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 5.3, Problem 102E

a.

To determine

To find: Domain of the given function.

a.

Expert Solution
Check Mark

Answer to Problem 102E

The domain of f(x) is all real values except 0 .

Explanation of Solution

Given information:

The following function:

  f(x)=sinxx

The following graph:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 102E , additional homework tip  1

The range in which all possible inputs of a function fall, is called the domain of a function.

When x=0 , sinxx is undefined.

Therefore, the domain of the function will be all real values of x except 0 .

b.

To determine

To identify: Any symmetry and asymptotes of the graph.

b.

Expert Solution
Check Mark

Answer to Problem 102E

The graph has y-axis symmetry.

The graph has a horizontal asymptote at y=0 as x

Explanation of Solution

Given information:

The following function:

  f(x)=sinxx

The following graph:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 102E , additional homework tip  2

The graph on the right side of y-axis appears to be a mirror image of the graph on the left side of the y-axis.

Hence the graph has y-axis symmetry.

An asymptote is a line representing a value towards which a function may approach but does not approach.

The graph has a horizontal asymptote at y=0 as x .

c.

To determine

To describe: Behavior of the function at x0 .

c.

Expert Solution
Check Mark

Answer to Problem 102E

As x0 , the graph approaches 1 from both sides.

Explanation of Solution

Given information:

The following function:

  f(x)=sinxx

The following graph:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 102E , additional homework tip  3

According to the graph, as x0 , the graph approaches the value 1 on the y-axis from both sides. In other words, the value of the function approaches 1 as x0 .

d.

To determine

To find: The solution of the given equation in the given interval.

d.

Expert Solution
Check Mark

Answer to Problem 102E

The equation has four solutions in the interval [8,8] and

  x=nπ,π,π,2π

Explanation of Solution

Given information:

The following equation:

  sinxx=0

The following interval:

  [8,8]

The following graph:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 102E , additional homework tip  4

The solutions of the equation are calculated as:

  sinxx=0              [Given]sinx=0              [Multiplying both sides by x]x=arcsin(0)       [Inverse trigonometric function]x=0+nπ            [Value of arcsin(0)]x=nπ

In the interval [8,8] , the equation has four solutions,

  x=nπ,π,π,2π

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
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Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
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Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
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Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY