Chapter 3.6, Problem 67ES

Let $f\left(x\right)=x^2\sin \left(1/x\right)$ .

(a) Are the limits ${\lim }_{x\to 0^{+}}f\left(x\right)$ and ${\lim }_{x\to 0^{-}}f\left(x\right)$ indeterminate forms?

(b) Use a graphing utility to generate the graph of $f$ , and use the graph to make conjectures about the limits in part (a).

(c) Use the Squeezing Theorem $\left(\mathrm{1.6.2}\right)$ to confirm that your conjectures in part (b) are correct.