Chapter 1.6, Problem 48ES

Use the Squeezing Theorem to show that $\underset{x\to 0}{\lim }{x}^2\sin \left(\frac{50\pi }{\sqrt[3]{x}}\right)=0$ and illustrate the principle involved by using a graphing utility to graph the equations $y=x^2,y=-x^2,$ and $y=x^2\sin \left(50\pi /\sqrt[3]{x}\right)$ on the same screen in the window $\left[-0.5,0.5\right]\times \left[-0.25,0.25\right]$ .