Chapter 5.3, Problem 88E

Graphical Reasoning Consider the function

$f(x)=\cos \frac{1}{x}$

and its graph, shown in the figure below.

(a) What is the domain of the function?

(b) Identify any symmetry and any asymptotes of the graph.

(c) Describe the behavior of the function as $x\to 0$.

(d) How many solutions does the equation

$\cos \frac{1}{x}=0$

have in the interval $\left[-1,1\right]$? Find the solutions.

(e) Does the equation $\cos \left(1/x\right)=0$ have a greatest solution? If so, then approximate the solution. If not, then explain why.