Chapter 4.6, Problem 74E

(a)

To determine

To Graph: To graph the given tangent and polynomial functions.

Explanation of Solution

Given information: Given function $f(x)=\tan \frac{\pi x}{2}\text{and}g(x)=\frac{1}{2}\sec \frac{\pi x}{2}$

Graph:

  

Interpretation:

In the graph it can be seen that in the interval of $(-1,1)$ the $f(x)$ is declining in $(-1,0)$ and increasing in the interval of $(0,1)$ whereas the curve of $g(x)$ is negative in the interval of $(-1,0)$ and positive in the interval of (0,1).

(b)

To determine

To Find: To find the interval in which $f(x)<g(x).$

Explanation of Solution

Given information: Given function $f(x)=\tan \frac{\pi x}{2}\text{and}g(x)=\frac{1}{2}\sec \frac{\pi x}{2}$

In the graph it can be seen that in the interval of $(0.33,1)$ the $f(x)$ is less than the $g(x)$ .

(c)

To determine

To Describe: To describe the behaviour of the given function as xapproaches to 0.

Explanation of Solution

Given information: Given function $f(x)=\tan \frac{\pi x}{2}\text{and}g(x)=\frac{1}{2}\sec \frac{\pi x}{2}$

In the graph it can be seen that as $x\text{approaches}\text{to}0$ the value of $f(x)$ is 0.5 whereas $g(x)$ is 0. Also, in the interval of $(-1,1)$ the $f(x)$ is declining in $(-1,0)$ and increasing in the interval of $(0,1)$ whereas the curve of $g(x)$ is negative in the interval of $(-1,0)$ and positive in the interval of (0,1).