given graph.

c.

Expert Solution
Check Mark

Answer to Problem 80E

The function f(2) is undefined in the given graph.

Explanation of Solution

Given:

  Precalculus with Limits: A Graphing Approach, Chapter 11.1, Problem 80E , additional homework tip 3

From the graph we can observe that there is a hole at x=2 .

The hole at x=2 means f(2) is been undefined.

Therefore we can conclude that the function f(2) is undefined.

d.

To determine

To find: To find the function limx→2f(x) exists in the given graph.

d.

Expert Solution
Check Mark

Answer to Problem 80E

The function limx→2f(x) exists in the given graph.

Explanation of Solution

Given:

  Precalculus with Limits: A Graphing Approach, Chapter 11.1, Problem 80E , additional homework tip 4

From the graph we can observe that,

From the left hand side and right hand side x→2 .

Therefore we can conclude that the function limx→2f(x) exists.

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Chapter 11.1, Problem 79E
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Chapter 11.1, Problem 81E

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
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - Prob. 60ECh. 11.1 - 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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY