Problem:
Investigate graphically the behavior of the function

for values of x near 0.


Visualization:
Using Maple:

> f:=x->((x^3+8)^(1/3)-2)/x^3;

> plot(f(x), x=-1..1);

At first, it appears that the limit may in fact exist. However, the following two graphs obtained by zooming in seem to indicate otherwise.

> plot(f(x), x=-0.001..0.001);

> plot(f(x),x=-0.0001..0.0001,y=0.07..0.09);

Despite the latter graph, the limit does exist and the latter graph is inaccurate!