a. Answer R − { 0 } Explanation Given information: Consider the function f ( x ) = sin x x and its graph, shown in the figure below, Calculation: Consider the function,and graph, f ( x ) = sin x x p u t , x = 0 y = sin x x y = sin 0 0 = 0 0 = 0 This is not defined , function f is defined everywhere except x = 0 Hence, the domain of the function is, R − { 0 } b. To determine Identify any symmetry and any asymptotes of the graph. Answer y − a x i s Explanation Given information: Consider the function f ( x ) = sin x x and its graph, shown in the figure below, Calculation: Consider the function,and graph, f ( x ) = sin x x The graph has no asymptotes because it does not approach to a particular value, For symmetry replace x to − x f ( − x ) = sin ( − x ) − x = − sin x − x = sin x x Which is equal to f ( x ) means the function is even and symmetrical about y − a x i s . Hence the function is symmetrical about y − a x i s c. To determine Describe the behaviour of the function as x → 0 . Answer f ( x ) = sin x x → 1 Explanation Given information: Consider the function f ( x ) = sin x x and its graph, shown in the figure below, Calculation: Consider the function,and graph, f ( x ) = sin x x According to the graph x → 0 then function f ( x ) = sin x x → 1 Hence, the behaviour of the function as x → 0 is f ( x ) = sin x x → 1 d. To determine Find the number of solutions. Answer 4 , − π , − 2 π , π , 2 π Explanation Given information: Consider the function f ( x ) = sin x x and its graph, shown in the figure below, How many solutions does the equation sin x x = 0 have in the interval [ − 8 , 8 ] ? Find the solutions. Calculation: Consider the function,and graph, f ( x ) = sin x x The function f ( x ) = sin x x is equal to zero only when sin x = 0 and x ≠ 0 So x = 0 is not the not the solution of function, Now with maple the graph of f ( x ) = sin x x in the interval [ − 8 , 8 ] will be, The function cuts the x − a x i s 4 times, Hence, the solutions are 4 which are − π , − 2 π , π , 2 π

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 5.3, Problem 87E

To determine

Find the domain of the function.

Expert Solution

Answer to Problem 87E

$R−{0}$

Explanation of Solution

Given information:

Consider the function $f(x)=sinxx$ and its graph, shown in the figure below,

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

Calculation:

Consider the function,and graph,

$f(x)=sinxx$

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

$put,x=0y=sinxxy=sin00=00=0$

This is not defined , function $f$ is defined everywhere except $x=0$

Hence, the domain of the function is, $R−{0}$

To determine

Identify any symmetry and any asymptotes of the graph.

Expert Solution

Answer to Problem 87E

$y−axis$

Explanation of Solution

Given information:

Consider the function $f(x)=sinxx$ and its graph, shown in the figure below,

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

Calculation:

Consider the function,and graph,

$f(x)=sinxx$

The graph has no asymptotes because it does not approach to a particular value,

For symmetry replace $x$ to $−x$

$f(−x)=sin(−x)−x=−sinx−x=sinxx$

Which is equal to $f(x)$ means the function is even and symmetrical about $y−axis$ .

Hence the function is symmetrical about $y−axis$

To determine

Describe the behaviour of the function as $x→0$ .

Expert Solution

Answer to Problem 87E

$f(x)=sinxx→1$

Explanation of Solution

Given information:

Consider the function $f(x)=sinxx$ and its graph, shown in the figure below,

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

Calculation:

Consider the function,and graph,

$f(x)=sinxx$

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

According to the graph $x→0$ then function $f(x)=sinxx→1$

Hence, the behaviour of the function as $x→0$ is $f(x)=sinxx→1$

To determine

Find the number of solutions.

Expert Solution

Answer to Problem 87E

$4$ , $−π,−2π,π,2π$

Explanation of Solution

Given information:

Consider the function $f(x)=sinxx$ and its graph, shown in the figure below,

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 6

How many solutions does the equation $sinxx=0$ have in the interval $[−8,8]$ ? Find the solutions.

Calculation:

Consider the function,and graph,

$f(x)=sinxx$

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 7

The function $f(x)=sinxx$ is equal to zero only when $sinx=0$ and $x≠0$

So $x=0$ is not the not the solution of function,

Now with maple the graph of $f(x)=sinxx$ in the interval $[−8,8]$ will be,

EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 87E , additional homework tip 8

The function cuts the $x−axis$

$4$ times,

Hence, the solutions are $4$ which are $−π,−2π,π,2π$

Chapter 5.3, Problem 86E

Chapter 5.3, Problem 88E

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

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