Chapter 5, Problem 67RE

a.

To determine

Identify the function even, odd, or neither.

Answer to Problem 67RE

  $\text{Odd}$

Explanation of Solution

Calculation:

With the help of graph of trigometric function $f\left(x\right)=\frac{{\sin }^{2}x}{x}$ , we can determine the function type,

  

The graph shows that the function is symmerical about the origin.

Hence the function is $\text{Odd}$ .

b.

To determine

Identify the $x-\mathrm{int}ercepts$ of the graph of $f$ .

Answer to Problem 67RE

  $0\pm n\pi$

Explanation of Solution

Calculation:

With the help of graph of trigometric function $f\left(x\right)=\frac{{\sin }^{2}x}{x}$ , we can determine $x-\mathrm{int}ercepts$ of the function.

  

The graph shows that $x-\mathrm{int}ercepts$ are $0\pm n\pi$ where, $n$ is any integer.

unction is symmerical about the origin.

Hence, $x-\mathrm{int}ercepts$ of the function is $0\pm n\pi$ .

c.

To determine

Identify the $x-\mathrm{int}ercepts$ of the graph of $f$ .

Answer to Problem 67RE

  

Explanation of Solution

Calculation:

Initially set the window for $xas\left[-4\pi ,4\pi \right]$ ,

  

The display will be,

  

Now use Calc key to get the first $x-\mathrm{int}ercepts$ which is $\pi$ ,because the function is periodic and

  $x-\mathrm{int}ercepts$ are $0\pm n\pi$ where, $n$ is any integer.

  

Hence, the function is plotted.

d.

To determine

Describe the behaviour of the function.

Answer to Problem 67RE

  $x\to \pm \infty ,f\left(x\right)\to 0$

Explanation of Solution

Calculation:

Consider the graph,

  

Hence, the behaviour of the function as $x$ becomes large is, $x\to \pm \infty ,f\left(x\right)\to 0$

e.

To determine

Define function when $x\to 0$ .

Answer to Problem 67RE

  $x\to 0,f\left(x\right)\to 0$

Explanation of Solution

Calculation:

Consider the graph,

  

Hence, when as $x$ approaches $0$ the function is $x\to 0,f\left(x\right)\to 0$ .