Part 4/5:
Graphically, if you were to plot (x^2), (-x^2), and (x^2 \sin\left(\frac{1}{x}\right)), you would observe that the latter function is constrained between the two bounding functions as (x) approaches 0. By continuously zooming in on this graph, it becomes apparent how (x^2 \sin\left(\frac{1}{x}\right)) is "squeezed" to 0.