(a) Answer The function Range=Variable . Domain= ( − ∞ , ∞ ) . The graph is increase with increase in the value of angle. Graph is like a sinx graph since it begins with origin. Explanation Given: y= | x | Cos3x . Concept used: Modulus function make the graph shifted in the region of positive. Cosx graph stared from 1. Its Domain= ( − ∞ , ∞ ) and Range= [ 0,1 ] Calculation: Graph of the y= | x | Cos3x . Graphing device use here is Desmos graphing calculator. from the graph modulus symbolize the positivity of the function which is shown in the graph and the Cos3x which is even function so bothare even hence over all function is even function. Through graph range can determined which is Range=Variable . Domain= ( − ∞ , ∞ ) . Hence the function Range=Variable . Domain= ( − ∞ , ∞ ) . (b) To determine To find: whether the Function is periodic if then described it. Answer The function is not periodic in nature. Explanation Given: y= | x | Cos3x Concept used: Period is measured as distance it takes for the entire graph to repeat. Since the period of the Cosine function is π . Calculation: y= | x | Cos3x Form the graph its clearly verified the periods as: the entire graph doesn’t repeat so its not he periodic function. It’s varies with varies in the value of angle. Hence the function is not periodic in nature. (c) To determine To find: The graph whether the function is even or odd. Answer The given function is even. Explanation Given: y= | x | Cos3x Concept used: f ( -x ) =f ( x ) the function is an even function. f ( -x ) =-f ( x ) the function is and odd function Calculation: y= | x | Cos3x Since Cos3x and | x | are even functions therefore its composition y= | x | Cos3x is also an even function. f ( -x ) = | -x | Cos3 ( -x ) = | x | Cos3x=f ( x ) ∀ x . Even function when multiply by the even function then whole composite function becomes even function. Hence the given function is even.

Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Question

Chapter 5, Problem 57RE

(a)

To determine

To find: TheGraphing device to graph the function.

(a)

Expert Solution

Answer to Problem 57RE

The function Range=Variable.

Domain=(−∞,∞) .

The graph is increase with increase in the value of angle.

Graph is like a sinx graph since it begins with origin.

Explanation of Solution

Given: y=|x|Cos3x .

Concept used:

Modulus function make the graph shifted in the region of positive.

Cosx graph stared from 1.

Its Domain=(−∞,∞) and Range=[0,1]

Calculation:

Graph of the y=|x|Cos3x .

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5, Problem 57RE

Graphing device use here is Desmos graphing calculator. from the graph modulus symbolize the positivity of the function which is shown in the graph and the Cos3x which is even function so bothare even hence over all function is even function.

Through graph range can determined which is

Range=Variable.

Domain=(−∞,∞) .

Hence the function Range=Variable.

Domain=(−∞,∞) .

(b)

To determine

To find:whether the Function is periodic if then described it.

(b)

Expert Solution

Answer to Problem 57RE

The function is not periodic in nature.

Explanation of Solution

Given: y=|x|Cos3x

Concept used:

Period is measured as distance it takes for the entire graph to repeat.

Since the period of the Cosine function is π .

Calculation:

y=|x|Cos3x

Form the graph its clearly verified the periods as:

the entire graph doesn’t repeat so its not he periodic function.

It’s varies with varies in the value of angle.

Hence the function is not periodic in nature.

(c)

To determine

To find: The graph whether the function is even or odd.

(c)

Expert Solution

Answer to Problem 57RE

The given function is even.

Explanation of Solution

Given:

y=|x|Cos3x

Concept used:

f(-x)=f(x) the function is an even function.

f(-x)=-f(x) the function is and odd function

Calculation:

y=|x|Cos3x

Since Cos3x and |x| are even functions therefore its composition y=|x|Cos3x is also an even function.

f(-x)=|-x|Cos3(-x)=|x|Cos3x=f(x)∀x.

Even function when multiply by the even function then whole composite function becomes even function.

Hence the given function is even.

Chapter 5, Problem 56RE

Chapter 5, Problem 58RE

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

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The cancellation property sin1(sin x) = x is valid...Ch. 5.5 - Prob. 3E Ch. 5.5 - Prob. 4E Ch. 5.5 - Prob. 5E Ch. 5.5 - Prob. 6E Ch. 5.5 - Prob. 7E Ch. 5.5 - Prob. 8E Ch. 5.5 - Prob. 9E Ch. 5.5 - Prob. 10E Ch. 5.5 - Prob. 11E Ch. 5.5 - Prob. 12E Ch. 5.5 - Prob. 13E Ch. 5.5 - Prob. 14E Ch. 5.5 - Prob. 15E Ch. 5.5 - Prob. 16E Ch. 5.5 - Prob. 17E Ch. 5.5 - Prob. 18E Ch. 5.5 - Prob. 19E Ch. 5.5 - Prob. 20E Ch. 5.5 - Prob. 21E Ch. 5.5 - Prob. 22E Ch. 5.5 - Prob. 23E Ch. 5.5 - Prob. 24E Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - Prob. 28E Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Prob. 31E Ch. 5.5 - Prob. 32E Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Prob. 35E Ch. 5.5 - Prob. 36E Ch. 5.5 - Prob. 37E Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5.5 - Prob. 43E Ch. 5.5 - Prob. 44E Ch. 5.5 - Prob. 45E Ch. 5.5 - Prob. 46E Ch. 5.5 - Prob. 47E Ch. 5.6 - For an object in simple harmonic motion with...Ch. 5.6 - For an object in damped harmonic motion with...Ch. 5.6 - Prob. 3E Ch. 5.6 - Prob. 4E Ch. 5.6 - Prob. 5E Ch. 5.6 - Prob. 6E Ch. 5.6 - Prob. 7E Ch. 5.6 - Prob. 8E Ch. 5.6 - Prob. 9E Ch. 5.6 - Prob. 10E Ch. 5.6 - Prob. 11E Ch. 5.6 - Prob. 12E Ch. 5.6 - Prob. 13E Ch. 5.6 - Prob. 14E Ch. 5.6 - Prob. 15E Ch. 5.6 - Prob. 16E Ch. 5.6 - Prob. 17E Ch. 5.6 - Prob. 18E Ch. 5.6 - Prob. 19E Ch. 5.6 - Prob. 20E Ch. 5.6 - Prob. 21E Ch. 5.6 - Prob. 22E Ch. 5.6 - Prob. 23E Ch. 5.6 - Prob. 24E Ch. 5.6 - Prob. 25E Ch. 5.6 - Prob. 26E Ch. 5.6 - A Bobbing Cork A cork floating in a lake is...Ch. 5.6 - FM Radio Signals The carrier wave for an FM radio...Ch. 5.6 - Blood Pressure Each time your heart beats, your...Ch. 5.6 - Predator Population Model In a predator/prey...Ch. 5.6 - Prob. 31E Ch. 5.6 - Tides The graph shows the variation of the water...Ch. 5.6 - Tides The Bay of Fundy in Nova Scotia has the...Ch. 5.6 - Prob. 34E Ch. 5.6 - Prob. 35E Ch. 5.6 - Prob. 36E Ch. 5.6 - Ferris Wheel A Ferris wheel has a radius of 10 m,...Ch. 5.6 - Cock Pendulum The pendulum in a grandfather clock...Ch. 5.6 - Variable Stars The variable star Zeta Gemini has a...Ch. 5.6 - Variable Stars Astronomers believe that the radius...Ch. 5.6 - Biological Clocks Circadian rhythms are biological...Ch. 5.6 - Electric Generator The armature in an electric...Ch. 5.6 - Electric Generator The graph shows an oscilloscope...Ch. 5.6 - Doppler Effect When a car with its horn blowing...Ch. 5.6 - Motion of a Building A strong gust of wind strikes...Ch. 5.6 - Shock Absorber When a car hits a certain bump on...Ch. 5.6 - Tuning Fork A tuning fork is struck and oscillates...Ch. 5.6 - Guitar String A guitar string is pulled at point P...Ch. 5 - Prob. 1RCC Ch. 5 - Prob. 2RCC Ch. 5 - Prob. 3RCC Ch. 5 - Prob. 4RCC Ch. 5 - Prob. 5RCC Ch. 5 - Prob. 6RCC Ch. 5 - Prob. 7RCC Ch. 5 - Prob. 8RCC Ch. 5 - Prob. 9RCC Ch. 5 - Prob. 10RCC Ch. 5 - Prob. 11RCC Ch. 5 - Prob. 12RCC Ch. 5 - Prob. 1RE Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - 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