Chapter 4.7, Problem 16E

a.

To determine

To complete: The given table using a graphing utility.

Explanation of Solution

Given Information: Given function is $y=\arctan x$ .

Table:

  $\begin{array}{l}\begin{array}{llllll}x\hfill & -10\hfill & -8\hfill & -6\hfill & -4\hfill & -2\hfill \\ y\hfill & -1.4711\hfill & -1.4464\hfill & -1.4056\hfill & -1.3258\hfill & -1.1071\hfill \end{array}\\ \\ \begin{array}{lllllll}x\hfill & 0\hfill & 2\hfill & 4\hfill & 6\hfill & 8\hfill & 10\hfill \\ y\hfill & 0\hfill & 1.1071\hfill & 1.3258\hfill & 1.4056\hfill & 1.4464\hfill & 1.4711\hfill \end{array}\end{array}$

b.

To determine

To graph: The points from the table in part (a) without using a graphing utility.

Explanation of Solution

Given Information: Given function is $y=\arctan x$ .

Graph:

  

c.

To determine

To graph: The function $y=\arctan x$ using a graphing utility and then to compare the result with graph in part (b).

Answer to Problem 16E

Both the graphs are same.

Explanation of Solution

Given Information: Given function is $y=\arcsin x$ .

Graph:

  

Comparison:

Both the graphs are same.

d.

To determine

To find: The horizontal asymptotes of the graph.

Answer to Problem 16E

Horizontal asymptotes are $y=\frac{\pi }{2}$ and $y=-\frac{\pi }{2}$ .

Explanation of Solution

Given Information: Given function is $y={\tan }^{-1}x$ .

  $y={\tan }^{-1}x$

Inverse of ${\tan }^{-1}x$ is $\tan x$ , as $\tan x$ doesn’t exist for angles $\frac{\pi }{2}and-\frac{\pi }{2}$ , the two horizontal asymptotes are $y=\frac{\pi }{2}$ and $y=-\frac{\pi }{2}$ .

Thus, horizontal asymptotes are $y=\frac{\pi }{2}$ and $y=-\frac{\pi }{2}$ .