a. Answer D ∈ ( − ∞ , ∞ ) Explanation Given: The given function is f ( x ) = sin x x and its graph shown below. Domain: It is input value of x . According to graph, the domain is all real number. D ∈ ( − ∞ , ∞ ) b. To determine To find: The symmetry and asymptotes of function. Answer Symmetry: x = 0 Explanation Given: The given function is f ( x ) = sin x x and its graph shown below. Numerator: sin x is continuous function. Denominator : x is continuous function. But at x = 0 denominator becomes 0. Using the limit property lim x → 0 sin x x = 1 So, It is symmetry about x = 0 as shown in figure. c. To determine To describe: The property of function as x → 0 . Answer lim x → ∞ sin x x = 0 Explanation Given: The given function is f ( x ) = sin x x and its graph shown below. Numerator: sin x is continuous function. Denominator : x is continuous function. But at x = 0 denominator becomes 0. Using the limit property lim x → 0 sin x x = 1 lim x → ∞ sin x x = 0 The value of sin x lie between 0 to 1. − 1 ≤ sin x ≤ 1 x → ∞ Numerator will be finite value. But x → ∞ ⇔ 1 x → 0 Hence, the function approaches to 0 d. To determine To find: The solution of function when sin x x = 0 on [ − 8 , 8 ] . Answer x = − 2 π , − π , π , 2 π Explanation Given: The given function is f ( x ) = sin x x and its graph shown below. Numerator: sin x is continuous function. Denominator : x is continuous function. Using graph, the x- intercept gives the solution of sin x x = 0 So, total 4 x-intercept as shown in above graph. The solutions of sin x x = 0 on [ − 8 , 8 ] are x = − 2 π , − π , π , 2 π

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ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 5.3, Problem 87E

To determine

To find: The domain of the function.

Expert Solution

Answer to Problem 87E

D∈(−∞,∞)

Explanation of Solution

Given:The given function is f(x)=sinxx and its graph shown below.

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 1

Domain: It is input value of x .

According to graph, the domain is all real number.

D∈(−∞,∞)

To determine

To find: The symmetry and asymptotes of function.

Expert Solution

Answer to Problem 87E

Symmetry: x=0

Explanation of Solution

Given: The given function is f(x)=sinxx and its graph shown below.

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 2

Numerator: sinx is continuous function.

Denominator: x is continuous function.

But at x=0 denominator becomes 0. Using the limit property

limx→0sinxx=1

So, It is symmetry about x=0 as shown in figure.

To determine

To describe: The property of function as x→0 .

Expert Solution

Answer to Problem 87E

limx→∞sinxx=0

Explanation of Solution

Given: The given function is f(x)=sinxx and its graph shown below.

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 3

Numerator: sinx is continuous function.

Denominator: x is continuous function.

But at x=0 denominator becomes 0. Using the limit property

limx→0sinxx=1

limx→∞sinxx=0

The value of sinx lie between 0 to 1.

−1≤sinx≤1x→∞

Numerator will be finite value.

But x→∞⇔1x→0

Hence, the function approaches to 0

To determine

To find: The solution of function when sinxx=0 on [−8,8] .

Expert Solution

Answer to Problem 87E

x=−2π,−π,π,2π

Explanation of Solution

Given: The given function is f(x)=sinxx and its graph shown below.

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 4

Numerator: sinx is continuous function.

Denominator: x is continuous function.

Using graph, the x- intercept gives the solution of sinxx=0

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 5

So, total 4 x-intercept as shown in above graph.

The solutions of sinxx=0 on [−8,8] are x=−2π,−π,π,2π

Chapter 5.3, Problem 86E

Chapter 5.3, Problem 88E

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

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