Table of Values

Question

How are the numbers selected when using a table of values to find the limit of a problem like: lim x->2 x^3-8/x-2

Answer 1

The numbers are selected to get as close as reasonably possible to the point you want to evaluate the limit at (in this case, 2) without actually equalling 2.  So for example, approaching 2 from below you might select numbers like 1.9, 1.99, 1.999, 1.9999, and so on.  Approaching 2 from above you might select numbers like 2.1, 2.01, 2.001, 2.0001, and so on.  The actual numbers that you select aren't really that important (for example, you could select 1.9998 instead of 1.9999), but what is important is that they keep getting closer and closer to 2, so you can see if the function seems to be approaching a limiting value as x approaches 2.