Chapter 4.6, Problem 80E

(a)

To determine

To Complete: To complete the given table of the function.

Explanation of Solution

Given information: Given function $f(x)=\frac{\tan 2x}{2x}$

Calculation:

$x$	$-1$	$-0.1$	$-0.01$	$-0.001$	0	0.001	0.01	0.1	1
$f(x)$	$-1.0925$	1.0136	1.0001	1.0000	undefined	1.0000	1.0001	1.0136	$-1.0925$

(b)

To determine

To Graph: To graph the given function.

Explanation of Solution

Given information: Given function $f(x)=\frac{\tan 2x}{2x}$

Graph:

  

In the graph it can be seen that $\text{as}x\text{approaches}\text{to}0\text{the}f(x)\text{nearer}\text{to}1.$

(c)

To determine

To Describe: To describe a brief statement regarding above results.

Explanation of Solution

Given information: Given function $f(x)=\frac{\tan 2x}{2x}$

In the table first we calculate negative values of the function nearer to 0 or left hand limit for 0 in which we get the value of function nearer to 1. Similarly, when we calculated positive values of the function nearer to 0 or right hand limit we get the same result that is we get the value of the function approaches to 1.

Thus, using limit we can say that

  $\underset{2x\to 0}{\lim }\frac{\tan 2x}{2x}=1$