as most of these discussion they go from "these number are impossible!" to "but wait! there's algebra!" without really providing a framing context of what's going on.
this is what's going when the article say "slides smoothly in toward 2"
and this is another common example, which "slides" toward a different number (which is why when you see the division alone is "undefined" and only acquires value in context)
this is what's going when the article say "slides smoothly in toward 2"
https://www.google.com/search?q=(x^2%2B2x)/x
and this is another common example, which "slides" toward a different number (which is why when you see the division alone is "undefined" and only acquires value in context)
https://www.google.com/search?q=sin(x)/x
but beyond the "just apply limits" party trick it's the implication however that's the most interesting part, and I'll use the words from here[1]:
> Things that appear to be zero may be nonzero in a different dimension (just like i might appear to be 0 to us, but isn’t)
[1] https://betterexplained.com/articles/why-do-we-need-limits-a...