Limits

[Lessa]

Hi!

I have a question that may be simple for you experts...
How to make HP Prime show that a given limit does not exist?

For example, I tried limit of x/(x-3) as x approaches 3+ and I get ∞. As x approached 3-, I get -∞. But as x approaches 3 (not one-sided limit), I get +-∞... I would like it to show there is no limit since one-sided limits are differents.

Other example:
Limit of SQ(x-2) as x approaches 2-
It gives me 0, when I would like to see that there is no real number.

Thanks in advance.

[Aries]

Hi Lessa,
in your first example I guess +-inf means the function is not defined for x-->3 (bilateral), though the Nspire CAS is more "explanatory" in this case:



In the second example the domain (real) of sqrt(x-2) is [2,+inf) so you cannot take the limit "outside" that domain, there's no left "neighborhood" of 2 in the definition domain and you can only talk about the right-sided limit.
But it depends on the context, there is a general case where the domain is C.
Best,

Aries ;-)