I would say that computers are not the right tool to enhance the understanding of the concept of limits. One reason for this is that there is no general way of “calculating” limits. Furthermore, the space of Floats is not a complete metric space.
What I mean by this is that there will always be an example where the plotting approach fails because of the finiteness of floating point numbers. (Plotting always depicts the function on a finite set of points)
If we look at your first example, the plot would suggest that the limit is 1. But are we sure? Luckily in this example it is quite easy to prove (L'Hôpital's rule - Wikipedia).
Hopefully, I understood your question correctly and manged to convey the message that plotting to get insights is helpul, but to be sure that a limit is correct a formal proof is needed.
2 Likes