Chapter 1.6, Problem 47ES

Use the Squeezing Theorem to show that $\underset{x\to 0}{\lim }x\cos \frac{50\pi }{x}=0$ and illustrate the principle involved by using a graphing utility to graph the equations $y=\left|x\right|,y=-\left|x\right|,$ and $y=x\cos \left(50\pi /x\right)$ on the same screen in the window $\left[-1,1\right]\times \left[-1,1\right]$ .